text
stringlengths 45
2.98k
| __index_level_0__
float64 0
11.7k
β |
|---|---|
Question: the hcf of two numbers is 42 and the other two factors of their lcm are 11 and 12 . what is the largest number .
A.462.
B.450.
C.480.
D.504.
e ) 555D.
"explanation : hcf of the two numbers = 42 hcf will be always a factor of lcm 42 is factor of lcm other two factors are 11 & 12 then the numbers are ( 42 11 ) and ( 42 x 12 ) = 462 and 504 answer : option d" | null |
Question: given f ( x ) = 3 x β 5 , for what value of x does 2 * [ f ( x ) ] + 8 = f ( 3 x β 6 )
A.0.
B.4.
C.6.
D.7.
e ) 13D.
"answer = d = 7 f ( x ) = 3 x β 5 2 * [ f ( x ) ] + 8 = f ( 3 x β 6 ) 2 ( 3 x - 5 ) + 8 = 3 ( 3 x - 6 ) - 5 6 x - 2 = 9 x - 23 x = 7" | null |
Question: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 468 per week . how much does she earn in dollars per hour ?
A.2.
B.8.
C.9.
D.11.
e ) 13E.
"explanation : total hours worked = 8 x 3 + 6 x 2 = 36 total earned = 468 . hourly wage = 468 / 36 = 13 answer : e" | null |
Question: a trader bought a car at 20 % discount on its original price . he sold it at a 50 % increase on the price he bought it . what percent of profit did he make on the original price ?
A.17 %.
B.72 %.
C.20 %.
D.82 %.
e ) 16 %C.
"original price = 100 cp = 80 s = 80 * ( 150 / 100 ) = 120 100 - 120 = 20 % answer : c" | null |
Question: we invested a total of $ 1,000 . we invested one part of the money at 3 % and the rest of the money at 6 % . the total investment with interest at the end of the year was $ 1 , 052.50 . how much money did we invest at 3 % ?
A.$ 160.
B.$ 190.
C.$ 220.
D.$ 250.
e ) $ 280D.
"let x be the money invested at 3 % . 1.03 x + 1.06 ( 1000 - x ) = 1052.50 . 0.03 x = 1060 - 1052.50 . 0.03 x = 7.50 . 3 x = 750 . x = 250 . the answer is d ." | null |
Question: | x + 3 | β | 4 - x | = | 9 + x | how many solutions will this equation have ?
A.0.
B.1.
C.2.
D.3.
e ) 4B.
"you have | x + 3 | - | 4 - x | = | 8 + x | first , look at the three values independently of their absolute value sign , in other words : | x + 3 | - | 4 - x | = | 8 + x | ( x + 3 ) - ( 4 - x ) = ( 8 + x ) now , you ' re looking at x < - 8 , so x is a number less than - 8 . let ' s pretend x = - 10 here to make things a bit easier to understand . when x = - 10 i . ) ( x + 3 ) ( - 10 + 3 ) ( - 7 ) ii . ) ( 4 - x ) ( 4 - [ - 10 ] ) ( double negative , so it becomes positive ) ( 4 + 10 ) ( 14 ) iii . ) ( 8 + x ) ( 8 + - 10 ) ( - 2 ) in other words , when x < - 8 , ( x + 3 ) and ( 8 + x ) are negative . to solve problems like this , we need to check for the sign change . here is how i do it step by step . i . ) | x + 3 | - | 4 - x | = | 8 + x | ii . ) ignore absolute value signs ( for now ) and find the values of x which make ( x + 3 ) , ( 4 - x ) and ( 8 + x ) = to zero as follows : ( x + 3 ) x = - 3 ( - 3 + 3 ) = 0 ( 4 - x ) x = 4 ( 4 - 4 ) = 0 ( 8 + x ) x = - 8 ( 8 + - 8 ) = 1 b" | null |
Question: the area of a rectangular plot is 460460 square metres . if the length is 15 % 15 % more than the breadth , what is the breadth of the plot ?
A.14 metres.
B.20 metres.
C.18 metres.
D.12 metres.
e ) 16 metresB.
"explanation : length 115 % of breadth . length Γ breadth = 460 m 2 β 115 % of breadth Γ breadth = 460 m 2 β 115 / 100 Γ breadth Γ breadth = 460 m 2 β breadth Γ breadth = 400 m 2 β breadth = 20 m answer : option b" | null |
Question: two pipes a and b can separately fill a tank in 16 and 18 minutes respectively . a third pipe c can drain off 45 liters of water per minute . if all the pipes are opened , the tank can be filled in 18 minutes . what is the capacity of the tank ?
A.590 liters.
B.720 liters.
C.740 liters.
D.860 liters.
e ) 620 litersB.
"1 / 16 + 1 / 18 - 1 / x = 1 / 18 x = 16 16 * 45 = 720 answer : b" | null |
Question: 17 balls are numbered 1 to 17 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?
A.1 / 7.
B.3 / 14.
C.5 / 23.
D.7 / 34.
e ) 9 / 41D.
p ( 1 st ball is even ) = 8 / 17 p ( 2 nd ball is also even ) = 7 / 16 p ( both balls are even ) = 8 / 17 * 7 / 16 = 7 / 34 the answer is d . | null |
Question: aarti can do a piece of work in 9 days . in how many days will she complete three time of work of same type ?
A.6 days.
B.18 days.
C.21 days.
D.27 days.
e ) 13 daysD.
"we have the important relation , more work , more time ( days ) a piece of work can be done in 9 days . three times of work of same type can be done in 9 x 3 = 27 days answer d" | null |
Question: what is the value of n if the sum of the consecutive odd intergers r from 1 to n equals 169 ?
A.47.
B.25.
C.37.
D.33.
e ) 29B.
"before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ." | null |
Question: a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 7 brown mice in the experiment , how many mice in total are in the experiment ?
A.39.
B.33.
C.26.
D.21.
e ) 10D.
"let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 7 = > m = 21 answer d" | null |
Question: there are 7 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
A.40.
B.49.
C.41.
D.56.
e ) 42E.
"first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 7 and for second = 6 so total methods = 7 * 6 = 42 answer : e" | null |
Question: what is the lowest positive integer that is divisible by 4 through 6 , inclusive ?
A.120.
B.48.
C.82.
D.76.
e ) 160A.
"the integer should be divisible by : 4 , 5 , and 6 . the least common multiple of these integers is lcm = 4 * 5 * 6 = 7920 answer : a" | null |
Question: when a stone is dropped from a building 200 m high , its speed is proportional to the time elapsed after dropping . the distance traveled is proportional to the square of the time elapsed . after 1 second the speed of the train was 10 m / sec and it was 190 m above the ground . when its speed is 25 m / sec , what would be its distance from the ground ?
A.140 m.
B.137.5 m.
C.125.75 m.
D.142.5 m.
e ) 152.5 mB.
v = x * t and s = y * t ^ 2 10 = x * 1 , hence x = 10 units ( 200 - 190 ) = y * 1 * 1 y = 10 when speed = 25 m / sec , time elapsed = 25 / 10 = 2.5 sec distance travelled by stone = 10 * ( 2.5 ) ^ 2 = 62.5 mts so distance of stone above ground = 200 - 62.5 = 137.5 mtrs answer : b | null |
Question: if 2 x = 3 y = 10 , then 15 xy = ?
A.1,200.
B.200.
C.120.
D.40.
e ) 250E.
"2 x = 10 ; x = 5 3 y = 10 ; y = 10 / 3 multiply : 15 xy = 15 * 5 * 10 / 3 = 250 answer : e ." | null |
Question: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 30 km / hr and 90 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
A.48.
B.30.
C.26.
D.23.
e ) 12B.
"relative speed = 90 + 30 = 120 km / hr . 120 * 5 / 18 = 100 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 100 = 30 sec . answer : b" | null |
Question: the ratio of three numbers is 5 : 1 : 4 and their sum is 1000 . the last number of the three numbers is ?
A.24.
B.26.
C.27.
D.400.
e ) 30D.
"5 : 1 : 4 total parts = 10 10 parts - - > 1000 1 part - - - - > 100 the last number of the three numbers is = 4 * 100 = 400 answer : d" | null |
Question: in a bag of small balls 1 / 4 are green , 1 / 8 are blue , 1 / 12 are yellow and the remaining 26 white . how many balls are blue ?
A.6.
B.5.
C.4.
D.3.
e ) 8A.
let us first find the fraction of green , blue and yellow balls 1 / 4 + 1 / 8 + 1 / 12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator = 11 / 24 , add numerators the fraction of white balls is given by 24 / 24 - 11 / 24 = 13 / 24 so the fraction 13 / 24 corresponds to 26 balls . if x is the total number of balls then ( 13 / 24 ) of x = 26 balls or ( 13 / 24 ) ? x = 26 x = 26 ? ( 24 / 13 ) = 48 , total number of balls the fraction of blue balls is 1 / 8 of x . the number of blue balls is given by ( 1 / 8 ) of 48 = 6 balls . correct answer a | null |
Question: a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 250 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
A.1.
B.3.
C.4.
D.5.
e ) 6D.
"the distance between the nest and the ditch is 250 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 250 = 7500 . d = st 7500 / 1.5 = t , i think we can take 7500 meters as 7.5 km , then only we get t = 5 . ( 1000 meters = 1 km ) d )" | null |
Question: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 15 percent alcohol by volume ?
A.50.
B.100.
C.150.
D.200.
e ) 250B.
"15 % is 5 % - points higher than 10 % but 15 % - points lower than 30 % . thus there should be 3 parts of solution x for 1 part of solution y . we should add 100 ml of solution y . the answer is b ." | null |
Question: on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 40 percent . what was the total rent the motel actually charged for that night ?
A.$ 500.
B.$ 800.
C.$ 1,000.
D.$ 1,600.
e ) $ 2,400A.
"let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 40 % . 4 x = 200 = > x = 500 answer a" | null |
Question: the length of the rectangular field is double its width . inside the field there is square shaped pond 9 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
A.54.
B.36.
C.75.
D.28.
e ) 11B.
"a / 8 = 9 * 9 = > a = 9 * 9 * 8 x * 2 x = 9 * 9 * 8 x = 18 = > 2 x = 36 answer : b" | null |
Question: how much time will a train of length 380 m moving at a speed of 72 kmph take to cross another train of length 540 m , moving at 36 kmph in the same direction ?
A.50.
B.99.
C.88.
D.92.
e ) 12D.
"the distance to be covered = sum of their lengths = 380 + 540 = 920 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 920 / 10 = 92 sec . answer : d" | null |
Question: the area of a circle is increased by 800 % . by what percent has the radius of the circle increased ?
A.100 %.
B.400 %.
C.300 %.
D.600 %.
e ) 200 %E.
"the area of the circle is increased by 800 % , thus the area is increased 9 times . the area of a circle it proportional to the square of the radius ( area = Ο r ^ 2 ) , therefore the radius must increase 3 times ( diameter increase 3 times = area increase 9 times ) , which is increase by 200 % . answer : e ." | null |
Question: adam borrowed some money at the rate of 6 % p . a . for the first two years , at the rate of 9 % p . a . for the next 3 years , and at the rate of 14 % p . a . for the period beyond 5 years . 1 Β£ he pays a total interest of rs . 11400 at the end of 9 years how much money did he borrow ?
A.rs . 8000.
B.rs . 09000.
C.rs . 11000.
D.rs . 10000.
e ) rs . 12000E.
let the sum borrowed be x . then , ( x * 2 * 6 ) / 100 + ( x * 9 * 3 ) / 100 + ( x * 14 * 4 ) / 100 = 11400 ( 3 x / 25 + 27 x / 100 + 14 x / 25 ) = 11400 95 x / 100 = 11400 x = ( 11400 * 100 ) / 95 = 12000 . hence , sum borrowed = rs . 12000 answer is e . | null |
Question: which number need to add to 859622 to get a number divisible by 456 ?
A.565771.
B.456578.
C.676885.
D.788090.
e ) 859622E.
"dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 β 62 = 394 should be added to 859622 . e" | null |
Question: if a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster , he would have covered 50 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day ?
A.100.
B.120.
C.140.
D.150.
e ) 160A.
"case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 50 ) = ( r + 5 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 2 ) x = 100 ans a" | null |
Question: in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 8,4 ) , and ( 8,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
A.1 / 2.
B.1 / 3.
C.2 / 3.
D.1 / 4.
e ) 2 / 5D.
"the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 32 . p ( x + y < 4 ) = 8 / 32 = 1 / 4 the answer is d ." | null |
Question: harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 5 of her books to their new home . what fraction of millicent ' s old library capacity is the new home ' s library capacity ?
A.1 / 2.
B.2 / 3.
C.3 / 4.
D.11 / 30.
e ) 5 / 6D.
"because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h ' = 1 / 3 h = 10 books m ' = 1 / 5 m = 12 books total = 22 books m ' = 22 = 11 / 30 * 60 ratio : 11 / 30 ans : d" | null |
Question: let the number which when multiplied by 16 is increased by 375 .
A.14.
B.20.
C.26.
D.25.
e ) 30D.
"solution let the number be x . then , 16 x - x = 375 βΉ = βΊ 15 x = 375 x βΉ = βΊ 25 . answer d" | null |
Question: a can finish a work in 60 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
A.10 days.
B.25 days.
C.6 days.
D.7 days.
e ) 8 daysB.
"b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 60 work is done by a in 1 day 5 / 12 work is done by a in 60 * 5 / 12 = 25 days answer is b" | null |
Question: jill has 14 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
A.3.
B.6.
C.9.
D.12.
e ) 24E.
let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 14 1 3 / 4 w = 14 w = 8 the total number of jars = 3 w = 24 answer : e | null |
Question: a cricket player whose bowling average was 21.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ?
A.64.
B.72.
C.111.
D.721.
e ) 108C.
"average = total runs / total wickets total runs after last match = 21.5 w + 52 total wickets after last match = w + 5 ( 21.5 w + 52 ) / ( w + 5 ) = 21.5 - 0.5 = 21 w = 106 so total wickets aftr last match = w + 5 = 111 answer : c" | null |
Question: 8 men , working 8 hours a day can complete a work in 18 days . how many hours a day must 12 men work to complete the same work in 12 days ?
A.6.
B.7.
C.8.
D.9.
e ) 10C.
"the number of hours required to complete the work is 8 * 8 * 18 = 1152 12 Γ 12 Γ ( x ) = 1152 x = 8 the answer is c ." | null |
Question: 1 , 8 , 27 , 64 , 125 , 216 , ( . . . . )
A.354.
B.343.
C.245.
D.392.
e ) 400B.
"the pattern is 1 ^ 3 , 2 ^ 3 , 3 ^ 3 , 4 ^ 3 , 5 ^ 3 , 6 ^ 3 , etc hence , next number is 7 ^ 3 = 343 answer is b" | null |
Question: if 3 men or 4 women can do a piece of work in 16 days , in how many days can 12 men and 8 women do the same piece of work ?
A.8 / 3.
B.6.
C.5.
D.4.
e ) 3A.
"3 men can finish a work in 16 days , so in 1 day 3 men finish 1 / 16 th of work and in 1 day 1 men can finish , 1 / 48 th of work . similarly , in 1 day 1 women can finish 1 / 64 th of work . 12 men in 1 day can finish , 12 / 48 = 1 / 4 , 8 women in 1 day can finish = 8 / 64 = 1 / 8 1 / 4 + 1 / 8 = 3 / 8 . hence number of days to complete is 8 / 3 days . answer : a" | null |
Question: two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 24 seconds , the speed of each train ( in km / hr ) is
A.18.
B.36.
C.28.
D.20.
e ) 24A.
"explanation : distance covered = 120 + 120 = 240 m time = 24 s let the speed of each train = v . then relative speed = v + v = 2 v 2 v = distance / time = 240 / 24 = 10 m / s speed of each train = v = 10 / 2 = 5 m / s = 5 Γ 36 / 10 km / hr = 18 km / hr answer : option a" | null |
Question: john has $ 1,600 at the beginning of his trip , after spending money , he still has exactly $ 600 less than he spent on the trip . how much money does john still have ?
A.$ 200.
B.$ 400.
C.$ 600.
D.$ 800.
e ) $ 500E.
suppose total money spent = x not spend ( money he still has ) = x - 600 x + x - 600 = 1600 x = 1100 money not spend = 1100 - 600 = 500 answer : e | null |
Question: a , b and c started a business by investing rs . 800 / - , rs . 1000 / - and rs . 1200 / - respectively for two years . total profit is rs . 1000 / - . find the c ' s share ?
A.rs . 600.
B.rs . 500.
C.rs . 400.
D.rs . 800.
e ) rs . 900C.
solution : a : b : c = ( 800 * 2 ) : ( 1000 * 2 ) : ( 12000 * 2 ) = 4 : 5 : 6 . so c ' s share = rs . ( 1000 * 6 / 15 ) = rs . 400 . answer : option c | null |
Question: the speed of a car is 85 km in the first hour and 45 km in the second hour . what is the average speed of the car ?
A.72 kmph.
B.65 kmph.
C.30 kmph.
D.80 kmph.
e ) 82 kmphB.
s = ( 85 + 45 ) / 2 = 65 kmph answer : b | null |
Question: find the number which multiplied by 15 is increased by 196 .
A.14.
B.20.
C.26.
D.28.
e ) 27A.
"let the number be x . then , 15 x - x = 196 x = 14 answer : a" | null |
Question: the positive value of x that satisfies the equation ( 3 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is between bunuel , can you please explain this one ?
A.0 and 0.5.
B.0.5 and 1.
C.1 and 1.5.
D.1.5 and 2.
e ) 2 and 2.5D.
trial and error would probably be the easiest way to solve this problem . when x is large enough positive number , then because of the exponents ( 5 > 4 ) , lhs will be more than rhs ( as you increase the positive value of x the distance between the values of lhs and rhs will increase ) . try x = 1 - - > lhs = 3 ^ 5 = 81 * 3 = 243 and rhs = 4 ^ 4 = 64 * 4 = 256 , so ( 1 + 2 x ) ^ 5 < ( 1 + 3 x ) ^ 4 . as you can see lhs is still slightly less than than rhs . so , the value of x for which ( 1 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is slightly more than 1 . answer : d . | null |
Question: the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
A.276.
B.300.
C.299.
D.322.
e ) 345B.
"the numbers are ( 20 x 11 ) and ( 20 x 15 ) . larger number = ( 20 x 15 ) = 300 . answer : b" | null |
Question: two numbers are in the ratio of 1 : 2 . if 6 be added to both , their ratio changes to 3 : 5 . the greater number is
A.20.
B.24.
C.28.
D.32.
e ) 36B.
"let the ratio be x : y , given x / y = 1 / 2 , ( x + 6 ) / ( y + 6 ) = 3 / 5 = > x = 12 and y = 24 answer : b" | null |
Question: carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 10 inches tall . how tall are the sculpture andbase together ?
A.3.1 feet.
B.3.66 feet.
C.3.3 feet.
D.3.4 feet.
e ) 3.5 feetB.
"we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 10 = 40 44 / 12 = 3.66 feet answer : b" | null |
Question: points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction w of the area of triangle abc is the area of triangle xyz ?
A.1 / 9.
B.1 / 8.
C.1 / 6.
D.1 / 5.
e ) 1 / 3A.
"if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives w = 1 / 9 . a" | null |
Question: the cash difference between the selling prices of an article at a profit of 4 % and 2 % is rs . 3 . the ratio of the two selling prices is ?
A.52 : 51.
B.52 : 53.
C.52 : 50.
D.22 : 56.
e ) 52 : 51A.
"let c . p . of the article be rs . x . then , required ratio = 104 % of x / 102 % of x = 104 / 102 = 52 / 51 = 52 : 51 answer : a" | null |
Question: two whole numbers whose sum is 100 can not be in the ratio
A.2 : 23.
B.5 : 45.
C.10 : 10.
D.2 : 6.
e ) 2 : 3D.
d ) 2 : 6 | null |
Question: what least number must be added to 696 , so that the sum is completely divisible by 20 ?
A.2.
B.4.
C.3.
D.5.
e ) 6B.
"if we divide 696 by 20 remainder is 16 20 - 16 = 4 answer : b" | null |
Question: line q has the equation 5 y β 3 x = 30 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s β s exist ? ( note : intersections on one of the axes do not count . )
A.22.
B.33.
C.36.
D.41.
e ) 58A.
"5 y - 3 x = 30 and so y = 3 x / 5 + 6 when x = 0 , then y = 6 . when y = 0 , then x = - 10 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 10 , 0 ) , 0 = - 5 ( - 10 ) / 3 + c the y - intercept is c = - 50 / 3 < - 16 . thus the perpendicular line s can have y - intercepts from - 16 up to 5 . the number of possible lines is 16 + 5 + 1 = 22 the answer is a ." | null |
Question: in a certain warehouse , 30 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?
A.8.
B.64.
C.24.
D.102.
e ) 144C.
"if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 30 % of the packages weigh less than 75 pounds so , 30 % oft = number of packages that weigh less than 75 pounds 30 % of 240 = 72 , so 72 packages weigh less than 75 pounds of those 72 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 72 - 48 = 24 = c" | null |
Question: a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10 . in all papers together , the candidate obtained 60 % of the total marks then , the number of papers in which he got more than 50 % marks is
A.1.
B.3.
C.4.
D.5.
e ) 7C.
solution : let the marks obtained in five subjects be 6 x , 7 x , 8 x , 9 x and 10 x . total marks obtained = 40 x max . marks of the five subjects = 40 x / 0.6 [ 40 x is 60 % of total marks ] max . marks in each subject = 40 x / 0.6 * 5 = 13.33 x hence , % of each subject = 6 x * 100 / 13.33 = 45.01 % or , 7 x * 100 / 13.33 = 52.51 in same way other percentage are 60.01 % , 67.52 % , 75.01 % . hence , number of subjects in which he gets more than 50 % marks = 4 . answer : option c | null |
Question: subtracting 5 % of a from a is equivalent to multiplying a by how much ?
A.0.95.
B.9.4.
C.0.094.
D.94.
e ) noneA.
"answer let a - 5 % of a = ab . β ( 95 x a ) / 100 = ab β΄ b = 0.95 correct option : a" | null |
Question: a bag consists of 20 marbles , of which 5 are blue , 7 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
A.3 / 4.
B.2 / 4.
C.1 / 4.
D.1 / 8.
e ) 1 / 16A.
"bag consists of 20 marbles , of which 5 are blue , 7 are red remainder are white . so , white = 20 - 5 - 7 = 8 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 7 / 20 + 8 / 20 = 15 / 20 = 3 / 4 hence , answer will be a ." | null |
Question: a trader bought a car at 20 % discount on its original price . he sold it at a 60 % increase on the price he bought it . what percent of profit did he make on the original price ?
A.28 %.
B.72 %.
C.12 %.
D.82 %.
e ) 16 %A.
"original price = 100 cp = 80 s = 80 * ( 160 / 100 ) = 128 100 - 128 = 28 % answer : a" | null |
Question: an aeroplane covers a certain distance at a speed of 150 kmph in 2 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
A.1300 kmph.
B.160 kmph.
C.180 kmph.
D.1080 kmph.
e ) noneC.
"explanation : distance = ( 150 x 2 ) = 300 km . speed = distance / time speed = 300 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = 300 x 3 / 5 km / hr = 180 km / hr . answer : option c" | null |
Question: what is the units digit of 17 ^ 83 Γ 13 ^ 82 Γ 11 ^ 67 ?
A.4.
B.5.
C.6.
D.7.
e ) 8A.
"to find : the units digit of 17 ^ 83 Γ 13 ^ 82 Γ 11 ^ 87 let ' s reduce the clutter and simplify the product ( 7 ^ 83 ) ( 3 ^ 82 ) ( 1 ^ 87 ) 7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4 th power so 7 ^ 5 has the same last digit as 7 ^ 1 , 7 ^ 9 , 7 ^ 13 thus , 7 ^ 83 has the same last digit as 7 ^ 3 , 7 ^ 7 , 7 ^ 11 i . e . 3 3 has a cyclicity of 4 : exactly the same routine as above thus , 3 ^ 82 has the same last digit as 3 ^ 2 , 3 ^ 6 , 3 ^ 10 i . e . 9 any power of 1 will result in 1 as the last digit so , product of our last digits = 3 x 9 x 1 = 27 . . . . last digit is 4 correct option : a" | null |
Question: how many seconds will a 550 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
A.12 sec.
B.30 sec.
C.33 sec.
D.16 sec.
e ) 18 secC.
"speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 550 * 3 / 50 = 33 sec . answer : c" | null |
Question: jansi went out for shopping . she had in her handbag approximately rs . 15 / - in one rupee notes and 20 p . coins . when she returned she had as many one rupee notes as she originally had and as many 20 p . coins as she originally had one rupee notes . she actually came back with about one - third of what she had started out with . how much did she spend and exactly how much did she have with her when she started out ?
A.9.6.
B.10.6.
C.11.0.
D.9.4.
e ) 8.1A.
a 9.60 let us assume that originally jansi had x rupees and y 20 paise coins . going shopping she had ( 100 x + 20 y ) paise . she returned with only ( 100 y + 20 x ) paise . this last sum , as we know , is one - third of the original and therefore 3 ( 100 y + 20 x ) = 100 x + 20 y simplifying we have x = 7 y if y is 1 thenx is 7 . assuming this so jansi had 7.20 rupees when she set out for shopping . this is wrong because jansi actually had about 15 rupees . let us see now what we get if y = 2 . then x = 14 . the original sum was 14.40 rupees which accords with the condition of the problem . if we assume that y = 3 then the sum will be too big β 21.60 rupees . therefore the only suitable answer is 14.40 rupees . after shopping jansi had 2 one rupee notes and 14 twenty paise coins . this is actually l / 3 rd of the original sum 1,440 : 3 = 480 . jansi ' s purchases , therefore , cost 14.40 β 4.80 = rs 9.60 | null |
Question: at a certain organisation , the number of male members went up by 15 % in the year 2001 from year 2000 , and the number of females members went down by 6 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?
A.1 : 2.
B.1 : 3.
C.2 : 3.
D.3 : 2.
e ) 2 : 1A.
"men increase by 15 % = = > 1.15 m = males in 2001 women decrease by 6 % = = > 0.94 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.15 m + 0.94 f = 1.012 * ( m + f ) 1.15 m + 0.94 f = 1.012 m + 1.012 f 1.15 m - 1.012 m = 1.012 f - 0.94 f 0.138 m = 0.072 f m / f = ( 0.072 ) / ( 0.138 ) = 72 / 138 = 1 / 2 answer = ( a )" | null |
Question: in a party every person shakes hands with every other person . if there were a total of 120 handshakes in the party then what is the number of persons present in the party ?
A.15.
B.16.
C.17.
D.18.
e ) 19B.
"explanation : let the number of persons be n β΄ total handshakes = nc 2 = 120 n ( n - 1 ) / 2 = 120 β΄ n = 16 answer : option b" | null |
Question: a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 21 inches and the width of the wall is 28 inches , what is the length of the wall , in inches ?
A.21.5.
B.31.5.
C.41.5.
D.61.5.
e ) 71.5B.
"since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 21 ^ 2 = 441 . area of rectangle is double of that 2 * 441 = 882 . now a = lw and we need find w so a / l = w ; 882 / 28 = 31.5 answer ! answer is b" | null |
Question: when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 96.15 , what is the value of y ?
A.96.
B.75.
C.40.
D.25.
e ) 12C.
"by the definition of a remainder , the remainder here is equal to 6 / y . the remainder in decimal form is given as . 15 therefore , 6 / y = . 15 solve for y and get 40 . c" | null |
Question: if the product of the integers w , x , y and z is 840 , and if 1 < w < x < y < z , what is the value of w + z ?
A.10.
B.11.
C.16.
D.18.
e ) 21B.
"840 = 4 * 5 * 6 * 7 so w = 4 , x = 5 , y = 6 , z = 7 w + z = 4 + 7 = 11 answer - b" | null |
Question: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets 1000 more than d , what is b β s share ?
A.500.
B.1500.
C.2000.
D.1400.
e ) none of theseC.
"let the shares of a , b , c and d be 5 x , 2 x , 4 x , 3 x respectively . then , 4 x β 3 x = 1000 β x = 1000 β΄ b β s share = 2 x = 2000 answer c" | null |
Question: in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let r be the average rental price for all apartments in the building . if r is $ 5,600 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 10,400 higher that r , then what percentage of apartments in the building are two - bedroom apartments ?
A.26 %.
B.35 %.
C.39 %.
D.42 %.
e ) 52 %B.
"ratio of 2 bedroom apartment : 1 bedroom apartment = 5400 : 104000 - - - - - > 7 : 13 let total number of apartments be x no . of 2 bedroom apartment = ( 7 / 20 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 7 / 20 ) * 100 - - - > 35 % option b is correct" | null |
Question: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 276 games will be played during the tournament . find the number of participants .
A.20.
B.22.
C.24.
D.26.
e ) 28C.
"let p be the number of participants . pc 2 = 276 ( p ) ( p - 1 ) = 552 = 24 * 23 p = 24 the answer is c ." | null |
Question: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
A.1 : 2.
B.2 : 1.
C.1 : 3.
D.3 : 1.
e ) 1 : 1B.
"explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 Γ 12 : 30000 Γ 9 = 45 Γ 12 : 30 Γ 9 = 3 Γ 12 : 2 Γ 9 = 2 : 1 answer : option b" | null |
Question: 3 friends had dinner at a restaurant . when the bill was received , akshitha paid 3 / 4 as much as veena paid and veena paid 1 / 2 as much as lasya paid . what fraction of the bill did veena pay ?
A.4 / 15.
B.3 / 12.
C.3 / 11.
D.3 / 10.
e ) 3 / 14A.
let veena paid x , so akshitha paid 3 x / 4 , and lasya paid 2 x , so total bill paid is given by x + ( 3 x / 4 ) + 2 x = 1 , we get i . e . x = 4 / 15 answer : a | null |
Question: a number x is 5 times another number y . the percentage that y is less than x is
A.12.5 %.
B.87.5 %.
C.80 %.
D.11 %.
e ) 1 %C.
"say y = 1 and x = 5 . then y = 1 is less than x = 5 by ( 5 - 1 ) / 5 * 100 = 4 / 5 * 100 = 80 % . answer : c ." | null |
Question: marketing executives for a certain chewing gum company projected a 40 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 30 % . what percent of the projected revenue was the actual revenue ?
A.50 %.
B.58 %.
C.62.5 %.
D.64 %.
e ) 75 %A.
last year revenue = 100 ( assume ) ; this year revenue = 70 ; projected revenue = 140 . actual / projected * 100 = 70 / 140 * 100 = 50 % . answer : a . | null |
Question: how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 9 m x 6 m x 22.5 cm ?
A.6400.
B.6410.
C.6440.
D.7200.
e ) 6800D.
"number of bricks = volume of wall / volume of bricks = 900 x 600 x 22.5 / 25 x 11.25 x 6 = = 7200 answer : d" | null |
Question: at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 65 . if the restaurant serves 120 customers today , raising the average to 90 customers per day , what is the value of x ?
A.1.
B.5.
C.9.
D.15.
e ) 30A.
withoutusing the formula , we can see that today the restaurant served 30 customers above the average . the total amount above the average must equal total amount below the average . this additional 30 customers must offset the β deficit β below the average of 90 created on the x days the restaurant served only 60 customers per day . 30 / 30 = 1 day . choice ( a ) . withthe formula , we can set up the following : 90 = ( 60 x + 120 ) / ( x + 1 ) 90 x + 90 = 60 x + 120 30 x = 30 x = 1 answer choice ( a ) | null |
Question: stacy has a 63 page history paper due in 7 days . how many pages per day would she have to write to finish on time ?
A.9.
B.8.
C.10.
D.8.5.
e ) 6A.
"63 / 7 = 9 a . 9" | null |
Question: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 148 , what is the difference between the ages of patrick and monica ?
A.27.
B.48.
C.45.
D.72.
e ) 18B.
"ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 148 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b" | null |
Question: you collect baseball cards . suppose you start out with 15 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
A.17.
B.18.
C.19.
D.20.
e ) 21B.
solution start with 15 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 15 + 1 which is 8 , so you ' re left with 15 - 8 = 7 . peter takes 1 baseball card from you : 7 - 1 = 6 baseball cards . paul triples the number of baseball cards you have : 6 Γ 3 = 18 baseball cards . so you have 18 at the end . correct answer : b | null |
Question: if the cost price of 18 articles is same as the selling price of 25 articles . find the gain or loss percentage ?
A.30 % gain.
B.28 % loss.
C.40 % gain.
D.40 % loss.
e ) 50 % lossB.
"explanation : 18 cp = 25 sp cost price cp = 25 selling price sp = 18 formula = ( sp - cp ) / cp * 100 = ( 18 - 25 ) / 25 * 100 = 28 % loss answer : option b" | null |
Question: evaluate 28 % of 450 + 45 % of 280
A.232.
B.242.
C.252.
D.262.
e ) 272C.
"explanation : = ( 28 / 100 ) * 450 + ( 45 / 100 ) * 280 = 126 + 126 = 252 option c" | null |
Question: xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 4 , 2 / 3 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?
A.1 / 16.
B.7 / 8.
C.9 / 64.
D.5 / 64.
e ) 3 / 64A.
p ( xavier will solve ) = 1 / 4 p ( yvonne will solve ) = 2 / 3 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 4 ) * ( 2 / 3 ) * ( 3 / 8 ) = 1 / 16 . ans . a . | null |
Question: in a certain lottery , the probability that a number between 1 and 15 , inclusive , is drawn is 1 / 3 . if the probability that a number 1 or larger is drawn is 2 / 3 , what is the probability that a number less than or equal to 15 is drawn ?
A.2 / 3.
B.1 / 3.
C.1 / 4.
D.1 / 6.
e ) 2 / 5A.
you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 1 or larger set 2 : number 15 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 12 or moreor 20 or less or both ) 2 / 3 + p ( set 2 ) - 1 / 3 = 1 p ( set 2 ) = 2 / 3 answer a | null |
Question: the distance from city a to city b is 120 miles . while driving from city a to city b , cara drives at a constant speed of 30 miles per hour . dan leaves city a 120 minutes after cara . what is the minimum constant speed in miles per hour that dan must exceed in order to arrive in city b before cara ?
A.42.
B.44.
C.60.
D.48.
e ) 50C.
"the time it takes cara to drive to city b is 120 / 30 = 4 hours . dan needs to take less than 2 hours for the trip . dan needs to exceed a constant speed of 120 / 2 = 60 miles per hour . the answer is c ." | null |
Question: a student travels from his house to school at 12 km / hr and reaches school 2 hours late . the next day he travels 20 km / hr and reaches school 1 hour early . what is the distance between his house and the school ?
A.90.
B.100.
C.110.
D.120.
e ) 130A.
"let x be the distance from his house to the school . x / 12 = x / 20 + 3 5 x = 3 x + 180 2 x = 180 x = 90 km the answer is a ." | null |
Question: if x is less than y by 25 % then y exceed x by :
A.33.33 %.
B.25 %.
C.75 %.
D.66.66 %.
e ) none of theseA.
"using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 25 ( 100 - 25 ) * 100 = 33.33 % answer : a" | null |
Question: a pharmaceutical company received $ 8 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
A.8 %.
B.15 %.
C.45 %.
D.52 %.
e ) 79 %E.
"solution : this is a percent decrease problem . we will use the formula : percent change = ( new β old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 8 / 20 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 8 / 20 ) x 60 = 24 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 24 and 5 into our percent change formula : ( new β old ) / old x 100 [ ( 5 β 24 ) / 24 ] x 100 - 475 / 6 x 100 at this point we can stop and consider the answer choices . since we know that 475 / 6 is just a bit less than Β½ , we know that - 475 / 6 x 100 is about a 79 % decrease . answer e ." | null |
Question: a square with sides of 15 units each . what would be the area of the square . consider a square as a combination of two right angled triangles .
['A.100', 'B.256', 'C.225', 'D.81', 'e ) 144']C.
a square can be considered as a set of two right angled triangles joined from the hypotenuse . since the sides are 10 units each . the height and base of both the triangles is 10 each . area of a right angled triangle is 1 / 2 * base * height area of both the triangles is 2 * 1 / 2 * base * height . since both triangles are similar . = base * height = 15 * 15 = 225 ans : c | null |
Question: a man is standing on a railway bridge which is 180 m long . he finds that a train crosses the bridge in 20 seconds but himself in 8 seconds . find the length of the train and its speed
A.50 km.
B.52 km.
C.54 km.
D.56 km.
e ) 58 kmC.
"explanation : let the length of the train be x meters , then , the train covers x meters in 8 seconds and ( x + 180 ) meters in 20 sec x / 8 = ( x + 180 ) / 20 β 20 x = 8 ( x + 180 ) < = > x = 120 length of the train = 120 m . speed of the train = ( 120 / 8 ) m / sec = m / sec = ( 15 Γ 18 / 5 ) kmph = 54 km answer : option c" | null |
Question: how many digits are required to number a book containing 240 pages ?
A.756.
B.612.
C.492.
D.372.
e ) 250B.
9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 240 - ( 90 + 9 ) = 141 pages will require 141 * 3 = 423 digits . the total number of digits is 9 + 180 + 423 = 612 . the answer is b . | null |
Question: out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many e applicants majored in political science and had a gpa higher than 3.0 ?
A.5.
B.10.
C.15.
D.25.
e ) 35A.
"total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) e = 20 - 15 = 5 answer : a" | null |
Question: george does 3 / 5 th of a piece of work in 9 days . he then calls in paul and they finish the work in 4 days . how long would paul take to do the work by himself ?
A.10.
B.20.
C.30.
D.40.
e ) 50C.
"9 day 3 / 5 1 day 1 / 15 remaing 1 - 3 / 5 = 2 / 5 both can do 2 / 5 work in 4 day one day work of both = 1 / 10 therfor paul would take 1 / 10 - 1 / 15 = 1 / 30 or 30 days answer : c" | null |
Question: in august , a cricket team that played 120 matches won 24 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?
A.40.
B.52.
C.68.
D.70.
e ) 98D.
let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 28.8 + x by solving we get x = 70 answer : d | null |
Question: in a survey of 340 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
A.7 / 12.
B.8 / 41.
C.39 / 68.
D.1 / 8.
e ) 41 / 91C.
- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 286 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 340 we have to find not part time and not uninsured . in other words not part time and insured = x / 340 = ( 286 - 104 + 13 ) / 340 = 39 / 68 answer is c . | null |
Question: a ( 3 , w ^ 3 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 - 1 . what is the value of w ?
A.2 ..
B.4 ..
C.5 ..
D.6 ..
e ) 9 .A.
y = x ^ 2 - 1 w ^ 3 = 3 ^ 2 - 1 w ^ 3 = 8 w = 2 answer a | null |
Question: in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 120 ?
A.30.
B.20.
C.25.
D.40.
e ) 50A.
x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 120 = ( 120 * 30 ) / 40 = 90 . in x game of 100 points , y gives ( 120 - 90 ) = 30 points to c . a | null |
Question: a house wife saved $ 2.50 in buying an item on sale . if she spent $ 25 for the item , approximately how much percent she saved in the transaction ?
A.8 %.
B.9 %.
C.10 %.
D.11 %.
e ) 12 %B.
actual price = 25 + 2.50 = $ 27.50 saving = 2.50 / 27.50 * 100 = 100 / 11 = 9 % approximately answer is b | null |
Question: after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6700 . find the actual price of the good .
A.s . 6000.
B.s . 9000.
C.s . 10800.
D.s . 9795.
e ) s . 9980D.
let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6700 1 = 6700 / 68.4 100 = ( 6700 * 100 ) / 68.4 = rs . 9795 . answer : option d | null |
Question: a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 25 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?
A.5 : 00.
B.5 : 34.
C.5 : 42.
D.6 : 00.
e ) 6 : 24C.
"c 1 loses 15 minutes every hour . so after 60 minutes have passed , c 1 displays that 60 - 15 = 45 minutes have passed . c 2 gains 15 minutes for every 60 minutes displayed on c 1 . thus , the time displayed on c 2 is 75 / 60 = 5 / 4 the time displayed on c 1 . so after 60 minutes have passed , c 2 displays the passing of ( 5 / 4 * 45 ) minutes . c 3 loses 20 minutes for every 60 minutes displayed on c 2 . thus , the time displayed on c 3 is 40 / 60 = 2 / 3 the time displayed on c 2 . so after 60 minutes have passed , c 3 displays the passing of ( 2 / 3 * 5 / 4 * 45 ) minutes . c 4 gains 20 minutes for every 60 minutes displayed on c 3 . thus , the time displayed on c 4 is 80 / 60 = 4 / 3 the time displayed on clock 3 . so after 60 minutes have passed , c 4 displays the passing of 4 / 3 * 2 / 3 * 5 / 4 * 45 = 50 minutes . c 4 loses 10 minutes every hour . in 6 hours , c 4 will lose 6 * 10 = 60 minutes = 1 hour . since the correct time after 6 hours will be 6 pm , c 4 will show a time of 6 - 1 = 5 : 42 pm . the correct answer is c ." | null |
Question: in a factory , an average of 60 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 58 sets / day . the average production per day for day last 5 days is ?
A.20.
B.36.
C.48.
D.50.
e ) 59C.
production during these 5 days = total production in a month - production in first 25 days . = 30 x 58 - 25 x 60 = 240 β΄ average for last 5 days = 240 / 5 = 48 c | null |
Question: a collection of books went on sale , and 2 / 3 of them were sold for $ 4.25 each . if none of the 30 remaining books were sold , what was the total amount received for the books that were sold ?
A.$ 260.
B.$ 255.
C.$ 285.
D.$ 290.
e ) $ 275B.
"if 30 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 60 books amount received for sold books = 60 * 4.25 = $ 255 answer : b" | null |
Question: the ratio between the present ages of a and b is 5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
A.3 : 9.
B.3 : 6.
C.3 : 1.
D.3 : 4.
e ) 3 : 2C.
"let the present ages of a and b be 5 x and 3 x years respectively . then , ( 5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 2 x = 8 = > x = 4 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 24 : 8 = 3 : 1 answer : c" | null |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.