text
stringlengths 45
2.98k
| __index_level_0__
float64 0
11.7k
β |
|---|---|
Question: of the 20,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
A.14.3 %.
B.16.67 %.
C.33 %.
D.28.6 %.
e ) 49.67 %E.
the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 49.67 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you β re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . e | null |
Question: if jimmy drinks 8 ounces of water each time for 8 times a day . how much gallons of water he would have to prepare ahead to drink for 5 days ? ( 1 ounce = 0.0078125 gallon )
A.1.
B.1.5.
C.2.
D.2.5.
e ) 3D.
8 ounces * 8 times / day = 64 ounces of water = 64 * 0.0078125 = 0.5 gallon . 5 days need 0.5 * 5 = 2.5 gallons . correct option : 2.5 answer : d | null |
Question: 100 people are attending a newspaper conference . 45 of them are writers and more than 36 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?
A.26.
B.24.
C.18.
D.20.
e ) 22C.
"{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 45 + { editors } - x + 2 x - - > x = 55 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 37 , thus x = { both } = 55 - 37 = 18 . answer : c ." | null |
Question: two trains , a and b , started simultaneously from opposite ends of a 120 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 120 - mile trip in 6 hours ; train b , traveling at a constant rate , completed the 120 - mile trip in 4 hours . how many miles had train a traveled when it met train b ?
A.28.
B.36.
C.48.
D.50.
e ) 54C.
"as the ratio of the rates of a and b is 4 to 6 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that x would cover 4 / ( 4 + 6 ) = 4 / 10 of 120 miles : 120 * 4 / 10 = 48 miles . answer : c ." | null |
Question: if a speaks the truth 55 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
A.0.29.
B.0.33.
C.0.41.
D.0.482.
e ) 0.411B.
"explanation : probability that a speaks truth is 55 / 100 = 0.55 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) Γ p ( b ) = 0.55 Γ 0.6 = 0.33 answer : b" | null |
Question: the closest approximation of ( 69.28 Γ 0.004 ) / 0.03 is
A.0.092.
B.0.92.
C.9.2.
D.92.
e ) 920C.
"( 69.28 Γ 0.004 ) / 0.03 1 . 0.004 = 4 Γ 10 ^ ( - 3 ) 2 . 0.03 = 3 Γ 10 ^ ( - 2 ) 3 . ( a Γ b ) / c = a Γ ( b / c ) 4 . 0.004 / 0.03 = 4 Γ 10 ^ ( - 3 ) / ( 3 Γ 10 ^ ( - 2 ) ) = 4 Γ 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 Γ 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) Γ 10 ^ ( - 1 ) = 1.333 Γ 10 ^ ( - 1 ) therefore , ( 69.28 Γ 0.004 ) / 0.03 = 69.28 Γ ( 0.004 / 0.03 ) = 69.28 Γ 1.33 Γ 10 ^ ( - 1 ) = 69.28 Γ 1.33 / 10 = 6.928 * 1.33 now , 7 Γ 2 = 14 7 Γ 1 = 7 or better : 6.9 Γ 1 = 6.9 6.9 Γ 2 = 13.8 hence , 6.9 < 6.928 Γ 1.33 < 13.8 9.2 is the only answer that satisfies this condition . answer : c" | null |
Question: to complete a work a and b takes 8 days , b and c takes 12 days , a , b and c takes 6 days . how much time a and c will take
A.24 days.
B.16 days.
C.12 days.
D.8 days.
e ) none of theseD.
explanation : a + b 1 day work = 1 / 8 b + c 1 day work = 1 / 12 a + b + c 1 day work = 1 / 6 we can get a work by ( a + b + c ) - ( b + c ) and c by ( a + b + c ) - ( a + b ) so a 1 day work = 1 / 6 β 1 / 12 = 1 / 12 similarly c 1 day work = 1 / 6 β 1 / 8 = 4 β 3 / 24 = 1 / 24 so a and c 1 day work = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 so a and c can together do this work in 8 days option d | null |
Question: 16 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
A.14.
B.12.
C.11.
D.8.
e ) 7E.
"x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 16 = 7 answer : e" | null |
Question: maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 34 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
A.3.
B.4.
C.5.
D.6.
e ) 8B.
"total distance = 34 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 30 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 30 / 10 = 3 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 3 = 12 + 4 = 16 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 16 / 4 = 4 hrs . . . answer b" | null |
Question: if log 2 x - 5 log x + 6 = 0 , then what would the value / values of x be ?
A.5.3296.
B.6.3296.
C.7.3296.
D.8.3296.
e ) 9.3296A.
log ( 2 x ) - 5 log ( x ) + 6 = 0 ( given ) log ( 2 x ) - log ( x ^ 5 ) = - 6 log ( 2 x / x ^ 5 ) = - 6 [ since log ( a ) - log ( b ) = log ( a / b ) ] apply anti log 2 / ( x ^ 4 ) = e ^ - 6 2 / ( x ^ 4 ) = 2.4788 * 10 ^ - 3 x ^ 4 = 806.85 x = 5.3296 answer : a | null |
Question: the salary of a person was reduced by 25 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
A.10 %.
B.33.33 %.
C.20 %.
D.25 %.
e ) 50 %B.
"let the original salary be $ 100 new salary = $ 75 increase on 75 = 25 increase on 100 = [ ( 25 / 75 ) 100 ] % = 33.33 % answer is b" | null |
Question: if a light flashes every 6 seconds , how many times will it flash in 1 / 3 of an hour ?
A.101.
B.201.
C.301.
D.401.
e ) 501B.
"in 1 / 3 of an hour there are 20 * 60 = 1200 seconds the number of 6 - second intervals = 1200 / 6 = 200 after the first flash , there will be 200 more flashes for a total of 201 . the answer is b ." | null |
Question: if ( x + 1 ) ( x + 3 ) = x ^ 2 + x , what is a possible value of x ?
A.2.
B.3.
C.- 1 / 3.
D.- 3.
e ) - 1E.
rearranging the given expression : ( x + 1 ) ( x + 3 ) = x ^ 2 + x i . e . x ^ 2 + 4 x + 3 = x ^ 2 + x i . e . 3 x = - 3 i . e . x = - 3 / 3 = - 1 answer : option e had it been a difficult expression to solve further , then we could have used options to check which one satisfies the expression after solving it as further as possible . | null |
Question: a company recently conducted a survey and found that 20,000 of its customers live in rural areas . if the number of customers who live in urban areas is 100 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
A.40,000.
B.45,000.
C.50,000.
D.55,000.
e ) 60,000A.
"the number of customers in urban areas is 20,000 + 1 * 20,000 = 40,000 . the answer is a ." | null |
Question: as a treat for her two children , a mother runs to the freezer in which she has 3 cherry ice pops , 4 orange ice pops , and 4 lemon ice pops . she chooses two at random to bring outside to the children , but realizes as she runs out the door that she can not bring them different flavors without one being jealous of the other and getting even more upset . what is the probability that she has to return to the freezer to make sure that they each receive the same flavor ?
A.3 / 5.
B.5 / 7.
C.8 / 11.
D.11 / 15.
e ) 13 / 20C.
p ( 2 cherry ) = 3 / 11 * 2 / 10 = 6 / 110 p ( 2 orange ) = 4 / 11 * 3 / 10 = 12 / 110 p ( 2 lemon ) = 4 / 11 * 3 / 10 = 12 / 110 p ( 2 of the same flavor ) = 30 / 110 p ( 2 different flavors ) = 1 - 30 / 110 = 80 / 110 = 8 / 11 the answer is c . | null |
Question: john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 70 miles per hour , what is v in miles per hour ?
A.30.
B.40.
C.50.
D.55.
e ) 60E.
"hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 70 = > v = 60 ( option e ) ." | null |
Question: a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing . if the poles of the fence are kept 10 metres apart , how many poles will be needed ?
A.28.
B.56.
C.57.
D.58.
e ) none of theseA.
"solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . β΄ number of poles = [ 280 / 10 ] = 28 m answer a" | null |
Question: if in a race of 80 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
A.16 m.
B.18 m.
C.15 m.
D.14 m.
e ) 11 mA.
"explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 80 * 5 ) / 25 = 16 m hence , a beats b by 16 m . answer : a" | null |
Question: when two dice are rolled , what is the probability that the sum of the two numbers is 6 ?
A.1 / 9.
B.5 / 36.
C.1 / 3.
D.2 / 36.
e ) none of the aboveB.
we have 5 outcomes that satisfy the question : 1 - 5 2 - 4 3 - 3 4 - 2 5 - 1 the probability is ( 1 / 6 * 1 / 6 ) * 5 = 5 / 36 . i think the answer is b | null |
Question: two trains start from a & b and travel towards each other at speed of 50 kmph and 60 kmph resp . at the time of the meeting the second train has traveled 100 km more than the first . the distance between them .
A.800 km.
B.900 km.
C.1000 km.
D.1100 km.
e ) 1200 kmD.
let the distance traveled by the first train be x km then distance covered by the second train is x + 100 km x / 50 = x + 100 / 60 x = 500 so the distance between a & b is x + x + 100 = 1100 km answer is d . | null |
Question: a dog takes 5 leaps for every 7 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
A.16 : 7.
B.15 : 7.
C.20 : 7.
D.7 : 15.
e ) 14 : 7B.
explanation : dog : hare = ( 5 * 3 ) leaps of hare : 7 leaps of hare = 15 : 7 answer : b | null |
Question: if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value a of z - x ?
A.6.
B.7.
C.8.
D.9.
e ) 10D.
"x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] a = z - x = x + 9 - x = 9 ans : d" | null |
Question: 0.1 + ( 0.1 ) ^ 2 + ( 0.1 ) ^ 3 =
A.0.1.
B.0.111.
C.0.1211.
D.0.2341.
e ) 0.3B.
"explanation : 0.1 + ( 0.1 ) ^ 2 + ( 0.1 ) ^ 3 = 0.1 + 0.01 + 0.001 = 0.111 answer : option b" | null |
Question: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 140 m long ?
A.38 sec.
B.35 sec.
C.44 sec.
D.40 sec.
e ) 48 secD.
"train length = 360 m platform length = 140 m time = ? length = speed * time total length = 360 + 140 = 500 m speed = 45 km / hr = 45 * ( 5 / 18 ) ( m / sec ) = 12.5 m / sec time = length / speed = 500 / 12.5 = 40 sec answer : d" | null |
Question: convert the 17 / 36 m / s into kilometers per hour ?
A.1.7.
B.1.5.
C.1.3.
D.1.1.
e ) 1.2A.
"17 / 36 m / s = 17 / 36 * 18 / 5 = 17 / 10 = 1.7 kmph . answer : a" | null |
Question: two guys a and b leave point a and point b simultaneously and travel towards point b and point a on the same route at their respective constant speeds . they meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively . how long will b take to cover the entire journey between point b and point a ?
A.65.
B.90.
C.70.
D.75.
e ) 80B.
let x per minute be the speed of a and y per minute be the speed of b . after meeting at a point , a travels for 32 mins and b travels for 50 mins . so distance covered by each of them post point of crossing a = 32 x and b = 50 y the distance covered by a and b before they cross each would be distance covered by b and a post crossing respectively . therefore distance covered by b before he meets a = 32 x time taken by b cover 32 x distance = 32 x / y mins therefore total time taken by b = 32 x / y + 50 mins . . . . . . . . . . . . . . . . . i we need to find value of x in terms of y to arrive at final answer . total distance = 32 x + 50 y combined speed of a and b = x + y therefore time taken before a and b meet en - route = ( 32 x + 50 y ) / ( x + y ) time taken by b reach destination after meeting a = 50 mins total travel time for b = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 mins . . . . . . . . . . . . . . . . . . . ii equate i and ii 32 x / y + 50 = [ ( 32 x + 50 y ) / ( x + y ) ] + 50 ( 32 x + 50 y ) / y = ( 82 x + 100 y ) / ( x + y ) 32 x ^ 2 + 50 xy + 32 xy + 50 y ^ 2 = 82 xy + 100 y ^ 2 32 x ^ 2 + 82 xy - 82 xy + 50 y ^ 2 - 100 y ^ 2 = 0 32 x ^ 2 - 50 y ^ 2 = 0 32 x ^ 2 = 50 y ^ 2 16 x ^ 2 = 25 y ^ 2 taking square root . . ( since x and y denote speed , square root ca n ' t be negative ) 4 x = 5 y y = 4 x / 5 . . . . . . . . . . . . iii substitute in i = 32 x / ( 4 x / 5 ) + 50 = 32 x * 5 / 4 x + 50 = 40 + 50 = 90 mins b | null |
Question: in what time will a train 140 m long cross an electric pole , it its speed be 190 km / hr ?
A.2.6 sec.
B.2.9 sec.
C.2.7 sec.
D.8.7 sec.
e ) 8.5 secA.
"speed = 190 * 5 / 18 = 53 m / sec time taken = 140 / 53 = 2.6 sec . answer : a" | null |
Question: if 63 percent of a class answered the first question on a certain test correctly , 50 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
A.24 %.
B.27 %.
C.30 %.
D.33 %.
e ) 36 %D.
"63 % answered the first question correctly and 20 % answered neither correctly . then 17 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 50 % - 17 % = 33 % . the answer is d ." | null |
Question: the area of a square garden is a square feet and the perimeter is p feet . if a = 2 p + 26.25 , what is the perimeter of the garden , in feet ?
A.28.
B.36.
C.40.
D.42.
e ) 64D.
"perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 26.25 ( p ^ 2 ) / 16 = 2 p + 26.25 p ^ 2 = 32 p + 420 p ^ 2 - 32 p - 420 = 0 p ^ 2 - 42 p + 10 p - 420 = 0 p ( p - 42 ) + 10 ( p + 42 ) = 0 ( p - 42 ) ( p + 10 ) = 0 p = 42 or - 10 discarding negative value , p = 42 answer is d" | null |
Question: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 95 units raises the average to 55 units per day , what is the value of n ?
A.6.
B.7.
C.8.
D.9.
e ) 10C.
"the average daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 95 - 55 = 40 n = 8 the answer is c ." | null |
Question: how many seconds will a 300 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.86 sec.
D.15 sec.
e ) 18 secE.
"speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 300 * 3 / 50 = 18 sec . answer : e" | null |
Question: by investing in 1623 % stock at 64 , one earns rs . 1600 . the investment made is
A.s . 9600.
B.s . 7500.
C.s . 5640.
D.s . 6144.
e ) s . 6760D.
"explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1600 , investment needed = 64 Γ 3 Γ 1600 / 50 = 6144 answer : option d" | null |
Question: abcd is a parallelogram . bd = 2 . the angles of triangle bcd are all equal . what is the perimeter of the parallelogram ?
['A.12', 'B.9 β 3', 'C.9', 'D.8', 'e ) 3 β 3']D.
so , bc = bd = cd = ba = ad = 2 the parallelogram has 4 equal sides bc = cd = ba = ad = 2 so the perimeter of the parallelogram will be 2 * 4 = 8 hence answer will be ( d ) 2 | null |
Question: the number 42 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
A.17.
B.10.
C.15.
D.14.
e ) 13B.
"i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 42 : 1 , 4 , 9 , 16 , 25 , 36 . now , 42 should be the sum of 3 of those 8 numbers . also to simplify a little bit trial and error , we can notice that as 42 is an odd numbers then either all three numbers must be odd ( odd + odd + odd = odd ) or two must be even and one odd ( even + even + odd = odd ) . we can find that 42 equals to 1 + 16 + 25 = 1 ^ 2 + 4 ^ 2 + 5 ^ 2 = 42 - - > 1 + 5 + 4 = 10 . answer : b ." | null |
Question: if the price of petrol increases by 40 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
A.25 %.
B.20 %.
C.16.67 %.
D.28.6 %.
e ) none of theseD.
"explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 40 ) i . e 140 . now , his consumption should be reduced to : - = ( 140 β 100 ) / 140 β 100 . hence , the consumption should be reduced to 28.6 % . answer : d" | null |
Question: how many factors does 36 ^ 2 have ?
A.2.
B.8.
C.24.
D.25.
e ) 26D.
"36 ^ 2 = 2 ^ 4 3 ^ 4 total factors = ( 4 + 1 ) ( 4 + 1 ) = 25 . answer is d ." | null |
Question: the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.8 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?
A.4.2.
B.4.4.
C.4.6.
D.5.6.
e ) 5.7A.
"sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.8 * 2 ) + ( 3.85 * 2 ) ] = 8.4 . required average = ( 8.4 / 2 ) = 4.2 . a" | null |
Question: 14 times a number gives 210 . the number is
A.11.
B.12.
C.15.
D.none.
e ) can not be determinedC.
"explanation : let the number be ' n ' 14 Γ n = 210 β n = 15 correct option : c" | null |
Question: the average of 7 numbers is 24 . if each number be multiplied by 5 . find the average of new set of numbers ?
A.110.
B.122.
C.120.
D.125.
e ) 145C.
"explanation : average of new numbers = 24 * 5 = 120 answer : option c" | null |
Question: a cycle is bought for rs . 900 and sold for rs . 1080 , find the gain percent ?
A.27 %.
B.20 %.
C.25 %.
D.40 %.
e ) 28 %B.
"900 - - - - 180 100 - - - - ? = > 20 % answer : b" | null |
Question: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 30 kmph . of how many minutes does the train stop per hour ?
A.A.5.
B.B.10.
C.C.20.
D.D.30.
e ) e ) 40C.
"explanation : t = 15 / 45 * 60 = 20 answer : option c" | null |
Question: if rs . 544 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
A.s . 300.
B.s . 360.
C.s . 389.
D.s . 384.
e ) s . 323D.
"( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 544 * 2 / 17 = rs . 64 b ' s share = 544 * 3 / 17 = rs . 96 c ' s share = 544 * 12 / 17 = rs . 384 . answer : d" | null |
Question: m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?
A.0.
B.1 / 3.
C.2 / 5.
D.1 / 2.
e ) 3 / 5D.
we will have a negative product only if 1 , 2 , 3 , or 4 are selected from set t . p ( negative product ) = 4 / 8 = 1 / 2 the answer is d . | null |
Question: a 300 m long train crosses a platform in 48 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
A.500.
B.350.
C.828.
D.277.
e ) 122A.
"speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 489 = 50 / 3 3 x + 900 = 2400 = > x = 500 m . answer : a" | null |
Question: the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 22 years . find the average age of the women ?
A.87.
B.98.
C.30.
D.29.
e ) 37D.
"20 + 22 + 8 * 2 = 58 / 2 = 29 answer : d" | null |
Question: a tank contains 7,000 gallons of a solution that is 5 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
A.4.77 %.
B.5.77 %.
C.6.77 %.
D.7.77 %.
e ) 8.77 %D.
"we start with 7,000 gallons of a solution that is 5 % sodium chloride by volume . this means that there are 0.05 x 7,000 = 350 gallons of sodium chloride . when 2,500 gallons of water evaporate we are left with 4,500 gallons of solution . from here we can determine what percent of the 4,500 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 350 / 4,500 ) x 100 = ? 0.077 x 100 = ? = 7.7 % answer is d ." | null |
Question: if 20 % of x is 15 less than 15 % of 1500 , then x is ?
A.872.
B.738.
C.837.
D.840.
e ) 1050E.
"20 % of x = x / 5 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 5 = 225 - 15 = > x / 5 = 210 = > x = 1050 . answer : e" | null |
Question: a certain fraction is equivalent to 2 / 5 . if the numerator of the fraction is increased by 4 and the denominator is doubled , the new fraction is equivalent to 1 / 3 . what is the difference of the numerator and denominator of the original fraction ?
A.49.
B.9.
C.28.
D.26.
e ) 21B.
"x / y = 2 / 5 - > 1 ( x + 4 ) / 2 y = 1 / 3 - > 2 divide 1 by 2 : = > 2 x / ( x + 4 ) = 6 / 5 = > 5 x = 3 x + 12 = > x = 6 = > y = 5 / 2 * 6 = 15 so x - y = 9 the answer is b" | null |
Question: the average of numbers 0.34204 , 0.34203 , 0.34202 and 0.34201 is ?
A.0.34202.
B.0.34204.
C.0.342022.
D.0.342025.
e ) noneD.
"answer average = ( 0.34204 + 0.34203 + 0.34202 + 0.34201 ) / 4 = 1.3681 / 4 = 0.342025 correct option : d" | null |
Question: what is the total number of integers between 10 and 100 ( exclusive ) that are divisible by 7 ?
A.10.
B.13.
C.15.
D.12.
e ) 11B.
"14 , 21 , 28 , . . . , 91,98 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 98 - 14 ) / ( 7 ) + 1 = 12 + 1 = 13 answer is b" | null |
Question: if the average of 5 positive integers is 70 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
A.50.
B.52.
C.69.
D.78.
e ) 84D.
"sum of 5 integer ( a , b , c , d , e ) = 5 * 70 = 350 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 350 i . e . 5 a = 340 i . e . a = 68 i . e . largest e = 68 + 10 = 78 answer : option d" | null |
Question: a rectangular photograph is surrounded by a border that is 3 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 6 inches wide on each side , the total area would have been ( m + 178 ) square inches . what is the perimeter of the photograph , in inches ?
A.34.
B.36.
C.38.
D.40.
e ) 20E.
"let length and breadth of photograph be l and b respectively . perimeter is given by 2 * ( l + b ) - - - - - ( 1 ) according to the question : ( l + 6 ) ( b + 6 ) = m - - - - ( 2 ) and ( l + 12 ) ( b + 12 ) = m + 178 - - - - - - - - - > ( l + 12 ) ( b + 12 ) - 178 = m - - - - - - ( 3 ) equating ( 2 ) and ( 3 ) ( l + 6 ) ( b + 6 ) = ( l + 12 ) ( b + 12 ) - 178 lb + 6 l + 6 b + 36 = lb + 12 l + 12 b + 144 - 168 simplify 6 l + 6 b = 60 - - - - - - > 2 ( l + b ) = 20 ( check eq ( 1 ) ) answer is e" | null |
Question: the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length e of a cube whose surface area is equal to 6 z ?
A.e = 16.
B.e = 8 β 2.
C.e = 8.
D.e = 2 β 2.
e ) ( β 2 ) / 3D.
"800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 4 , - 4 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 4 Γ 4 ) = 8 ; so z = 8 . the next step requires us to find the length of a side of a cube that has a face area equal to 8 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 8 . since the area of a square is equal to s Β² , where s is the length of one of its side , we can write and solve the equation s Β² = 8 . clearly s = β 8 = 2 β 2 , oranswer choice ( d ) ." | null |
Question: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 1 : 2 . the first number is :
A.A.27.
B.B.98.
C.C.34.
D.D.35.
e ) e ) 62A.
"( 3 x - 9 ) : ( 5 x - 9 ) = 9 : 17 x = 9 = > 3 x = 27 answer : a" | null |
Question: what number times ( 1 β 6 ) ^ 2 will give the value of 6 ^ 3 ?
A.6.
B.36.
C.216.
D.1296.
e ) 7776E.
"x * ( 1 / 6 ) ^ 2 = 6 ^ 3 x = 6 ^ 2 * 6 ^ 3 = 6 ^ 5 = 7776 the answer is e ." | null |
Question: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 18 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?
A.32.
B.52.
C.62.
D.42.
e ) 48D.
"ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 18 ) = ( 7 / 16 ) * v 1 ( v 1 - 18 ) / v 1 = 3 / 4 18 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 18 = 72 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 72 = 42 litres . answer : d" | null |
Question: angelo and isabella are both salespersons . in any given week , angelo makes $ 560 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
A.23,500.
B.24,000.
C.25,500.
D.26,500.
e ) 27,500B.
"let the weekly sales of both = x 560 + ( x β 1000 ) 8 / 100 = 10 / 100 x x = 24000 answer : b" | null |
Question: a can do a piece of work in 16 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
A.18.
B.77.
C.66.
D.55.
e ) 12E.
"8 / 16 + 6 / x = 1 x = 12 days answer : e" | null |
Question: what is the normal price of an article sold at $ 72 after two successive discounts of 10 % and 20 % ?
A.$ 92.
B.$ 96.
C.$ 100.
D.$ 104.
e ) $ 108C.
0.8 * 0.9 * cost price = $ 72 cost price = $ 100 the answer is c . | null |
Question: during a certain two - week period , 76 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
A.16 a.
B.19 a.
C.17 a.
D.18 a.
e ) 20 aB.
"total movies = 100 . comedies = 76 . action + drama = 24 . since there were 5 times as many dramas as action movies , then action + 5 * action = 24 - - > action = a = 4 . comedies = 76 = 19 a . answer : b ." | null |
Question: of the 200 stamps in a collection , 80 are foreign and 50 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?
A.60.
B.90.
C.100.
D.130.
e ) 150B.
"20 stamps are both foreign and more than 10 years old . 60 stamps are foreign only . 30 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 60 + 30 ) = 90 the answer is b ." | null |
Question: running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 3 w widgets ?
A.4.
B.6.
C.18.
D.10.
e ) 12C.
"let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 3 * 6 = 18 days to produce 3 w widgets . answer : c" | null |
Question: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 3 of the remaining paint . how many gallons of paint has joe used ?
A.18.
B.180.
C.175.
D.216.
e ) 250B.
"total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 3 ) * 270 = 90 gallons total paint used = 180 gallons . option b" | null |
Question: the cost of 2 chairs and 3 tables is rs . 1400 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
A.228.
B.287.
C.277.
D.188.
e ) 200E.
"explanation : 2 c + 3 t = 1400 - - - ( 1 ) 3 c + 2 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 200 = > t - c = 200 answer : e" | null |
Question: if a truck is traveling at a constant rate of 108 kilometers per hour , how many seconds will it take the truck to travel a distance of 600 meters ? ( 1 kilometer = 1000 meters )
A.20.
B.24.
C.30.
D.36.
e ) 48A.
speed = 108 km / hr = > 108,000 m / hr in one minute = > 108000 / 60 = 1800 meters in one sec = > 1800 / 60 = 30 meters time = total distance need to be covered / avg . speed = > 600 / 30 = 20 and hence the answer : a | null |
Question: if x + y = 4 and x 2 y 3 + y 2 x 3 = 36 , what is the value of xy ?
A.1.
B.2.
C.3.
D.4.
e ) 5D.
"xy = 3 as x + y = 4 x 2 y 3 + y 2 x 3 = 36 x 2 y 2 ( y + x ) = 36 substituting x + y x 2 y 2 = 4 xy = 4 answer : d" | null |
Question: what is the least number that should be added to 1054 , so the sum of the number is divisible by 23 ?
A.1.
B.2.
C.3.
D.4.
e ) 5D.
"( 1054 / 23 ) gives a remainder 19 so we need to add 4 . the answer is d ." | null |
Question: two bullet trains of equal lengths take 10 seconds and 12 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
A.11 sec ..
B.15 sec ..
C.12 sec ..
D.17 sec ..
e ) 19 sec .A.
"speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 12 m / sec = 10 m / sec . relative speed = ( 12 + 10 ) = 22 m / sec . required time = ( 120 + 120 ) / 22 sec = 11 sec . a" | null |
Question: if d is the standard deviation a , b , and c , what is the standard deviation of a + 6 , b + 6 , c + 6 ?
A.d.
B.6 d.
C.6 d + 6.
D.6 d + 12.
e ) 6 d + 18A.
"concept : standard deviation is defined as average deviation of terms in the set from the mean value of the set . i . e . 1 ) it depends on the separation between the successive terms of the set 2 ) if a constant value is added / subtracted in every terms of set then the separation between successive terms does not change hence s . d . remains constant e . g . { 1 , 2 , 3 , 4 , 5 } will have same standard deviation as { 1 + 10 , 2 + 10 , 3 + 10 , 4 + 10 , 5 + 10 } 3 ) if a constant value is multiplied in every terms then the separation between succesive terms gets multiplied by the constant hence s . d . remains gets multiplied by same number e . g . { 0.7 , 1.4 , 2.1 , 2.8 , 3.5 } will have standard deviation = 0.7 * standard deviation of set { 1 , 2 , 3 , 4 , 5 } when 6 is added in each term of set { a , b , c } then the new set { a + 6 , b + 6 , c + 6 } will remain same as the previous standard deviation i . e . d answer : a" | null |
Question: 70 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
A.100.
B.200.
C.300.
D.350.
e ) 400C.
"7 x / 10 - x / 3 = 110 11 x / 30 = 110 x = 300 answer : c" | null |
Question: eight machines , each working at the same constant rate , together can complete a certain job in 20 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 16 days ?
A.4.
B.6.
C.8.
D.10.
e ) 2E.
"rate of one machine = 1 job / ( 20 * 8 ) days let x = number of machines needed to complete the job in 16 days 1 / ( 8 * 20 ) * 16 * x = 1 job x = 10 10 - 8 = 2 answer : e" | null |
Question: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 80 more candidates got selected than a . what was the number of candidates appeared from each state ?
A.7000.
B.8000.
C.8800.
D.8900.
e ) 9000B.
"state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 80 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 80 = > total appeared candidates in state b = 80 x 100 = 8000 = > total appeared candidates in state a = total appeared candidates in state b = 8000" | null |
Question: the sector of a circle has perimeter of 144 cm and central angle 180 o . find its radius ?
A.25 cm.
B.32 cm.
C.14 cm.
D.28 cm.
e ) 21 cmD.
"let the radius is x cm perimeter of the sector = length of the arc + 2 ( radius ) 144 = ( 180 / 360 * 2 * 22 / 7 * x ) + 2 ( x ) 144 = 22 x / 7 + 2 x 144 = 36 x / 7 36 x = 1008 x = 28 answer : d" | null |
Question: the dimensions of a room are 10 m x 7 m x 5 m . there are 2 doors and 3 windows in the room . the dimensions of the doors are 1 m x 3 m . one window is of size 2 m x 1.5 m and the other 2 windows are of size 1 m x 1.5 m . the cost of painting the walls at rs . 3 per sq m is ?
A.rs . 229.
B.rs . 429.
C.rs . 129.
D.rs . 474.
e ) rs . 111D.
"area of 4 walls = 2 ( l + b ) h = 2 ( 10 + 7 ) x 5 = 170 sq m area of 2 doors and 3 windows = 2 ( 1 x 3 ) + ( 2 x 1.5 ) + 2 ( 1 x 1.5 ) = 12 sq m area to be planted = 170 - 12 = 158 sq m cost of painting = rs . 158 x 3 = rs . 474 answer : d" | null |
Question: ravi and kavi start a business by investing Γ’ β ΒΉ 2000 and Γ’ β ΒΉ 72000 , respectively . find the ratio of their profits at the end of year .
A.2 : 36.
B.5 : 36.
C.7 : 36.
D.1 : 36.
e ) 3 : 36D.
"ratio of profit = ratio of investments = 2000 : 72000 = 1 : 36 answer : d" | null |
Question: the owner of a furniture shop charges his customer 25 % more than the cost price . if a customer paid rs . 1000 for a computer table , then what was the cost price of the computer table ?
A.620.
B.400.
C.45.
D.500.
e ) 800E.
"cp = sp * ( 100 / ( 100 + profit % ) ) = 1000 ( 100 / 125 ) = rs . 800 . answer : e" | null |
Question: a worker earns $ 20 on the first day and spends $ 15 on the second day . the worker earns $ 20 on the third day and spends $ 15 on the fourth day . if this pattern continues , on which day will the worker first reach a net total of $ 100 ?
A.30.
B.33.
C.35.
D.38.
e ) 40B.
"every two days , the net total is $ 5 . after 32 days , the worker will have $ 80 . on day 33 , the worker will receive $ 20 for a net total of $ 100 . the answer is b ." | null |
Question: john makes $ 60 a week from his job . he earns a raise and now makes $ 100 a week . what is the % increase ?
A.16 %.
B.66.67 %.
C.17 %.
D.17.61 %.
e ) 17.56 %B.
"increase = ( 40 / 60 ) * 100 = ( 4 / 6 ) * 100 = 66.67 % . b" | null |
Question: 6 men and 8 women can complete a work in 10 days . 26 men and 48 women can finish the same work in 2 days . 15 men and 20 women can do the same work in - days .
A.4 days.
B.6 days.
C.2 days.
D.8 days.
e ) 10 daysA.
"explanation : let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b work done by 6 men and 8 women in 1 day = 1 / 10 = > 6 m + 8 b = 1 / 10 = > 60 m + 80 b = 1 - - - ( 1 ) work done by 26 men and 48 women in 1 day = 1 / 2 = > 26 m + 48 b = Β½ = > 52 m + 96 b = 1 - - - ( 2 ) solving equation 1 and equation 2 . we get m = 1 / 100 and b = 1 / 200 work done by 15 men and 20 women in 1 day = 15 / 100 + 20 / 200 = 1 / 4 = > time taken by 15 men and 20 women in doing the work = 4 days answer : option a" | null |
Question: a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 153 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
A.22.
B.33.
C.55.
D.27.
e ) 88D.
"let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 153 = > . 1 x + 3 / 4 x = 153 = > x = 180 180 - 153 = pure gala = 27 . d" | null |
Question: how long does a bus 100 m long traveling at 50 kmph takes to cross a bridge of 150 m in length ?
A.18.
B.16.
C.15.
D.11.
e ) 12A.
d = 100 + 150 = 250 m s = 50 * 5 / 18 = 125 / 9 t = 250 * 9 / 125 = 18 sec answer : a | null |
Question: a cistern 5 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
A.49 m 2.
B.42.5 m 2.
C.53.5 m 2.
D.55 m 2.
e ) 57 m 2B.
"area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 5 x 1.25 ) + 5 x 4 ] m 2 = 42.5 m 2 . answer : option b" | null |
Question: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 63 , what is the total amount ?
A.115.
B.273.
C.117.
D.118.
e ) 119B.
"x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 63 39 - - - ? = > 273 answer : b" | null |
Question: find the value of 1 / ( 3 + 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) )
A.21 / 29.
B.27 / 89.
C.89 / 21.
D.29 / 21.
e ) noneB.
1 / [ 3 + ( 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ] = > 1 / [ 3 + 1 / ( 3 + 1 / ( 8 / 3 ) ) ] = > 1 / [ 3 + 1 / ( 3 + 3 / 8 ) ] = > 1 / [ 3 + 8 / 27 ] = > 1 / ( 89 / 27 ) = > 27 / 89 b | null |
Question: if a - b = 5 and a 2 + b 2 = 31 , find the value of ab .
A.9.
B.2.
C.3.
D.7.
e ) 12C.
"2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 31 - 25 = 6 ab = 3 . answer : c" | null |
Question: if circles x and y have the same area and circle x has a circumference of 18 Ο , half of the radius of circle y is :
A.16.
B.4.5.
C.4.
D.2.
e ) 1B.
"x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 18 * pi x = 9 thus y = 9 y / 2 = 4.5 ans : b" | null |
Question: the present population of a town is 2000 . population increase rate is 20 % p . a . find the population of town after 1 years ?
A.1000.
B.2400.
C.1500.
D.1600.
e ) 1250B.
"p = 2000 r = 20 % required population of town = p ( 1 + r / 100 ) ^ t = 2000 ( 1 + 20 / 100 ) = 2000 ( 6 / 5 ) = 2400 answer is b" | null |
Question: the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 490 , krishan has ?
A.rs . 2890.
B.rs . 2330.
C.rs . 1190.
D.rs . 1620.
e ) rs . 2680A.
"ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 490 : n & there n = 289 x 490 / 49 = rs . 2890 answer : a" | null |
Question: by selling an article for $ 195 , a person gains $ 45 . what is the gain % ?
A.25 %.
B.30 %.
C.50 %.
D.20 %.
e ) 10 %B.
s . p . = $ 195 gain = $ 45 c . p . = 195 - 45 = 150 gain % = 45 / 150 * 100 % = 30 % answer is b | null |
Question: by selling an article at rs . 600 , a profit of 60 % is made . find its cost price ?
A.228.
B.267.
C.375.
D.480.
e ) 811C.
"sp = 600 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / ( 100 + 60 ) ] = 600 * [ 100 / 160 ] = rs . 375 answer : c" | null |
Question: ray writes a two digit number . he sees that the number exceeds 4 times the sum of its digits by 3 . if the number is increased by 18 , the result is the same as the number formed by reversing the digits . find the number .
A.2.
B.5.
C.6.
D.7.
e ) 8B.
solution : let the two digit number be xy . 4 ( x + y ) + 3 = 10 x + y . . . . . . . ( 1 ) 10 x + y + 18 = 10 y + x . . . . ( 2 ) solving 1 st equation we get 2 x - y = 1 . . . . . ( 3 ) solving 2 nd equation we get y - x = 2 . . . . . ( 4 ) solving 3 and 4 , we get x = 3 and y = 5 answer : b | null |
Question: how many 3 - digit integers between 311 and 401 , exclusive , are divisible by 3 when the tens digit and the hundered digit are switched ?
A.30.
B.19.
C.22.
D.3.
e ) 90A.
answer is 30 no of digits between 311 and 401 ( exclusive ) = 401 - 311 - 1 = 89 no intergers divisble by 3 = ~ 89 / 3 ~ 30 divsiblivity rule for 3 is sum of all digits must be divisble by 3 . it does n ' t matter if hundred digit and tens digits are switched . e . g 372 is divisble by 3 ( becae 3 + 7 + 2 = 12 ( divisble by 3 ) ) switch digits 732 also divisble by 3 ( becae 7 + 3 + 2 = 12 ( divisble by 3 ) ) divsiblivity rule for 3 is sum of all digits must be divisble by 3 . it does n ' t matter if hundred digit and tens digits are switched . you have right . so it is enough to proceed like usual to find the numbers in a given range that are divisible by 3 . so 399 - 312 / 3 + 1 = 30 . answer : a | null |
Question: the length of a rectangle is reduced by 22 % . by what % would the width have to be increased to maintain the original area ?
A.14 %.
B.15 %.
C.28 %.
D.30 %.
e ) 35 %C.
"sol . required change = ( 22 * 100 ) / ( 100 - 22 ) = 28.2 % c" | null |
Question: a can do a piece of work in 28 days and b alone can do it in 10 days . b works at it for 5 days and then leaves . a alone can finish the remaining work in
A.5 days.
B.6 days.
C.7.5 days.
D.14 days.
e ) 9 daysD.
"explanation : b ' s 5 days work = 1 / 10 β 5 = 1 / 2 remaining work = 1 β 1 / 2 = 1 / 2 a can finish work = 28 β 1 / 2 = 14 days option d" | null |
Question: if ( x + 3 ) ^ 2 / ( 3 x + 5 ) = 2 , then the difference between the two possible values of x is :
A.2.
B.4.
C.6.
D.8.
e ) 10A.
"( x + 3 ) ^ 2 / ( 3 x + 5 ) = 2 ( x + 3 ) ^ 2 = 2 ( 3 x + 5 ) x ^ 2 + 6 x + 9 = 6 x + 10 x ^ 2 - 1 = 0 ( x - 1 ) ( x + 1 ) = 0 x = 1 or x = - 1 the answer is a ." | null |
Question: a train 110 m long is running with a speed of 90 km / h . in how many seconds will the train pass a man who is running at 9 km / h in the direction opposite to that in which the train is going ?
A.3.
B.4.
C.5.
D.6.
e ) 7B.
the speed of the train relative to the man = 90 + 9 = 99 km / h . 99000 m / h * 1 h / 3600 s = ( 990 / 36 ) m / s ( 110 m ) / ( 990 / 36 m / s ) = ( 110 * 36 ) / 990 = 36 / 9 = 4 seconds the answer is b . | null |
Question: the ratio between the length and the breadth of a rectangular park is 2 : 3 if a man cycling along the boundary of the park at the speed of 10 km / hr completes one round in 18 min , then the area of the park ( in sq . m ) is ?
A.3000 m.
B.9000 m.
C.540000 m.
D.10000 m.
e ) 54000 mC.
"perimeter = distance covered in 8 min . = ( 10000 x 18 ) / 60 m = 3000 m . let length = 2 x metres and breadth = 3 x metres . then , 2 ( 2 x + 3 x ) = 3000 or x = 300 . length = 600 m and breadth = 900 m . area = ( 600 x 900 ) m 2 = 540000 m c" | null |
Question: a car drives 60 miles on local roads at 20 mph , and 195 miles on the highway at 65 mph , what is the average speed of the entire trip ?
A.36 mph.
B.40 mph.
C.44 mph.
D.43 mph.
e ) 58 mphD.
"so the answer is plainly d . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 60 miles , and v = 20 mph so we can obtain time : 20 * t = 60 or t = 60 / 20 = 3 hours the needed time to cover 60 miles in the same way we should divide 195 to 65 to find the needed time to cover 195 miles , so t = 3 hours so the total time for covering total distance would be 3 + 3 = 6 hours and total distance is 60 + 195 = 255 miles final stage : average speed is total distance divide to total time : 255 / 6 = 42.5 miles per hour rounded up to 43 mph . . . ." | null |
Question: a number x is mistakenly divided by 10 instead of being multiplied by 10 . what is the percentage error in the result ?
A.- 99 %.
B.- 100 %.
C.+ 99 %.
D.+ 100 %.
e ) noneA.
solution : actual result = 10 x by mistake it has been divided by 10 = x / 10 % change = [ 10 x - ( 10 / x ) / 10 x ] * 100 = 99 = - 99 % . since , actual value is greater than the wrong value . alternatively , let , x = 10 actual result = 10 * 10 = 100 wrong result = 10 / 10 = 1 . change = ( 1 - 100 ) = - 99 % change = - 99 % . answer : option a | null |
Question: if x > 3000 , then the value of ( 1.2 x ) / ( 0.5 x - 406 ) is closest to ?
A.1 / 6.
B.1 / 3.
C.10 / 21.
D.1 / 2.
e ) 3 / 1E.
assume x = 3002 ( 1.2 x ) / ( 0.5 x - 406 ) = 3602.4 / ( 3002 * 0.5 - 406 ) = 3602.4 / 1095 = = 3 / 1 e | 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.