text
stringlengths 45
2.98k
| __index_level_0__
float64 0
11.7k
⌀ |
|---|---|
Question: a , b and c started a business with a total investment of rs . 72000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find b ' s share .
A.rs . 3240.
B.rs . 2520.
C.rs . 2880.
D.rs . 3360.
e ) none of theseB.
"explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 72000 = > x + ( x - 3000 ) + ( x + 3000 ) = 72000 = > 3 x = 72000 = > x = 24000 hence , a ' s investment = rs . 27000 b ' s investment = rs . 21000 c ' s investment = rs . 24000 ratio of the capitals of a , b and c = 27000 : 21000 : 24000 = 9 : 7 : 8 a ' s share = rs . [ ( 7 / 24 ) ã — 8640 ] = rs . 2520 answer : option b" | null |
Question: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 20 % ?
A.33 %.
B.44 %.
C.55 %.
D.56 %.
e ) 73 %B.
"the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 20 % increase a surface = 6 * ( ( 1.2 a ) ^ 2 ) = 6 * 1.44 * a ^ 2 the increase in the surface area = ( 6 * 1.44 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.44 - 1 ) ) / ( 6 * a ^ 2 ) = 1.44 - 1 = 0.44 = 44 % answer : b" | null |
Question: two pipes a and b can separately fill a tank in 12 and 15 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 15 minutes . what is the capacity of the tank ?
A.399.
B.540.
C.772.
D.272.
e ) 121B.
"1 / 12 + 1 / 15 - 1 / x = 1 / 15 x = 12 12 * 45 = 540 answer : b" | null |
Question: what is the diagonal of a square field whose perimeter is 64 m ?
A.15 m.
B.16 √ 2 m.
C.20 m.
D.25 m.
e ) 18 mB.
"sol : let the side of the square be xm . therefore , 4 x = 64 x = 16 diagonal of the square is = √ 2 * ( 16 ) ^ 2 = 16 √ 2 answer : b" | null |
Question: the difference between simple interest and compound interest on rs . 1400 for one year at 20 % per annum reckoned half - yearly is :
A.$ 185.63.
B.$ 852.36.
C.$ 875.5.
D.$ 989.9.
e ) $ 875.8D.
"s . i = [ ( 1400 * 20 * 1 ) / 100 ] = $ 280 . c . i = [ 1400 * ( 1 + ( 5 / 100 ) ^ 2 ) - 1400 ] = $ 1269.8 . difference = ( 1269.8 - 280 ) = $ 989.8 answer ( d )" | null |
Question: a semicircular shaped window has diameter of 63 cm . its perimeter equals
['A.162', 'B.766', 'C.298', 'D.277', 'e ) 198']A.
explanation : perimeter of window = { \ color { blue } \ pi } r + 2 r = [ { ( 22 / 7 ) * ( 63 / 2 ) } + 63 ] = 99 + 63 = 162 cm answer : a ) 162 | null |
Question: by selling 100 pens , a trader gains the cost of 30 pens . find his gain percentage ?
A.30 %.
B.33 %.
C.31 %.
D.32 %.
e ) 34 %A.
"let the cp of each pen be rs . 1 . cp of 100 pens = rs . 100 profit = cost of 30 pens = rs . 30 profit % = 30 / 100 * 100 = 30 % answer : a" | null |
Question: out of 3 consecutive odd numbers 11 times the first number is equal to addition of thrice the third number and adding 16 to 4 times the second . what is the first number ?
A.5.
B.6.
C.7.
D.8.
e ) 9E.
description : = > 11 x = 4 ( x + 2 ) + 16 + 3 ( x + 4 ) = > 11 x = 7 x + 36 = > 4 x = 36 x = 9 answer e | null |
Question: working together at their respective constant rates , machine a and machine b can produce 1600 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 1600 unit total would it produce ?
A.25.
B.33.
C.50.
D.67.
e ) 75B.
1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 1600 units in 24 hrs , so it can produce 1600 * 8 / 24 = 533.33 units is 8 hrs . 533.33 is 33.33 % of 1600 . b is the answer | null |
Question: according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 26 , by how much does the temperature in degrees celsius ( c ) increase ?
A.9.
B.14.44.
C.47.
D.48 3 / 5.
e ) 59B.
"you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 26 = 58 - - > c = 5 / 9 * 26 = 14.44 . increase = 14.44 degrees . answer : b ." | null |
Question: if price of t . v set is reduced by 20 % , then its sale increases by 80 % , find net effect on sale value
A.44.
B.45.
C.46.
D.47.
e ) 48A.
"- a + b + ( ( - a ) ( b ) / 100 ) = - 20 + 80 + ( - 20 * 80 ) / 100 = - 20 + 80 - 16 = 44 answer : a" | null |
Question: 9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 8 miles per hour faster than the first runner ' s rate . how far apart , to the nearest mile , will they be after 1 / 2 hour ?
A.6.
B.7.
C.8.
D.12.
e ) 9E.
"if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 8 m / h - - > 4 m in 1 / 2 hr side 2 = 16 m / h - - > 8 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 8 ^ 2 d ^ 2 = 80 = ~ 9 answer option e" | null |
Question: the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average of the team ?
A.23.
B.25.
C.30.
D.22.
e ) 40A.
"let the average of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = 11 x - 9 x = 46 = 2 x = 46 = > x = 23 so , average age of the team is 23 years . answer a" | null |
Question: tom and marry each have a bag of marbles , each of which contains 4 red marbles , 10 blue marbles , and 6 yellow marbles . if tom and marry each select one marble from their respective bags , what is the probability that either tom or marry select a blue marble ?
A.1 / 7.
B.2 / 4.
C.3 / 4.
D.1 / 8.
e ) 1 / 16C.
probability that either selects a red marble , p ( either ) = 1 - probability that neither selects a blue marble , p ( neither ) probability that tom selects non blue = 10 c 1 / 20 c 1 = 1 / 2 probability that marry selects non blue = 10 c 1 / 20 c 1 = 1 / 2 = > p ( either ) = 1 - ( 1 / 2 * 1 / 2 ) = 1 - 1 / 4 = 3 / 4 . c ) | null |
Question: if 7 cats can kill 7 rats in 7 minutes , how long will it take 100 cats to kill 100 rats ?
A.5 minutes.
B.6 minutes.
C.7 minutes.
D.8 minutes.
e ) 9 minutesC.
"it will take 7 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 7 minutes , so 100 cats can kill 100 rats in 7 minutes answer c" | null |
Question: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 20.95 . what is the greatest number of hot dogs you can buy at this store with $ 300 ?
A.3,108.
B.3,100.
C.3,108.
D.3,540.
e ) 3,256D.
to maximize number of hot dogs with 300 $ total number of hot dogs bought in 250 - pack = 20.95 * 14 = 293.30 $ amount remaining = 300 - 293.30 = 6.7 $ total number of hot dogs bought in 20 - pack = 3.05 * 2 = 6.10 $ amount remaining = 6.70 - 6.10 = 0.6 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 300 $ = 250 * 14 + 20 * 2 = 3,540 answer d | null |
Question: a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 200 . how much did he have with him in the beginning ?
A.s 200.
B.s 500.
C.s 300.
D.s 450.
e ) s 550B.
suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 200 = 500 answer : b | null |
Question: the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 76 % of the required amount . what is the net difference in the expenditure on that product ?
A.12.5 %.
B.13 %.
C.5 %.
D.17 %.
e ) 19 %C.
quantity x rate = price 1 x 1 = 1 0.76 x 1.25 = 0.95 decrease in price = ( 0.05 / 1 ) × 100 = 5 % c ) | null |
Question: if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability r that n is divisible by 3 ?
A.1 / 3.
B.¼.
C.9 / 25.
D.5 / 16.
e ) 0D.
"prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ." | null |
Question: 0 - - - : - | - - - : - - | - : - - : - | - - : - - - | - : - - - - 1 on the number line above , the segment from 0 to 1 has been divided into fifths , as indicated by the large tick marks , and also into sevenths , as indicated by the small tick marks . what is the least possible distance x between any two of the tick marks ?
A.1 / 70.
B.1 / 35.
C.2 / 35.
D.1 / 12.
e ) 1 / 7B.
divisions are 0 1 / 7 2 / 7 3 / 7 4 / 7 5 / 7 6 / 7 1 1 / 5 2 / 5 3 / 5 4 / 5 5 / 5 expressing the same in terms of the lcm of 57 , i . e 35 0 7 / 35 14 / 35 21 / 35 28 / 35 35 / 35 5 / 35 10 / 35 15 / 35 20 / 35 25 / 35 30 / 35 by comparing the divisions with each other we can see 1 / 35 is the shortest possible distance between any two selected divisions . x = 1 / 35 answer is b . | null |
Question: find the area of a parallelogram with base 21 cm and height 11 cm ?
A.231 cm 2.
B.384 cm 2.
C.672 cm 2.
D.267 cm 2.
e ) 286 cm 2A.
"area of a parallelogram = base * height = 21 * 11 = 231 cm 2 answer : a" | null |
Question: a cycle is bought for rs . 1120 and sold for rs . 1200 , find the gain percent ?
A.7 %.
B.2 %.
C.6 %.
D.1 %.
e ) 8 %A.
"explanation : 1120 - - - - 80 100 - - - - ? = > 7 % answer : a" | null |
Question: a trader bought a car at 20 % discount on its original price . he sold it at a 70 % increase on the price he bought it . what percent of profit did he make on the original price ?
A.17 %.
B.72 %.
C.12 %.
D.82 %.
e ) 36 %E.
"original price = 100 cp = 80 s = 80 * ( 170 / 100 ) = 136 100 - 136 = 36 % answer : e" | null |
Question: a boat having a length 9 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
A.100 kg.
B.120 kg.
C.189 kg.
D.180 kg.
e ) 270 kgE.
"volume of water displaced = ( 9 x 3 x 0.01 ) m 3 = 0.27 m 3 . mass of man = volume of water displaced x density of water = ( 0.27 x 1000 ) kg = 270 kg . answer : e" | null |
Question: what annual payment will discharge a debt of rs . 1030 due in 2 years at the rate of 5 % compound interest ?
A.553.94.
B.551.25.
C.534.33.
D.543.33.
e ) 646.33A.
"explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1030 820 x + 1030 * 441 x = 553.94 so , value of each installment = rs . 553.94 answer : option a" | null |
Question: in a factory , there are 90 % technicians and 10 % non - technicians . if the 90 % of the technicians and 10 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
A.62 %.
B.57 %.
C.52 %.
D.82 %.
e ) 42 %D.
"total = 100 t = 90 nt = 10 90 * ( 10 / 100 ) = 910 * ( 90 / 100 ) = 9 9 + 9 = 18 = > 100 - 18 = 82 % answer : d" | null |
Question: how many seconds will a 450 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 60 km / hr ?
A.25.
B.30.
C.40.
D.45.
e ) 60B.
explanation : speed of train relatively to man = ( 60 - 6 ) km / hr = 54 km / hr = ( 54 x 5 / 18 ) m / sec = 15 m / sec time taken to pass the man = ( 450 / 15 ) sec = 30 sec . answer : b | null |
Question: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 60 percent on clothing , 20 percent on food , and 20 percent on other items . if jill paid a 10 percent tax on the clothing , no tax on the food , and an 10 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
A.10.
B.20.
C.30.
D.25.
e ) 15A.
"assume she has $ 200 to spend . tax clothing = 60 % = $ 120 = $ 12.00 food = 20 % = $ 40 = $ 0.00 items = 20 % = $ 40 = $ 8.00 total tax = $ 20.00 % of total amount = 20 / 200 * 100 = 10 % answer a" | null |
Question: 90 kg of an alloy a is mixed with 140 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 4 and alloy b has tin and copper in the ratio 2 : 5 , then the amount of tin in the new alloy is ?
A.100.6 kg.
B.95.4 kg.
C.117.5 kg.
D.91.4 kg.
e ) 92 kgD.
"quantity of tin in 90 kg of a = 90 * 4 / 7 = 51.4 kg quantity of tin in 140 kg of b = 140 * 2 / 7 = 40 kg quantity of tin in the new alloy = 51.4 + 40 = 91.4 kg answer is d" | null |
Question: a rectangular garden is to be twice as long as it is wide . if 180 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?
A.60.
B.70.
C.80.
D.90.
e ) 100A.
"alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 180 so , 2 ( l + b ) = 180 or , l + b = 90 now use the answer options ( given length ; breath will be half the length ) ( a ) 60 l = 60 ; b = 30 l + b = 90 ( b ) 70 l = 70 ; b = 35 l + b = 105 ( c ) 80 l = 80 ; b = 40 l + b = 120 ( d ) 90 l = 90 ; b = 45 l + b = 135 ( e ) 100 l = 100 ; b = 50 l + b = 150 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( a )" | null |
Question: what is the value of 3 x ^ 2 − 1.8 x + 0.3 for x = 0.6 ?
A.− 0.3.
B.0.
C.0.3.
D.1.08.
e ) 2.46C.
"3 x ^ 2 - 1.8 x + 0.3 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.3 = 0 + 0.3 = 0.3 answer : c" | null |
Question: three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 20 minutes . if a , b & c are kept open successively for 1.5 minute each , how soon will the tank be filled ?
A.2 hours.
B.4 hours.
C.5 hours.
D.2 hours 15 min.
e ) 3 hoursD.
"in three minute 1 / 20 + 1 / 30 - 1 / 20 = 2 / 60 = 1 / 30 part is filled 4.5 min - - - - - - - - 1 / 30 parts x min - - - - - - - - - 1 part ( full ) x = 135 min = 2 hours 15 min answer : d" | null |
Question: a train passes a station platform in 30 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
A.120 m.
B.240 m.
C.168 m.
D.75 m.
e ) 60 mE.
"speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 30 = 15 = > x = 60 m answer : e" | null |
Question: if the sides of a cube are in the ratio 9 : 7 . what is the ratio of their diagonals ?
A.4 : 3.
B.16 : 9.
C.9 : 7.
D.3 : 4.
e ) 3 : 8C.
"explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 9 : 7 d 1 : d 2 = 9 : 7 where √ 3 cancelled both side answer : c" | null |
Question: last year elaine spent 20 % of her annual earnings on rent . this year she earned 20 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?
A.185.5.
B.180.0.
C.167.5.
D.172.5.
e ) 177.5B.
"for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 20 % more , or $ 120 she would ' ve spent 30 % of this on rent , or $ 36 do $ 36 / $ 20 this will give you 180 % b is the correct answer ." | 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 $ 500 more than d , what is c ' s share ?
A.$ 1200.
B.$ 1600.
C.$ 1800.
D.$ 2000.
e ) $ 2400D.
"let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 c ' s share = 4 x = 4 * $ 500 = $ 2000 the answer is d ." | null |
Question: two bullet train s 140 m and 200 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
A.15.8 sec ..
B.12.24 sec ..
C.11.8 sec ..
D.10.8 sec ..
e ) 08.8 sec .B.
relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 200 ) m = 340 m . required time = 340 x 9 / 250 = 54 / 5 = 12.24 sec . answer b | null |
Question: in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.5 times as old as robert ?
A.1960.
B.1965.
C.1970.
D.1975.
e ) 2000E.
"in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 2000 : ri = 60 , ro = 90 thus ans : e" | null |
Question: the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 300,000 bacteria
A.10.
B.12.
C.14.
D.16.
e ) 18D.
"the question basically asks how many minutes it takes for a population to increase by factor 300 ( 300,000 / 1,000 = 300 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 300 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . hence , 2 ^ 8 = 256 , i . e . the population has to double 8 times . since it takes the population 2 minutes to double once it takes 8 * 2 minutes = 16 minutes to double 8 times . thus , solution d = 16 is correct ." | null |
Question: in what ratio must tea at rs . 60 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 67.5 per kg ?
A.3 : 1.
B.3 : 2.
C.4 : 3.
D.1 : 3.
e ) noneD.
"required ratio = 250 : 750 = 1 : 3 answer d" | null |
Question: in what time will a train 50 m long cross an electric pole , it its speed be 360 km / hr ?
A.0.25.
B.0.5.
C.1.5.
D.2.5.
e ) 3.5B.
"speed = 360 * 5 / 18 = 100 m / sec time taken = 50 / 100 = 0.5 sec . answer : b" | null |
Question: each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.74 % , what fraction of the products was checked by worker y ?
A.1 / 2.
B.2 / 3.
C.3 / 5.
D.3 / 4.
e ) 4 / 5E.
"x : 0.5 % is 0.24 % - points from 0.74 % . y : 0.8 % is 0.06 % - points from 0.74 % . therefore the ratio of products checked by y : x is 4 : 1 . thus , worker y checked 4 / 5 of the products . the answer is e ." | null |
Question: a sum of 11,500 amounts to 13,500 in 5 years at the rate of simple interest . what is the rate of interest ?
A.2 %.
B.3 %.
C.6 %.
D.5 %.
e ) 8 %B.
"b 3 % s . i . = ( 13500 - 11500 ) = 2000 . rate = ( 100 x 2000 ) / ( 11500 x 5 ) % = 3 %" | null |
Question: workers at a campaign office have 2000 fliers to send out . if they send out 1 / 4 of them in the morning and 1 / 5 of the remaining ones out during the afternoon , how many are left for the next day ?
A.300.
B.800.
C.1100.
D.1200.
e ) 1180E.
"( 1 / 4 ) * 2000 = 500 remaining = 2000 - 500 = 1500 ( 1 / 5 ) of remaining = ( 1 / 5 ) * 1600 = 320 remaining now = 1500 - 320 = 1180 answer : option e" | null |
Question: abcd is a square where ab = â ˆ š 4032 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
['A.3008', 'B.2002', 'C.1008', 'D.2016', 'e ) 3000']D.
note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4032 / 2 = 2016 . correct answer d | null |
Question: if n = ( 33 ) ^ 40 + ( 43 ) ^ 33 what is the units digit of n ?
A.1.
B.2.
C.4.
D.6.
e ) 8A.
"first of all , the units digit of ( 33 ) ^ 40 is the same as that of 3 ^ 43 and the units digit of ( 40 ) ^ 33 is the same as that of 3 ^ 33 . so , we need to find the units digit of 3 ^ 40 + 3 ^ 33 . next , the units digit of 3 in positive integer power repeats in blocks of four { 3 , 9 , 7 , 1 } : 3 ^ 1 = 3 ( the units digit is 3 ) 3 ^ 2 = 9 ( the units digit is 9 ) 3 ^ 3 = 27 ( the units digit is 7 ) 3 ^ 4 = 81 ( the units digit is 1 ) 3 ^ 5 = 243 ( the units digit is 3 again ! ) . . . thus : the units digit of 3 ^ 40 is the same as the units digit of 3 ^ 3 , so 7 ( 43 divided by the cyclicity of 4 gives the remainder of 3 ) . the units digit of 3 ^ 30 is the same as the units digit of 3 ^ 1 , so 3 ( 33 divided by the cyclicity of 4 gives the remainder of 1 ) . therefore the units digit of ( 33 ) ^ 40 + ( 40 ) ^ 33 is 7 + 4 = 1 . answer : a ." | null |
Question: a circular ground whose diameter is 35 metres , has a 1.4 metre - broad garden around it . what is the area of the garden in square metres ?
A.160.16.
B.6.16.
C.122.66.
D.data inadequate.
e ) none of theseA.
"req . area = π [ ( 17.5 + 1.4 ) 2 – ( 17.5 ) 2 ] = 22 ⁄ 7 × ( 36.4 × 1.4 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = 22 × 36.4 × 0.2 = 160.16 sq m answer a" | null |
Question: a sports equipment store sold ping pong rackets for a total of $ 637 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
A.50.
B.100.
C.65.
D.500.
e ) 980C.
"average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 637 x = 65 pairs were sold . answer : c" | null |
Question: a farmer has enough food to feed her 1000 cows for 50 days . after 10 days some of the cows run away and the food was now enough for the same period of 50 days as before . how many cows ran away ?
A.300.
B.200.
C.500.
D.400.
e ) 250B.
1000 - - - - 50 1000 - - - - 40 x - - - - 50 x * 50 = 1000 * 40 x = 800 1000 - - - - - - - 200 answer = b | null |
Question: a certain number of men can do a work in 60 days . if there were 8 men less it could be finished in 10 days more . how many men are there ?
A.56.
B.42.
C.60.
D.45.
e ) 36A.
"the original number of men = 8 ( 60 + 10 ) / 10 = 56 men answer is a" | null |
Question: if - 3 x + 4 y = 28 and 3 x - 2 y = 8 , what is the product of x and y ?
A.264 ..
B.428.
C.464 ..
D.622.
e ) 642A.
given - 3 x + 4 y = 28 - - - eq 1 3 x - 2 y = 8 - - eq 2 sum both eqns we get 2 y = 36 = > y = 18 sub 2 y in eq 2 = > 3 x - 36 = 8 . = > x = 44 / 3 now xy = 44 / 3 * 18 = 264 . option a is correct answer . | null |
Question: a rectangle having length 89 cm and width 34 cm . if the length of the rectangle is increased by eighty percent then how much percent the breadth should be decreased so as to maintain the same area .
A.25 %.
B.33.33 %.
C.47.33 %.
D.75 %.
e ) none of theseC.
"explanation : solution : ( 80 / ( 89 + 80 ) * 100 ) % = 47.33 % answer : c" | null |
Question: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 25 hours and 81 hours respectively . the ratio of their speeds is :
A.2 : 3.
B.4 : 3.
C.9 : 5.
D.9 : 16.
e ) none of theseC.
"let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 81 : â ˆ š 25 = 9 : 5 . answer c" | null |
Question: a train 100 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
A.45 kmph.
B.55 kmph.
C.32 kmph.
D.61 kmph.
e ) 70 kmphB.
"let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 100 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 1800 x = 55 kmph answer is b" | null |
Question: evaluate : 96385 + 12 * 3 * 25 = ?
A.96385.
B.96358.
C.96785.
D.96485.
e ) 96855D.
"according to order of operations , 12 ? 3 ? 25 ( division and multiplication ) is done first from left to right 12 / 2 = 4 * 25 = 100 hence 96385 + 12 * 3 * 2 = 96385 + 100 = 96485 correct answer d" | null |
Question: how many positive integers less than 100 have a remainder of 3 when divided by 13 ?
A.6.
B.7.
C.8.
D.9.
e ) 3E.
"we have to include 3 also . as 13 * 0 + 3 = 3 if somebody says to divide 3 by 13 , we will be telling we have 0 quotient and remainder as 3 . answer is e" | null |
Question: if y > 0 , ( 9 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
A.40 %.
B.50 %.
C.60 %.
D.70 %.
e ) 75 %E.
"can be reduced to 9 y / 20 + 6 y / 20 = 15 y / 20 = 75 % answer e" | null |
Question: all the students of class are told to sit in circle shape . here the boy at the 5 th position is exactly opposite to 20 th boy . total number of boys in the class ?
A.30.
B.40.
C.45.
D.25.
e ) 20A.
"as half the circle shape consist of 20 - 5 = 15 boys , so total number of boys in full circle = 2 * 15 = 30 answer : a" | null |
Question: a boy swims downstream 56 km and upstream 42 km taking 7 hours each time ; what is the speed of the current ?
A.5.
B.4.
C.3.
D.2.
e ) 1E.
"56 - - - 7 ds = 8 ? - - - - 1 42 - - - - 7 us = 6 ? - - - - 1 s = ? s = ( 8 - 6 ) / 2 = 1 answer : e" | null |
Question: an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters f long ?
A.0.5.
B.1.
C.1.5.
D.2.
e ) 3B.
"let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1" | null |
Question: a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 9 managers , if 3 managers will not attend the meeting together .
A.1.24.
B.2.91.
C.3.12.
D.4.126.
e ) 5.15A.
"9 managers , but 3 of them can not attend the meeting together . we can split it into two cases . 1 . meeting without these 3 managers in it . that would mean selecting 5 , from the remaining 6 which is 6 c 5 = 6 2 . meeting with one of the 3 managers . select 1 manager from 3 , and then select 4 from the remaining 6 , which is 3 c 1 + 6 c 4 = 18 + 6 = 24 . answer : a" | null |
Question: for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 24 ) ?
A.23.
B.19.
C.17.
D.13.
e ) 11E.
f ( 24 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 = 2 ^ 12 * ( 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 ) - - > the greatest prime factor is 11 . answer : e . | null |
Question: an employee ’ s annual salary was increased $ 5,000 . if her new annual salary now equals $ 70,000 , what was the percent increase ?
A.15 %.
B.0.77 %.
C.20 %.
D.22 %.
e ) 24 %B.
"new annual salary = $ 70,000 salary increase = $ 5,000 . original salary = $ 70,000 - $ 5,000 . = $ 65,000 % increase = ( $ 5,000 / $ 65,000 ) * 100 = 0.77 % hence b ." | null |
Question: how many two - digit whole numbers yield a remainder of 1 when divided by 20 and also yield a remainder of 1 when divided by 5 ?
A.none.
B.one.
C.two.
D.three.
e ) fourE.
"the possible number n can be written as follow : n = multiple of lcm ( 20,5 ) + 1 st such number n = 20 x + 1 possible values = 1 , 21 , 41 , 61,81 answer : 4 such 2 digit number . e ." | null |
Question: j is faster than p . j and p each walk 24 km . sum ofthe speeds of j and p is 7 kmph . sum of time taken by them is 14 hours . then j speed is equal to ?
A.4.
B.5.
C.6.
D.7.
e ) 8A.
"let j ' s speed is x then p ' s speed would be 7 - x . and given , sum of time taken by them is 14 hours = > ( 24 / x ) + ( 24 / ( 7 - x ) = 14 = > x = 4,3 therefore j ' s speed will be 4 as j walks faster than p . answer : a" | null |
Question: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 80 percent of books that were loaned out are returned and there are 66 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
A.20.
B.30.
C.35.
D.45.
e ) 55D.
"there are 9 books less ( 75 - 66 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 45 answer d" | null |
Question: 50 men took a dip in a water tank 30 m long and 20 m broad on a religious day . if the average displacement of water by a man is 4 m 3 , then the rise in the water level in the tank will be :
A.20 cm.
B.25 cm.
C.33.3 cm.
D.50 cm.
e ) none of theseC.
"explanation : total volume of water displaced = ( 4 x 50 ) m 3 = 200 m 3 rise in water level = 200 / 30 ã — 20 = 0.333 m = 33.3 cm answer : c" | null |
Question: find the simple interest on rs . 70,000 at 16 2 / 3 % per year for 9 months .
A.7500.
B.6500.
C.8750.
D.9500.
e ) none of themC.
"p = rs . 70000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 70,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8750 answer is c ." | null |
Question: a is twice as good a workman as b and they took 6 days together to do the work b alone can do it in .
A.18 days.
B.12 days.
C.29 days.
D.25 days.
e ) 27 daysA.
"wc = 2 : 1 2 x + x = 1 / 6 x = 1 / 18 = > 18 days answer : a" | null |
Question: donovan and michael are racing around a circular 400 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 36 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?
A.8.
B.7.
C.6.
D.5.
e ) 9D.
"one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 400 / 45 = > 80 / 9 2 . speed / rate of michael = distance / time = > 400 / 36 = > 100 / 9 relative speed between them = 100 / 9 - 80 / 9 = > 20 / 9 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 400 , relative rate = 20 / 9 total time taken by micheal to surpass donovan = distance / rate = > 400 * 9 / 20 = > 3600 / 10 = > 180 no . of laps taken by michael = total time / michael ' s rate = > 180 / 36 = > 5 hence correct answer is 5 laps . d" | null |
Question: if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 9 people to do 9 times of that particular work ?
A.1.
B.2.
C.3.
D.9.
e ) 12C.
"3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 9 people can do 9 / 3 of the work in one day . 9 people can do 9 times the work in 3 days . the answer is c ." | null |
Question: a and b can do a work in 5 days and 10 days respectively . a starts the work and b joins him after 2 days . in how many days can they complete the remaining work ?
A.6.
B.2.
C.8.
D.9.
e ) 3B.
"work done by a in 2 days = 2 / 5 remaining work = 3 / 5 work done by both a and b in one day = 1 / 5 + 1 / 10 = 3 / 10 remaining work = 3 / 5 * 10 / 3 = 2 days . answer : b" | null |
Question: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.5 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :
A.2 : 5.
B.2 : 3.
C.2 : 4.
D.2 : 1.
e ) 4 : 7E.
"let the ratio be k : 1 . then , k * 16.5 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.5 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.7 = 4 / 7 required ratio = 4 / 7 : 1 = 4 : 7 . answer : e" | null |
Question: before 6 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ?
A.36.
B.42.
C.54.
D.60.
e ) 64E.
"a - 6 = 4 ( b - 6 ) - - > a - 4 b = - 18 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 26 - - > a = 3 ( 30 ) = 90 a - b = 90 - 26 = 64 answer : e" | null |
Question: 4 wolves , wolverine , man - hunter , blue - wolf , and jasmine , caught rabbits for their evening meal . if man - hunter caught 3 more rabbits than blue - wolf did , jasmine caught 3 less than wolverine did , and wolverine caught 1 more than man - hunter did , how many more fewer rabbits did blue - wolf catch than jasmine ?
A.- 3.
B.- 2.
C.- 5.
D.- 12.
e ) - 1E.
in this word problem , the first key is to turn the story into equations : man - hunter caught 3 more than blue - wolf did : m = 3 + b jasmine caught 3 less than wolverine did : j = w - 3 wolverine caught 3 more than man - hunter did : w = 1 + m then , in classic gmat style , the problem does n ' t ask you to solve for a single variable , but instead to solve for the difference between b and j ( how many more rabbits did blue - wolf catch than jasmine did ? ) . this means that your goal is to get the equations in terms of b and j so that you can solve for the expression b - j . taking the first equation and solving for b , you have b = m - 3 . taking the second equation and solving for j you have j = w - 3 , and then with the third equation you can replace w with 1 + m so that both b and j are in terms of m : j = ( 1 + m ) - 3 . so if b = m - 3 and j = m - 2 , then : b - j = ( m - 3 ) - ( m - 2 ) b - j = m - 3 - m + 2 ( remove the parentheses by distributing the multiplication ) b - j = - 1 , so the answer is e . | null |
Question: a bullet train 160 m long is running with a speed of 70 kmph . in what time will it pass a man who is running at 8 kmph in the direction opposite to that in which the bullet train is going ?
A.23 sec.
B.15 sec.
C.7.38 sec.
D.6.92 sec.
e ) 16 secC.
"c 7.38 sec speed of the bullet train relative to man = ( 70 + 8 ) kmph = 78 * 5 / 18 m / sec = 65 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 160 m at ( 65 / 3 ) m / sec = ( 160 * 3 / 65 ) sec = 7.38 sec" | null |
Question: what is the remainder when 103 * 505 * 607 is divided by 9
A.6.
B.18.
C.2.
D.4.
e ) 7E.
"103 / 9 = = > remainder = 4 505 / 9 = = > remainder = 1 607 / 9 = = > remainder = 4 = 4 * 4 * 1 = 16 / 9 = = > remainder = 7 answer : e" | null |
Question: a man can do a job in 5 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?
A.6.3.
B.6.9.
C.3.5.
D.6.1.
e ) 6.2C.
"1 day work of the three persons = ( 1 / 5 + 1 / 20 + 1 / 25 ) = 29 / 100 so , all three together will complete the work in 100 / 29 = 3.5 days . answer : c" | null |
Question: what is the value of 3 x ^ 2 − 1.8 x + 0.3 for x = 0.9 ?
A.− 0.3.
B.0.
C.0.3.
D.1.11.
e ) 2.46D.
"3 x ^ 2 - 1.8 x + 0.3 for x = 0.5 = 3 ( 0.9 * 0.9 ) - 2 * 0.9 * ( 0.9 ) + 0.3 = 0.9 * 0.9 + 0.3 = 0.81 + 0.3 = 1.11 correct option : d" | null |
Question: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 26 white marbles . how many red marbles could be in bag a ?
A.1.
B.3.
C.4.
D.2.
e ) 8D.
"# of red marbles in bag a can be either 2 or 6 . no 2 in the choices , so 6 . d . bag a : r : w : b = 2 : 6 : 9 bag b r : w = 1 : 4 6 x + 4 y = 26 i . e 3 x + 2 y = 13 x has to be odd to make an odd sum from the eq . x = 1 , y = 5 or x = 3 , y = 2 so r can be 2 x i . e 2 or 6 . answer d" | null |
Question: a restaurant spends one quarter of its monthly budget for rent and two thrid of the rest for food and beverages . what percentage of the budget does the restaurant spend for food and beverages ?
A.23.5 %.
B.50 %.
C.35 %.
D.37.5 %.
e ) 75 %B.
"spend on rent = 1 / 4 spend on food and beverage = 2 / 4 of remaining = 2 / 3 * 3 / 4 = 1 / 2 so 1 / 2 = 50.0 % b is the answer" | null |
Question: in a kilometer race , a beats b by 52 meters or 18 seconds . what time does a take to complete the race ?
A.277 sec.
B.190 sec.
C.328 sec.
D.367 sec.
e ) 376 secC.
"time taken by b run 1000 meters = ( 1000 * 18 ) / 52 = 346 sec . time taken by a = 346 - 18 = 328 sec . answer : c" | null |
Question: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular octagon ?
A.1 / 4.
B.1 / 3.
C.1 / 2.
D.2 / 5.
e ) 7 / 8D.
"from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 5 . the answer is d ." | null |
Question: a towel , when bleached , lost 30 % of its length and 25 % of its breadth . what is the percentage decrease in area ?
A.24 %.
B.30 %.
C.44 %.
D.54 %.
e ) 47.5 %E.
"percentage change in area = ( − 30 − 25 + ( 30 × 25 ) / 100 ) % = − 47.5 % i . e . , area is decreased by 47.5 % answer : e" | null |
Question: two women can do a work in 4 days . six men can complete the same work in 3 days . what is the ratio between the capacity of a man and a woman ?
A.1 : 2.
B.2 : 1.
C.4 : 9.
D.3 : 2.
e ) none of theseC.
"explanation : ( 2 ã — 4 ) women can complete the work in 1 day . â ˆ ´ 1 woman ' s 1 day ' s work = 1 / 8 ( 6 ã — 3 ) men can complete the work in 1 day . â ˆ ´ 1 man ' s 1 day ' s work = 1 / 18 so , required ratio = 1 / 8 : 1 / 18 = 4 : 9 answer : c" | null |
Question: 10 x 0.5 = ?
A.0.0001.
B.0.001.
C.0.01.
D.0.1.
e ) 5E.
"explanation : 10 x 5 = 50 . sum of decimal places = 1 10 x 0.5 = 5 answer - e" | null |
Question: what is the remainder when 54617 ^ ( 42788234 ) is divided by 5 ?
A.0.
B.1.
C.2.
D.3.
e ) 4E.
"we need to find the units digit of the number . the units digit of powers of seven repeats 7 , 9 , 3 , and 1 cyclically . since 42788234 has the form 4 a + 2 , the units digit is 9 . then the remainder when dividing by 5 is 4 . the answer is e ." | null |
Question: a cube of side two meter length is cut into small cubes of side 10 cm each . how many such small cubes can be obtained ?
A.2878.
B.2778.
C.1000.
D.8000.
e ) 8900D.
"along one edge , the number of small cubes that can be cut = 200 / 10 = 20 along each edge 10 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 20 * 20 * 20 = 8000 answer : d" | null |
Question: how many numbers between 200 and 600 are divisible by 4 , 5 and 6 ?
A.5.
B.6.
C.8.
D.10.
e ) 12B.
"sol . every such numbers must be divisible by l . c . m . of 4 , 5 , 6 , i . e . 60 . such numbers are 240 , 300 , 360 , 420 , 480 , 540 . clearly , there are 6 such numbers . answer b" | null |
Question: a train 270 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
A.30 sec.
B.32 sec.
C.36 sec.
D.38 sec.
e ) 40 secC.
"relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 270 × 2 / 15 ) sec = 36 sec answer : c" | null |
Question: speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph . a man rows to a place at a distance of 4864 km and comes back to the starting point . the total time taken by him is :
A.700.
B.200.
C.540.
D.120.
e ) 635A.
"explanation : speed downstream = ( 14 + 1.2 ) = 15.2 kmph speed upstream = ( 14 - 1.2 ) = 12.8 kmph total time taken = 4864 / 15.2 + 4864 / 12.8 = 320 + 380 = 700 hours . answer : a" | null |
Question: you enter a weight loss challenge game and manage to lose 13 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
A.13 %.
B.9.22 %.
C.11.26 %.
D.14 %.
e ) 12 %C.
( 100 % - 13 % ) * ( 100 % + 2 % ) = 0.87 * 1.02 = 11.26 % the weigh in records your weight loss at 11.26 % ! the answer is c | null |
Question: i bought two books ; for rs . 500 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
A.337.
B.280.
C.299.67.
D.266.67.
e ) 291.67E.
"x * ( 85 / 100 ) = ( 500 - x ) 119 / 100 x = 291.67 answer : e" | null |
Question: 252 ã · ? ã — 15 + 270 = 405
A.24.
B.25.
C.28.
D.39.
e ) 43C.
"explanation : 252 ã · ? ã — 15 = 405 - 270 = 135 ( 252 ã — 15 ) / ? = 135 ? = ( 252 ã — 15 ) / 135 = 28 answer : option c" | null |
Question: a and b put in rs . 300 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 196 where as b does not . in what ratio should they divide the second year ' s profit ?
A.39 : 40.
B.39 : 49.
C.24 : 25.
D.39 : 47.
e ) 39 : 41C.
"explanation : 3 : 4 a = 3 / 7 * 196 = 84 384 : 400 24 : 25 answer : c" | null |
Question: in a group of ducks and cows , the total number of legs are 40 more than twice the number of heads . find the total number of cows .
A.12.
B.14.
C.16.
D.18.
e ) 20E.
"let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 40 more than twice the number of heads = > 2 ( d + 2 c ) = 40 + 2 ( c + d ) = > d + 2 c = 20 + c + d = > 2 c = 20 + c = > c = 20 i . e . , total number of cows = 20 answer is e ." | null |
Question: a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 102 . what was the number he chose ?
A.90.
B.100.
C.120.
D.160.
e ) 200C.
"solution : let x be the number he chose , then 2 * x * 138 = 102 2 x = 240 x = 120 correct answer c" | null |
Question: the product of two successive numbers is 4160 . which is the smaller of the two numbers ?
A.78.
B.64.
C.88.
D.67.
e ) 37B.
"b 4160 from the given alternatives , 64 × 65 = 4160 ∴ smaller number = 64" | null |
Question: soymilk are sold in packages of two or 3 only . if hannah bought 17 soymilk exactly , what could be the number of large packs hannah bought ?
A.1.
B.4.
C.3.
D.5.
e ) 8C.
let number of packs of three = t let number of packs of two = w 3 t + 2 w = 17 now , we need to test for values of w . since sum 17 is odd and 2 w will always be even , therefore w ca n ' t be even . now , we can test for values w = 1 , 3 and 5 2 * 4 + 3 * 3 = 8 + 9 = 17 answer c | null |
Question: what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 21.50 ?
A.10 : 7.
B.9 : 8.
C.7 : 11.
D.13 : 11.
e ) 14 : 8C.
"correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 3.50 : 5.50 = 7 : 11" | 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.