regisss/math_qa huggingface dataset:
Problem: if a 2 - b 2 = 11 and a * b = 5 , find a 4 + b 4 .
Options: a ) 62 , b ) 181 , c ) 170 , d ) 171 , e ) 50
Rationale: "a 2 - b 2 = 11 : given a 4 + b 4 - 2 a 2 b 2 = 112 : square both sides and expand . a * b = 2 : given a 2 b 2 = 52 : square both sides . a 4 + b 4 - 2 ( 25 ) = 121 : substitute a 4 + b 4 = 171 correct answer d"
Answer: d
Problem: on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent of that before july 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: "let the number of employees before jul 1 be 100 then av sal 1 = total 1 / 100 after jul 1 employees = 90 av sal 2 = total 2 / 90 now from the question av 2 = av 1 + 10 % total 2 / 90 = total 1 / 100 + 1 / 10 * total 1 / 100 total 2 / 90 = 11 total 1 / 1000 total 2 = 99 total 1 / 100 now percent = total 2 / total 1 * 100 = 99 total 1 / total 1 = 99 answer : b"
Answer: b
Problem: if q and d are both integers , q > d , and - 3 q > 19 , then the largest value of d would be ?
Options: a ) - 5 , b ) - 6 , c ) - 7 , d ) - 8 , e ) - 10
Rationale: no , your thinking is incorrect . when we know that q > d and q < - 6.33 , the largest value of q can be - 7 while if q = - 7 , then largest value of d < - 7 will be - 8 . for negative numbers , - 7 > - 8 and - 8 > - 10 . you are right in saying that d can take any value less than - 7 - - - > d could be - 8 , - 9 , - 10 . . . . and out of all these values , - 8 is the greatest . look at the numbers on the number line . for any 2 numbers , the ones on the right are greater than the ones on the left : . . . . . . . - 11 - 10 - 9 - 8 - 7 - 6 - 5 . . . . . 0 1 2 3 4 5 6 . . . ( - 11 < - 10 , - 10 < - 8 , 4 < 5 etc ) . so , as per the question if d < q and q = - 7 , then d ' s largest ' possible ' value has to be - 8 . - 10 is smaller than - 8 = d
Answer: d
Problem: a small company reduced its faculty by approximately 15 percent to 195 employees . what was the original number of employees ?
Options: a ) a ) 182 , b ) b ) 208 , c ) c ) 220 , d ) d ) 229 , e ) e ) 302
Rationale: "if x is the original number of employees , then after 15 % reduction in employees number is . 85 x but we are given . 85 x = 195 x = 229 so the original number of employees is 229 correct answer - d"
Answer: d
Problem: a man is 30 years older than his son . in three years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 20 , b ) 21 , c ) 27 , d ) 23 , e ) 24
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 30 ) years . ( x + 30 ) + 3 = 2 ( x + 3 ) x + 33 = 2 x + 6 x = 27 . answer : c"
Answer: c
Problem: henry earns $ 120 a week from his job . his income increased and now makes $ 180 a week . what is the percent increase ?
Options: a ) 70 % , b ) 60 % , c ) 50 % , d ) 40 % , e ) 30 %
Rationale: increase = ( 60 / 120 ) * 100 = ( 1 / 2 ) * 100 = 50 % . c
Answer: c
Problem: a train 120 m long crosses a platform 120 m long in 6 sec ; find the speed of the train ?
Options: a ) 144 kmph , b ) 58 kmph , c ) 54 kmph , d ) 94 kmph , e ) 59 kmph
Rationale: "d = 120 + 120 = 240 t = 6 s = 240 / 6 * 18 / 5 = 144 kmph answer : a"
Answer: a
Problem: an investor can sell her microtron stock for 36 $ per share and her dynaco stock for 48 $ per share , if she sells 300 shares altogether , some of each stock , at an average price per share of 40 $ , how many shares of dynaco stock has she sold ?
Options: a ) 52 , b ) 75 , c ) 92 , d ) 100 , e ) 184
Rationale: "w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) = ( 48 - 40 ) / ( 40 - 36 ) = 8 / 4 = 2 / 1 = number of microtron stocks / number of dynaco stocks so for every 2 microtron stock , she sold 1 dynaco stock . so out of 300 total stocks , ( 1 / 3 ) th i . e . 300 / 3 = 100 must be dynaco stock . answer ( d )"
Answer: d
Problem: working at constant rate , pump x pumped out half of the water in a flooded basement in 3 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ?
Options: a ) a . 20 , b ) b . 12 , c ) c . 14 , d ) d . 18 , e ) e . 24
Rationale: "rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 20 hours a"
Answer: a
Problem: two spherical balls lie on the ground touching . if one of the balls has a radius of 10 cm , and the point of contact is 12 cm above the ground , what is the radius of the other ball ?
Options: a ) 2 cm , b ) 5 / 2 cm , c ) 5 cm , d ) 15 / 2 cm , e ) none of the these
Rationale: "similar triangle properties . . 2 / r + 10 = 10 / r - 10 giving r = 15 / 2 . answer : d"
Answer: d
Problem: ( 753 x 753 + 247 x 247 - 753 x 247 ) / ( 753 x 753 x 753 + 247 x 247 x 247 ) = ?
Options: a ) 1 / 1000 , b ) 1 / 506 , c ) 253 / 500 , d ) 253 / 1000 , e ) none of these
Rationale: given exp . = ( a ^ 2 + b ^ 2 - ab ) / ( a ^ 3 + b ^ 3 ) = 1 / ( a + b ) = 1 / ( 753 + 247 ) = 1 / 1000 answer : a
Answer: a
Problem: the area of a square field is 7201 sq m . how long will a lady take to cross the field diagonally at the rate of 1.2 km / hr ?
Options: a ) 6 min , b ) 5 min , c ) 5.5 min , d ) 4 min , e ) 3 min
Rationale: "area of a square field = 7201 sq m let the side of square = a a ^ 2 = 7201 = > a = 84.86 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 84.86 = 120 speed of lady = 1.2 km / hour = 1200 m / hour = 20 m / min time taken by lady to cross the field diagonally = 120 / 20 = 6 min answer a"
Answer: a
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in :
Options: a ) 144 min , b ) 145 min , c ) 150 min , d ) 200 min , e ) 250 min
Rationale: "slower pipe alone fill the tank = x faster pipe will fill in x / 3 min 1 / x + 3 / x = 1 / 36 x = 144 min answer a"
Answer: a
Problem: the tax on a commodity is diminished by 22 % but its consumption is increased by 9 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 %
Rationale: "100 * 100 = 10000 78 * 109 = 8502 10000 - - - - - - - 1200 100 - - - - - - - ? = 15 % answer : c"
Answer: c
Problem: each of the three people individually can complete a certain job in 4 , 6 , and 8 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?
Options: a ) 3 / 8 , b ) 5 / 12 , c ) 7 / 24 , d ) 11 / 36 , e ) 13 / 48
Rationale: "the two slowest people work at rates of 1 / 6 and 1 / 8 of the job per hour . the sum of these rates is 1 / 6 + 1 / 8 = 7 / 24 of the job per hour . the answer is c ."
Answer: c
Problem: a man can row at 4 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 2.4 km , b ) 2.9 km , c ) 3.4 km , d ) 1.9 km , e ) 5.6 km
Rationale: "explanation : speed in still water = 4 kmph speed of the current = 1 kmph speed downstream = ( 4 + 1 ) = 5 kmph speed upstream = ( 4 - 1 ) = 3 kmph let the required distance be x km total time taken = 1 hour â ‡ ’ x / 5 + x / 3 = 1 â ‡ ’ 3 x + 5 x = 15 â ‡ ’ 8 x = 15 â ‡ ’ x = 1.9 km answer : option d"
Answer: d
Problem: two numbers are respectively 20 % and 25 % more than a third number . the percentage that is first of the second is ?
Options: a ) 80 % , b ) 85 % , c ) 96 % , d ) 125 % , e ) 150 %
Rationale: "explanation : i ii iii 120 125 100 125 - - - - - - - - - - 120 100 - - - - - - - - - - - ? = > 96 % answer is c"
Answer: c
Problem: if 5 % more is gained by selling an article for rs . 360 than by selling it for rs . 340 , the cost of the article is
Options: a ) 289 , b ) 400 , c ) 200 , d ) 288 , e ) 111
Rationale: "explanation : let c . p . be rs . x . then , 5 % of x = 360 - 340 = 20 x / 20 = 20 = > x = 400 answer : b"
Answer: b
Problem: weights of two friends ram and shyam are in the ratio 6 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
Options: a ) 19 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none
Rationale: "solution : given ratio of ram and shayam ' s weight = 6 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 6 / 5 or , x = 21 % . answer : option c"
Answer: c
Problem: how many of the positive factors of 36 , 84 and how many common factors are there in numbers ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 6
Rationale: "factors of 36 - 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36 factors of 84 - 1 , 2 , 3 , 4 , 6 , 7 , 12 , 14 , 21 , 28 , 42 , 84 comparing both , we have six common factors of 36 and 84 - 1,2 , 3,4 , 6,12 , answer ( e )"
Answer: e
Problem: jaclyn buys $ 20 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 475 , b ) 234 , c ) 289 , d ) 345 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 = 30000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 475 answer : a"
Answer: a
Problem: if 5 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ?
Options: a ) 280 , b ) 63 , c ) 120 , d ) 160 , e ) 1260
Rationale: parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 5 c 2 for vertical 8 c 2 total parallelogram is 5 c 2 * 8 c 2 = 10 * 28 = 280 answer : a
Answer: a
Problem: in a group of buffaloes and ducks , the number of legs are 24 more than twice the number of heads . what is the number of buffaloes in the group ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: let no . of buffaloes be x & no . of ducks be y buffaloes have 4 legs while ducks have 2 4 x + 2 y = 2 * ( x + y ) + 24 = > 4 x + 2 y - 2 x - 2 y = 24 = > x = 12 number of buffaloes in the group = 12 answer : a
Answer: a
Problem: a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 24 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s )
Options: a ) 6810 , b ) 7920 , c ) 9030 , d ) 10,140 , e ) 11,250
Rationale: the distance the sound traveled to the man is 24 * 330 = 7920 meters the answer is b .
Answer: b
Problem: what is the thousandths digit in the decimal equivalent of 57 / 5000 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 5 , e ) 6
Rationale: 57 / 5000 = 57 / ( 5 * 10 ^ 3 ) = ( 57 / 5 ) * 10 ^ - 3 = 11.4 * 10 ^ - 3 = . 0114 thousandths digit = 1 answer b
Answer: b
Problem: 6 / 8 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is
Options: a ) 28 % , b ) 54 % , c ) 45 % , d ) 72 % , e ) 78 %
Rationale: "total population = 80 ( assume ) . 6 / 8 * 80 = 60 people from montague . 2 / 8 * 80 = 20 people from capulet . 0.2 * 60 = 12 people from montague support juliet . 0.7 * 20 = 14 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 14 / ( 12 + 14 ) = ~ 54 answer : b ."
Answer: b
Problem: 45 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 15 , c ) 13 , d ) 18 , e ) 19
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 45 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 45 x 5 x 12 x = ( 45 x 5 x 12 ) / ( 30 x 6 ) x = 15 answer b"
Answer: b
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?
Options: a ) 75 , b ) 65 , c ) 85 , d ) 95 , e ) 80
Rationale: "total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 65 = > 20 = x - 65 = > x = 20 + 65 = 85 answer is c ."
Answer: c
Problem: it takes 60 identical printing machines 4 hours to print 200,000 cards . how long would it take 50 of these machines to print the same total ?
Options: a ) 10 hr , b ) 5 hr , c ) 6 hr , d ) 4 hr 30 min , e ) 5 hr 12 min
Rationale: "50 % of 60 = 40 % or 0.30 4 hr x 60 min = 240 min 240 min x 0.30 = 72 min or 1 hr and 12 min 1 hr and 12 min + 4 hr = 5 hr and 12 min answer is e"
Answer: e
Problem: in a party , there are rows arranged with 1220 and 30 chairs and there were 3 left in all the cases . when there were 11 rows . there were no chair left . if 30 chairs were added . then what will be the reminder ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: lcm of 12 , 2030 is 120 . so the number is in the form of 120 x + 3 which is divisible by 11 , by placing x = 3 , we get 363 which is divisible by 11 and the multiple of 120 when 3 is subtracted from 363 . so the no . is 363 . so when 30 is added to it and is divided by 11 we get remainder as 8 answer : a
Answer: a
Problem: for every integer n ≥ 3 , the function g ( n ) is defined as the product of all the odd integers from 1 to n , inclusive . what is the value of g ( 106 ) – g ( 103 ) ?
Options: a ) 100 , b ) 99 , c ) 98 , d ) 102 , e ) 104
Rationale: "g ( 106 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 * 105 g ( 103 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 g ( 106 ) - g ( 103 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 * 105 - 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 = 1 * 3 * 5 * 7 * 9 * . . . * 103 * ( 105 - 1 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 * 101 * 103 * 104 hence : e"
Answer: e
Problem: if x is 11 percent greater than 90 , then x =
Options: a ) 99.9 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2
Rationale: "11 % of 90 = ( 90 * 0.11 ) = 9.9 11 % greater than 90 = 90 + 9.9 = 99.9 answer is clearly a ."
Answer: a
Problem: the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 240 m , its area is ?
Options: a ) 150 , b ) 882 , c ) 277 , d ) 261 , e ) 120
Rationale: "5 x + 12 x + 13 x = 240 = > x = 8 a = 40 , b = 96 , c = 104 s = ( 40 + 96 + 104 ) / 2 = 120 answer : e"
Answer: e
Problem: total 22 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 24 , b ) 26 , c ) 21 , d ) 20 , e ) 19
Rationale: "21 players answer : c"
Answer: c
Problem: in an intercollegiate competition that lasted for 3 days , 150 students took part on day 1 , 110 on day 2 and 140 on day 3 . if 75 took part on day 1 and day 2 and 25 took part on day 2 and day 3 and 15 took part on all three days , how many students took part only on day 2 ?
Options: a ) 50 , b ) 35 , c ) 45 , d ) 25 , e ) 60
Rationale: "day 1 & 2 = 75 ; only day 1 & 2 ( 75 - 15 ) = 60 , day 2 & 3 = 25 ; only day 2 & 3 ( 25 - 15 ) = 10 , only day 2 = 110 - ( 60 + 10 + 15 ) = 25 answer : d"
Answer: d
Problem: what is the remainder when you divide 2 ^ 200 + 2 by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 5
Rationale: answer is d . this is very similar to the 32 ^ 32 ^ 32 + 2 divided by 7 question .
Answer: d
Problem: jim drove 923 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 113 miles , b ) 277 miles , c ) 456 miles , d ) 887 miles , e ) 767 miles
Rationale: the number of miles to drive to finish his journey is given by 1200 - 923 = 277 miles correct answer b
Answer: b
Problem: on increasing the price of t . v . sets by 70 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 4 , b ) 5 , c ) 36 , d ) 2 , e ) 7
Rationale: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 170 × 80 ) = rs . 13600 increase % = 3600 / 10000 × 100 = 36 % answer : c"
Answer: c
Problem: how many cubes of 10 cm edge can be put in a cubic box of 1 m edge ?
Options: a ) 4000 , b ) 2000 , c ) 3000 , d ) 5000 , e ) 1000
Rationale: "( 110 × 100 × 100 ) / 10 × 10 × 10 = 1000 answer is e ."
Answer: e
Problem: what is the remainder when you divide 2 ^ 200 + 1 by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: answer is e . this is very similar to the 32 ^ 32 ^ 32 + 1 divided by 7 question .
Answer: e
Problem: a train running at the speed of 60 km / hr crosses a pole in 36 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 600 meter , c ) 167 meter , d ) 719 meter , e ) 169 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 36 = 600 meter answer : b"
Answer: b
Problem: the area of a parallelogram is 128 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 8
b ) 7
c ) 6
d ) 5
e ) 2
Rationale: 2 x * x = 128 = > x = 8 answer : a
Answer: a
Problem: the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together ?
Options: a ) 40 , b ) 99 , c ) 88 , d ) 77 , e ) 66
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 20 ) / 2 = 40 . answer : a"
Answer: a
Problem: a , b , and c were started a business , the total profit for one year is $ 56700 . the profit sharing ratio is 8 : 9 : 10 ( according to their investment they divide their profit ) . what is the profit of c ?
Options: a ) $ 5670 , b ) $ 18900 , c ) $ 21000 , d ) $ 13500 , e ) $ 27000
Rationale: a : b : c = 8 + 9 + 10 = 27 ; c ' share = 10 / 27 of the total profit . c will get = 10 / 27 * $ 56700 = $ 21000 . answer : c
Answer: c
Problem: if the product of the integers from 1 to n is divisible by 1029 , what is the least possible value of n ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: 1029 = 7 x 7 x 7 x 3 n must include at least 7 , 2 * 7 , and 3 * 7 . the answer is c .
Answer: c
Problem: average families of 4 pay $ 3000 for their health insurance deductibles annually . there will be a 2 / 3 increase in the deductibles for next year . how much more will the average family pay in deductibles next year ?
Options: a ) $ 1000 , b ) $ 2000 , c ) $ 3000 , d ) $ 4000 , e ) $ 5000
Rationale: a certain percentage of questions in the quant section of the gmat are just ' math questions ' - you ' ll use a formula , do some calculations and you ' ll have the answer . this is one of those types of questions . you still have to write everything down and stay organized , but the work involved is relatively straight - forward . here , we ' re told that the current annual deductible is $ 3000 and that the deductible is to be increased by 2 / 3 . we ' re asked how much more will the deductible cost a family next year . original deductible = $ 3000 increase in deductible = 2 / 3 the answer is calculated by the equation : $ 3000 × 2 / 3 = $ 2000 . b
Answer: b
Problem: a certain university will select 1 of 3 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 135 , e ) 315
Rationale: "1 of 3 will be chosen for the math 2 of 10 will be chosen for the computer none of the 3 chosen people can be in more than one departments . we can choose any of the 3 candidates for the math dep . , which gives as 3 selections . we can choose 2 of the 10 candidates for the computer dep . , which gives us 2 selections and 8 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 2 ! * 8 ! = ( 9 * 10 ) / 2 = 90 / 2 = 45 . we are multiplying our individual selections : 3 * 45 = 135 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans d"
Answer: d
Problem: at the end of the month , a certain ocean desalination plant ’ s reservoir contained 6 million gallons of water . this amount is twice the normal level . if this amount represents 60 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?
Options: a ) 15 , b ) 10 , c ) 5 , d ) 20 , e ) 25
Rationale: "the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 6 mg = 60 % of total . . total = 6 / . 6 = 10 mg . . normal level = 1 / 2 of 10 = 5 mg . . shortage of normal level = 10 - 5 = 5 mg . . c"
Answer: c
Problem: two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 60 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 6 : 5 , b ) 9 : 25 , c ) 5 : 6 , d ) 25 : 9 , e ) can not be determined from the information provided
Rationale: "same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 30 / speed b since the times are same , 50 pi / speed a = 60 pi / speed b speeda / speed b = 50 pi / 60 pi = 5 / 6 correct option : c"
Answer: c
Problem: a sum of money lent out at s . i . amounts to a total of $ 600 after 2 years and to $ 850 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 500 , b ) $ 520 , c ) $ 540 , d ) $ 560 , e ) $ 580
Rationale: s . i for 5 years = $ 850 - $ 600 = $ 250 the s . i . is $ 50 / year s . i . for 2 years = $ 100 principal = $ 600 - $ 100 = $ 500 the answer is a .
Answer: a
Problem: a train passes a station platform in 46 sec and a man standing on the platform in 16 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 227 , b ) 240 , c ) 460 , d ) 450 , e ) 455
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 16 = 240 m . let the length of the platform be x m . then , ( x + 240 ) / 46 = 15 = > x = 450 m . answer : d"
Answer: d
Problem: if the area of a square with sides of length 5 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 7 , e ) 18
Rationale: "let length of rectangle = l 5 ^ 2 = l * 4 = > l = 25 / 4 = 7 answer d"
Answer: d
Problem: a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . metre
Options: a ) rs 680 , b ) rs 780 , c ) rs 880 , d ) rs 480 , e ) rs 980
Rationale: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 80 = 68000 p in rs = 68000 / 100 = rs 680 answer : a"
Answer: a
Problem: a certain board game is played by rolling a pair of fair 6 - sided dice and then moving one ' s piece forward the number of spaces indicated by the sum showing on the dice . a player is frozen if her opponent ' s piece comes to rest in the space already occupied by her piece . if player a is about to roll and is currently 8 spaces behind player b , what is the probability that player b will be frozen after player a rolls ?
Options: a ) 1 / 12 , b ) 5 / 36 , c ) 1 / 6 , d ) 1 / 3 , e ) 17 / 36
Rationale: no . of possible outcomes = 6 * 6 = 36 no . of outcomes that result a total of 8 ( as a is 8 spaces behind b ) = 5 ( ( 2,6 ) , ( 3,5 ) , ( 4,4 ) , ( 5,3 ) , ( 6,2 ) ) so , the probability = 5 / 36 ( option b )
Answer: b
Problem: we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 548 . how many green hats did we buy ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 44
Rationale: "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 548 . 6 ( 85 - g ) + 7 g = 548 . 510 - 6 g + 7 g = 548 . g = 548 - 510 = 38 . the answer is b ."
Answer: b
Problem: in a 100 m race , sam beats john by 5 seconds . on the contrary , if sam allowed john to start 35 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?
Options: a ) 13 seconds , b ) 25 seconds , c ) 29 seconds , d ) 21 seconds , e ) 6.25 seconds
Rationale: "their difference is 5 second but this difference is 0 if john allows sam to start the race from 35 m ahead . that means jhon was 35 m away from finishing line when they started together . so he will cover 35 m in 5 seconds . so his speed = 35 / 5 = 7 metre / second . so time taken = 100 / 5 = 20 seconds . so sam took = 13 seconds . correct answer = a"
Answer: a
Problem: when a train travels at a speed of 110 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 12.5 km , b ) 50 km , c ) 60 km , d ) 8.5 km , e ) 9.5 km
Rationale: "let x be the time reached with the speed 110 km / h 50 km / h - - - - > x + 15 distance is equal so 110 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 110 x = 50 x + 750 so the would be in km and x = 12.5 answer : a"
Answer: a
Problem: three runners running around a circular track can complete one revolution in 2 , 4 and 5.5 respectively . when will they meet at starting point ?
Options: a ) 40 h
b ) 44 h
c ) 38 h
d ) 20 h
e ) 22 h
Rationale: time at which they meet at starting point = lcm of 2 , 4 and 5.5 = 44 h answer : b
Answer: b
Problem: 3 bottles contain equal mixtures of spirit and water in the ratio 6 : 1 , 5 : 2 and 3 : 1 respectively . if all the solutions are mixed together , the ratio of spirit to water in the final mixture will be
Options: a ) 64 : 65 , b ) 65 : 64 , c ) 19 : 65 , d ) 65 : 19 , e ) none of these
Rationale: given that all bottles contain equal amount of mixture say v . so in the first vessel - > water : spirit = 1 / 7 : 6 / 7 in the second bottle - > 2 / 7 : 5 / 7 in the third bottle - > l / 4 : 3 / 4 . hence , the final ratio is = ( ( 6 / 7 ) + ( 5 / 7 ) + ( 3 / 4 ) ) / ( ( 1 / 7 ) + ( 2 / 7 ) + ( 1 / 4 ) ) = 65 / 19 answer : d
Answer: d
Problem: 12 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 3 , c ) 4 , d ) 7 , e ) 5
Rationale: required number of machines = 12 * 10 / 40 = 3 answer is b
Answer: b
Problem: the age of somu is one - third his father ' s . 10 years back he was one - fifth of his father ' s age . what is his persent age ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 20
Rationale: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 10 = 3 x - 10 / 5 = x = 20 answer : option e"
Answer: e
Problem: from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 8 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "soln : - 8 x = 45 - - > 27 / 25 * x = 45 - - > x = 45 * 25 / 27 = 125 / 3 = ~ 42 . answer : e ."
Answer: e
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 92.16 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 96
Rationale: "explanation : money collected = ( 92.16 x 100 ) paise = 9216 paise . ∴ number of members = √ ( 9216 ) = 96 . answer : e"
Answer: e
Problem: if a person walks at 10 km / hr instead of 5 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 76 km , c ) 20 km , d ) 16 km , e ) 97 km
Rationale: "let the actual distance traveled be x km . then , x / 5 = ( x + 20 ) / 10 5 x - 100 = > x = 20 km . answer : c"
Answer: c
Problem: in a public show 75 % of the seats were filled . if there were 700 seats in the hall , how many seats were vacant ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 175 , e ) 150
Rationale: "75 % of 600 = 75 / 100 × 700 = 450 therefore , the number of vacant seats = 700 - 450 = 175 . answer : d"
Answer: d
Problem: find the value of m 82519 x 9999 = m ?
Options: a ) 724533811 , b ) 353654655 , c ) 825107481 , d ) 725117481 , e ) 477899932
Rationale: "82519 x 9999 = 82519 x ( 10000 - 1 ) = 82519 x 10000 - 82519 x 1 = 825190000 - 82519 = 825107481 c"
Answer: c
Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 3 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 4 attempts ?
Options: a ) 4 / 9 , b ) 5 / 9 , c ) 17 / 27 , d ) 23 / 27 , e ) 65 / 81
Rationale: "p ( missing all 3 ) = ( 2 / 3 ) ^ 4 = 16 / 81 p ( success on at least one attempt ) = 1 - 16 / 81 = 65 / 81 the answer is e ."
Answer: e
Problem: if one root of the equation 2 x ^ 2 + 3 x – k = 0 is 4 , what is the value of k ?
Options: a ) 35 , b ) 40 , c ) 44 , d ) 45 , e ) 56
Rationale: "we just enter this root into the equation in order to recieve an equation to find the answer ! 2 * 4 ^ 2 + 3 * 4 - k = 0 k = 32 + 12 = 44 the answer is c"
Answer: c
Problem: 4 different airplanes owned by a rock band will be refueling today at the same airport . there are 2 larger planes carrying people and 2 smaller planes carrying equipment . all tanks are empty and will need to be filled completely . the 2 smaller tanks hold 60 liters each and the larger tanks are 50 % bigger . fuel is . 50 cents a liter and there is a charge of $ 100 service for each plane . how much will it cost to fill all 4 planes ?
Options: a ) $ 475 , b ) $ 500 , c ) $ 525 , d ) $ 550 , e ) $ 575
Rationale: lots of calculations . 100 * 4 + 2 * 60 * . 50 + 60 * ( 3 / 2 ) * 2 * . 50 answer = $ 550 the correct option is d
Answer: d
Problem: how many litres of pure acid are there in 12 litres of a 40 % solution
Options: a ) 3.6 , b ) 4.8 , c ) 3.5 , d ) 2.3 , e ) 4.4
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 12 * 40 / 100 = 4.8 answer : option b
Answer: b
Problem: a train 100 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 60 kmph , e ) 70 kmph
Rationale: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 100 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 1800 < = > x = 55 speed of the train is 55 kmph . answer : option c"
Answer: c
Problem: if the length of the diagonal of a square is 20 cm , then its perimeter must be
Options: a ) 40
b ) 38
c ) 27
d ) 29
e ) 11
Rationale: explanation : d = √ 2 l answer : a ) 40
Answer: a
Problem: line m lies in the xy - plane . the y - intercept of line m is - 4 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 8 ) . what is the slope of line m ?
Options: a ) - 2 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: "ans : a solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 8 ) . midpoint is ( 4 , - 2 ) as we can see that the y axis of intercept point is ( 0 , - 4 ) means line m is parallel to x axis slope m = - 2 ans : a"
Answer: a
Problem: two pipes a and b can fill a tank in 6 hours and 4 hours respectively . if they are opened on alternate hours and if pipe a is opened first , in how many hours , the tank shall be full ?
Options: a ) 2 hrs , b ) 4 hrs , c ) 5 hrs , d ) 6 hrs , e ) 7 hrs
Rationale: "a ' s work in 1 hour = 1 / 6 b ' s work in 1 hour = 1 / 4 a + b 2 hour ' s work when opened alternately = 1 / 6 + 1 / 4 = 5 / 12 a + b 4 hour ' s work when opened alternately = 10 / 12 = 5 / 6 remaining part = 1 - 5 / 6 = 1 / 6 it is a ' s turn and 1 / 6 part is filled by a in 1 hour . total time taken to fill the tank = 4 + 1 = 5 hrs answer is c"
Answer: c
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train catches and completely passes the slower train in 45 seconds . what is the length of each train ( in meters ) ?
Options: a ) 48.5 , b ) 62.5 , c ) 73.5 , d ) 87.5 , e ) 96.5
Rationale: the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 45 seconds , the relative difference in distance traveled is 45 * 25 / 9 = 125 meters this distance is twice the length of each train . the length of each train is 125 / 2 = 62.5 meters the answer is b .
Answer: b
Problem: a certain lab experiments with white and brown mice only . in one experiment , 4 / 9 of the mice are brown . if there are 20 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 32 , b ) 26 , c ) 36 , d ) 28 , e ) 24
Rationale: "let total number of mice = m number of brown mice = 4 / 9 m number of white mice = 5 / 9 m = 20 = > m = 36 answer c"
Answer: c
Problem: if a + b + c = 21 , what is the total number of non - negative integral solutions ?
Options: a ) 223 , b ) 233 , c ) 240 , d ) 243 , e ) 253
Rationale: think of it is a problem of diving 21 items to three people a , b & c which may or may not receive an item . so simply use combination here as ( n - r + 1 ) c ( r - 1 ) i . e . ( 21 + 3 - 1 ) c ( 3 - 1 ) = > 23 c 2 = = > 253 solutions . answer : e
Answer: e
Problem: a driver goes on a trip of 60 kilometers , the first 30 kilometers at 48 kilometers per hour and the remaining distance at 24 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 30 , b ) 32 , c ) 36 , d ) 40 , e ) 42
Rationale: "the time for the first part of the trip was 30 / 48 = 5 / 8 hours . the time for the second part of the trip was 30 / 24 = 5 / 4 hours . the total time fro the trip was 5 / 8 + 5 / 4 = 15 / 8 hours . the average speed for the trip was 60 / ( 15 / 8 ) = 32 kph the answer is b ."
Answer: b
Problem: a train travelled from point a to point b at 160 km / h . on its way back the train travelled at 120 km / h and therefore the trip back lasted one hour longer . what is the distance ( in km ) between a and b ?
Options: a ) 480 . , b ) 500 . , c ) 510 . , d ) 600 . , e ) 800 .
Rationale: distance = speed * time d 1 = s 1 t 1 d 2 = s 2 t 2 the distance from point a to point b is the same for each trip so , d 1 = d 2 and t 2 = t 1 + 1 thus , s 1 t 1 = s 2 ( t 1 + 1 ) 160 t 1 = 120 ( t 1 + 1 ) t 1 = 3 160 * 3 = 480 answer : a
Answer: a
Problem: the length of the bridge , which a train 120 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 328 , b ) 279 , c ) 255 , d ) 288 , e ) 211
Rationale: speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 120 + x ) / 30 = 25 / 2 = = > 2 ( 120 + x ) = 750 = = > x = 255 m . answer : c
Answer: c
Problem: if a is an integer greater than 8 but less than 15 and b is an integer greater than 6 but less than 21 , what is the range of a / b ?
Options: a ) 140 / 217 , b ) 156 / 185 , c ) 217 / 140 , d ) 263 / 149 , e ) 241 / 163
Rationale: the way to approach this problem is 8 < a < 15 and 6 < b < 21 minimum possible value of a is 9 and maximum is 14 minimum possible value of b is 7 and maximum is 20 range = max a / min b - min a / max b ( highest - lowest ) 14 / 7 - 9 / 20 = 217 / 140 hence c
Answer: c
Problem: the average ( arithmetic mean ) of the integers from 25 to 225 , inclusive , is how much lower than the average of the integers from 50 to 1050 inclusive ?
Options: a ) 450 , b ) 375 , c ) 500 , d ) 425 , e ) 400
Rationale: "for an ap the mean or average of series is average of first and last term . so , average of numbers between 50 to 1050 , inclusive = ( 50 + 1050 ) / 2 = 550 average of numbers between 25 to 225 , inclusive = ( 25 + 225 ) / 2 = 125 difference = 550 - 125 = 425 answer is d"
Answer: d
Problem: 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 5 such machines to perform the same job ?
Options: a ) 2.25 hours , b ) 8.75 hours , c ) 12 hours , d ) 14.25 hours , e ) 9.6 hours
Rationale: "let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 5 machines 5 units of work ( 5 machines ) - - - > 1 hour for 48 units of work 5 * 9.6 - - - > 1 * 9.6 hours e 9.6 hours"
Answer: e
Problem: the length and breadth of a rectangle is increased by 10 % and 25 % respectively . what is the increase in the area ?. a . 27.5 %
Options: a ) 37.2 %
b ) 37.5 %
c ) 30.2 %
d ) 37.7 %
e ) 33.2 %
Rationale: explanation : 100 * 100 = 10000 110 * 125 = 13750 - - - - - - - - - - - 3750 10000 - - - - - - 3750 100 - - - - - - - ? = > 37.5 % answer : option b
Answer: b
Problem: the sum of 3 numbers is 98 . if the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8 , then the second number is :
Options: a ) 20 , b ) 30 , c ) 38 , d ) 48 , e ) none of these
Rationale: a : b = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15 and b : c = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24 therefore , a : b : c = 10 : 15 : 24 ∴ a : b : c = 10 : 15 : 24 let the number be 10 x , 15 x and 24 x . then , 10 x + 15 x + 24 x = 98 or 49 x = 98 or x = 2 ⇒ second number = 15 x = 15 × 2 = 30 answer b
Answer: b
Problem: if 20 men can build a water fountain 56 metres long in 42 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 3 m , b ) 4 m , c ) 7 m , d ) 9 m , e ) 10 m
Rationale: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 42 : 3 : : 56 : x therefore ( 20 x 42 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 840 = 7 hence , the required length is 7 m . answer : c"
Answer: c
Problem: find large number from below question the difference of two numbers is 1500 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1234 , b ) 1345 , c ) 1456 , d ) 1797 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1500 ) . x + 1500 = 6 x + 15 5 x = 1485 x = 297 large number = 297 + 1500 = 1797 d"
Answer: d
Problem: from below option 27 is divisible by which one ?
Options: a ) a ) 4 , b ) b ) 8 , c ) c ) 9 , d ) d ) 10 , e ) e ) 911
Rationale: "27 / 9 = 3 c"
Answer: c
Problem: the amounts of time that three secretaries worked on a special project are in the ratio of 2 to 3 to 5 . if they worked a combined total of 80 hours , how many hours did the secretary who worked the longest spend on the project ?
Options: a ) 80 , b ) 70 , c ) 56 , d ) 16 , e ) 40
Rationale: "10 x = 80 = > x = 8 therefore the secretary who worked the longest spent 8 x 5 = 40 hours on the project option ( e )"
Answer: e
Problem: the ratio of number of boys and girls in a class is 3 : 2 . in the 1 st semester exam 20 % of boys and 25 % of girls get more than or equal to 90 % marks . what percentage of students get less than 90 % marks ?
Options: a ) 56 , b ) 70 , c ) 78 , d ) 80 , e ) 85
Rationale: let boys = 3 x and girls = 2 x . number of those who get less than 90 % mark = ( 80 % of 3 x ) + ( 75 % of 2 x ) = ( 80 / 100 ) * 3 x + ( 75 / 100 * 2 x ) = 39 x / 10 required percentage = ( 39 x / 10 * 1 / 5 x * 100 ) % = 78 % . answer : c
Answer: c
Problem: if x = 4 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.015 , c ) 0.25 , d ) 4 , e ) 8
Rationale: "quickly we can spot that answer is neither integer nor negative . eliminate a , de by inversing and squaring 0.015 answer : b"
Answer: b
Problem: an urn contains 5 red , 6 blue and 8 green balls . 4 balls are randomly selected from the urn , find the probability that the drawn ball are 1 blue and 2 red and 1 green balls ?
Options: a ) 20 / 323 , b ) 40 / 323 , c ) 60 / 273 , d ) 50 / 373 , e ) 40 / 373
Rationale: "sample space = no . of ways 4 balls were drawn from urn = 19 c 4 = 3876 no . ways 1 blue and 2 red and 1 green balls were drawn from bag = 6 c 1 * 5 c 2 * 8 c 1 = 480 probability = 480 / 3876 = 40 / 323 ans - b"
Answer: b
Problem: a car takes 6 hours to cover a distance of 504 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 60 kmph
Rationale: time = 6 distence = 504 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 504 / 9 = 56 kmph d
Answer: d
Problem: one - seventh of the light switches produced by a certain factory are defective . 4 - fifths of the defective switches are rejected and 1 / 15 of the non defective switches are rejected by mistake . if all the switches not rejected are sold , what percent of the switches sold by the factory are defective ?
Options: a ) 2.3 % , b ) 3.4 % , c ) 4.5 % , d ) 5.6 % , e ) 6.7 %
Rationale: 1 / 7 of the switches are defective . the defective switches that are not rejected are 1 / 5 * 1 / 7 = 1 / 35 = 3 / 105 of all switches . the non defective switches that are sold are 6 / 7 * 14 / 15 = 84 / 105 of all switches . the percent of switches sold that are defective is 3 / 87 which is about 3.4 % . the answer is b .
Answer: b
Problem: the average of 10 numbers is calculated as 23 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) a ) 16 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24
Rationale: "explanation : 10 * 23 + 36 – 26 = 240 = > 240 / 10 = 24 e )"
Answer: e
Problem: a survey was sent to 80 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 14 % , d ) 28 % , e ) 63 %
Rationale: "case 1 : ( 7 / 80 ) = x / 100 x = 9 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 9 ) % = 5 % answer is b"
Answer: b
Problem: average age of students of an adult school is 42 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 120 , c ) 360 , d ) 200 , e ) none of these
Rationale: "explanation : let the original no . of students be x . according to situation , 42 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 80 so , required no . of students after joining the new students = x + 120 = 200 . answer : d"
Answer: d
Problem: you have been given a physical balance and 7 weights of 45 , 50 , 53 , 46 , 52 , 46 and 80 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 188 kgs .
Options: a ) 183 , b ) 185 , c ) 182 , d ) 184 , e ) 181
Rationale: "80 + 52 + 53 = 185 answer : b"
Answer: b
Problem: a person has to make 146 pieces of long bar . he take $ seconds to cut piece . what is total time taken by him to make 146 pieces ?
Options: a ) 580 seconds , b ) 680 seconds , c ) 500 seconds , d ) 540 seconds , e ) 560 seconds
Rationale: if it is 4 seconds , as u have mistaken with shift key , then . . . . we ' ll have to make 145 cuts for 146 pieces . so 145 * 5 = 580 seconds answer : a
Answer: a
Problem: a tank can supply water to a village for 60 days . if a leak at the bottom of the tank drains out 10 liters per day , the supply lasts for 45 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
Options: a ) 15 , b ) 18 , c ) 20 , d ) 24 , e ) 36
Rationale: losing 10 liters per day results in a loss of 450 liters in 45 days . so , those 450 liters were for 15 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 60 = 1800 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 1800 / 50 = 36 days . the answer is e .
Answer: e
Problem: how many plants will be there in a circular bed whose outer edge measure 32 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 24 , d ) 20 , e ) none of these
Rationale: "circumference of circular bed = 32 cm area of circular bed = ( 32 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 32 ) 2 â  „ 4 ï € ã · 4 = 20.36 = 20 ( approx ) answer d"
Answer: d
Problem: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 55 kg , c ) 80 kg , d ) 85 kg , e ) 25 kg
Rationale: "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 60 + 20 ) kg = 80 kg . answer : c"
Answer: c
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 65000 , then the share of b is ?
Options: a ) a ) 30000 , b ) b ) 34000 , c ) c ) 34098 , d ) d ) 33007 , e ) e ) 44098
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 65000 share of b = 6 / 13 ( 65000 ) = rs . 30000 answer : a"
Answer: a
Problem: if the radius of a circle is decreased 10 % , what happens to the area ?
Options: a ) 10 % decrease , b ) 19 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 50 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 0.9 * old radius so new area = ( 0.9 ) ^ 2 old area = > 0.81 of old area = > 81 % old area ans : b"
Answer: b
Problem: average age of students of an adult school is 44 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 180 , c ) 360 , d ) 240 , e ) none of these
Rationale: "explanation : let the original no . of students be x . according to situation , 44 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 60 so , required no . of students after joining the new students = x + 120 = 180 answer : b"
Answer: b
Problem: a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 2 . find his average after 17 th inning .
Options: a ) 36 , b ) 39 , c ) 42 , d ) 45 , e ) none of the above
Rationale: "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 2 ) . ∴ 16 ( x – 2 ) + 87 = 17 x or x = ( 87 – 32 ) = 55 . answer e"
Answer: e