Cheukting/mathqa huggingface dataset:
Question (general): if ( a - b - c + d = 13 ) and ( a + b - c - d = 3 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 8 . , c ) 12 . , d ) 25 . , e ) 64 .
Rationale: "eq 1 : a - b - c + d = 13 eq 2 : a + b - c - d = 3 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 13 - a + b - c - d = 3 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 10 ( 2 ) simplify - b + d = 5 b - d = - 5 ( b - d ) ^ 2 = ( - 5 ) ^ 2 = 25 my answer : d"
Answer: d
Question (gain): dhoni spent 20 percent of his earning last month on rent and 5 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ?
Options: a ) 61 % , b ) 62 % , c ) 65 % , d ) 64 % , e ) 50 %
Rationale: say dhoni ' s earning last month was $ 100 . dhoni spent 20 percent of his earning last month on rent - - > $ 20 on rent ; 5 percent less than what he spent on rent to purchase a new dishwasher - - > $ 20 * 0.95 = $ 19 on the dishwasher . left over amount 100 - ( 20 + 19 ) = $ 61 answer : a
Answer: a
Question (general): if a ' s height is 20 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 86.66 % , e ) 25 %
Rationale: "excess of b ' s height over a ' s = [ ( 20 / ( 100 - 20 ) ] x 100 % = 25 % answer : e )"
Answer: e
Question (general): a set of football matches is to be organized in a ` ` round - robin ' ' fashion , i . e . , every participating team plays a match against every other team once and only once . if 15 matches are totally played , how many teams participated ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: 2 ways to solve this problem . . summation ( x ) = n ( n - 1 ) / 2 n ( n - 1 ) / 2 = 15 ; n ^ 2 - n - 30 = 0 ans : 6 answer : c
Answer: c
Question (general): the average weight of 8 sailors in a boat is increased by 1 kg if one of them weighing 56 kg is replaced by a new sailor . the weight of the new sailor is ?
Options: a ) 57 kg , b ) 60 kg , c ) 64 kg , d ) 62 kg , e ) 66 kg
Rationale: the sailor weighing 56 kg is replaced and the average is increased by 1 kg . hence , the weight of the new sailor is ( 56 + increase in total weight ) = 56 + 1 x 8 = 56 + 8 = 64 kg . answer : c
Answer: c
Question (general): there are some sweets in party , 1 / 3 rd eaten by kids . then 2 / 5 th of the remaining by men , then 2 / 3 rd of the remaining by women . at last 2 were remaining . how many sweets were in total ?
Options: a ) 45 , b ) 27 , c ) 15 , d ) 26 , e ) 91
Rationale: sol : if x sweets were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 2 x × 2 / 3 × 3 / 5 × 1 / 3 = 2 x = 15 answer : c
Answer: c
Question (gain): the cost of 100 articles is equal to selling price of 90 . find the gain or loss percent ?
Options: a ) 11 % , b ) 20 % , c ) 27 % , d ) 32 % , e ) 49 %
Rationale: "c . p . of each article be $ 1 c . p . of 90 articles = 100 gain % = 10 / 90 * 100 = 11 % approximately answer is a"
Answer: a
Question (other): a bag contains 5 green balls and 9 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?
Options: a ) 11 / 21 , b ) 17 / 42 , c ) 23 / 42 , d ) 46 / 91 , e ) 51 / 91
Rationale: "the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 5 c 2 = 10 the number of ways to draw two white balls is 9 c 2 = 36 p ( two balls of the same colour ) = 46 / 91 the answer is d ."
Answer: d
Question (general): a no . when divided by 223 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 15
Rationale: "223 + 43 = 266 / 17 = 11 ( remainder ) d"
Answer: d
Question (gain): find the 25 % of rs . 400 .
Options: a ) s . 50 , b ) s . 70 , c ) s . 100 , d ) s . 80 , e ) s . 60
Rationale: "explanation : 25 % of 400 = > 25 / 100 * 400 = rs . 100 answer : c"
Answer: c
Question (gain): a shop owner sells 40 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 33.33 % , b ) 40 % , c ) 50 % , d ) 66.67 % , e ) 70 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 40 m cloth ) – ( c . p . of 40 m cloth ) selling price of 30 m cloth = selling price of 40 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 30 m cloth = rs . 3000 and s . p . of 30 m cloth = rs . rs . 4000 profit % = 10 / 30 × 100 = 33.33 % profit of 33.33 % was made by the merchant . a"
Answer: a
Question (gain): ajay spends 50 % of his monthly income on household items , 25 % of his monthly income on buying cloths , 15 % of his monthly income on medicines and saves the remaining amount which is rs . 9000 . find his monthly income .
Options: a ) rs . 90000 , b ) rs . 36000 , c ) rs . 50000 , d ) rs . 45000 , e ) none of these
Rationale: savings 10 % - 9000 expenditure 90 % - 81000 total - 90000 answer : a
Answer: a
Question (geometry): the measurement of a rectangular box with lid is 50 cmx 30 cmx 38 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 288 , b ) 4500 , c ) 7200 , d ) 864 , e ) 9640
Rationale: "d = 30 , r = 15 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 15 * 15 * 15 = 4500 π cm 3 answer : b"
Answer: b
Question (gain): if an article is sold at 12 % profit instead of 16 % profit , then the profit would be rs . 105 less . what is the cost price ?
Options: a ) rs . 3000 , b ) rs . 4000 , c ) rs . 3500 , d ) rs . 4500 , e ) rs . 6000
Rationale: "explanation : let the cost price of an article be rs . x . ( 16 % of x ) - ( 12 % of x ) = 105 16 x / 100 - 12 x / 100 = 105 = > 4 x = 160 * 100 = > x = 1500 cost price = rs . 4000 answer : b"
Answer: b
Question (general): gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 16 times as heavy as water ?
Options: a ) 1 : 2 , b ) 7 : 3 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5
Rationale: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 16 w 19 + 9 x = 16 ( x + 1 ) x = 3 / 7 ratio of gold with copper = 1 : 3 / 7 = 7 : 3 answer is b"
Answer: b
Question (probability): a question paper has 2 parts , a & b , each containing 7 questions . if a student has to choose 5 from part a & 4 from part b , in how many ways can he choose the questions ?
Options: a ) 1100 , b ) 1200 , c ) 1235 , d ) 1354 , e ) 735
Rationale: "there 7 questions in part a out of which 5 question can be chosen as = 7 c 5 . similarly , 4 questions can be chosen from 7 questions of part b as = 7 c 4 . hence , total number of ways , = 7 c 5 * 7 c 4 = [ 7 ! / ( 2 ! 5 ! ) ] * [ 7 ! / ( 3 ! * 4 ! ) ] = { 21 } * { 7 * 6 * 5 * 4 / ( 4 * 3 * 2 * 1 ) } = 735 . e"
Answer: e
Question (general): a man has some hens and cows . if the number of heads be 60 and the number of feet equals 200 , then the number of hens will be :
Options: a ) 22 , b ) 25 , c ) 24 , d ) 20 , e ) 28
Rationale: "explanation : let the number of hens be x and the number of cows be y . then , x + y = 60 . . . . ( i ) and 2 x + 4 y = 200 x + 2 y = 100 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 40 . the required answer = 20 . answer : d"
Answer: d
Question (gain): what is the difference between 62 % of 150 nd 20 % of 250 .
Options: a ) 16 , b ) 17 , c ) 43 , d ) 19 , e ) 20
Rationale: ( 62 / 100 ) * 150 â € “ ( 20 / 100 ) * 250 93 - 50 = 43 answer : c
Answer: c
Question (general): of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 25 percent on food , and 25 percent on other items . if jill paid a 10 percent tax on the clothing , no tax on the food , and an 20 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 ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "assume she has $ 200 to spend . tax clothing = 50 % = $ 100 = $ 10.00 food = 25 % = $ 50 = $ 0.00 items = 25 % = $ 50 = $ 10.00 total tax = $ 20.00 % of total amount = 20 / 200 * 100 = 10 % answer b"
Answer: b
Question (general): 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
Question (general): 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
Question (other): 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
Question (gain): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (general): ( 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
Question (geometry): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (gain): 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
Question (gain): 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
Question (gain): 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
Question (other): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (probability): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (general): 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