Cheukting/mathqa huggingface dataset:
Question (geometry): if abc is a quarter circle and a smaller circle is inscribed in it ; if radius of quarter circle is 1.414 units . find the radius of smaller circle
Options: a ) 0.586
b ) 0.687
c ) 0.784
d ) 0.874
e ) 0.974
Rationale: if r be radius of smaller circle then distance b / n centres = √ 2 * r so , r + r √ 2 = r here , r = 1.414 = √ 2 = > r = ( √ 2 - 1 ) r r = 0 . 586 unit answer : a
Answer: a
Question (general): a bag of potatoes weighs 16 kg divided by a quarter of its weight . how much does the bag weigh ?
Options: a ) 4 kg , b ) 8 kg , c ) 7 kg , d ) 3 kg , e ) 9 kg
Rationale: b 8 kg 8 kg : 16 / 2
Answer: b
Question (gain): the cost price of a radio is rs . 1590 and it was sold for rs . 1450 , find the loss % ?
Options: a ) 8 % , b ) 12 % , c ) 10 % , d ) 14 % , e ) 21
Rationale: "1590 - - - - 140 100 - - - - ? = > 8 % answer : a"
Answer: a
Question (gain): a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "my solution : wholesale price = 90 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 90 + 1 / 5 ( 90 ) x = 120 ; answer : c"
Answer: c
Question (general): what is the least number should be added to 1056 , so the sum of the number is completely divisible by 27 ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "( 1056 / 27 ) gives remainder 3 24 + 3 = 27 , so we need to add 24 d"
Answer: d
Question (other): if 30 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 620 , b ) 630 , c ) 616 , d ) 600 , e ) 650
Rationale: "we know 37.5 % people study biology , therefore the no of people not studying = 100 - 30 = 70 % > therefore the people not studying biology out of a total 880 people are = 70 % of 880 > ( 70 / 100 ) * 880 = 616 people c"
Answer: c
Question (general): the average of 9 observations was 9 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?
Options: a ) 6 , b ) 9 , c ) 8 , d ) 2 , e ) 3
Rationale: "1 to 9 = 9 * 9 = 81 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 81 = 9 answer : b"
Answer: b
Question (gain): in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 30 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 33 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: "total men in company 30 % means total women in company 70 % ( assume total people in company 100 % ) no of men employees attended picnic = 30 x ( 20 / 100 ) = 6 no of women employees attended picnic = 70 x ( 40 / 100 ) = 28 total percentage of employees attended the picnic = 6 + 28 = 34 % answer : b"
Answer: b
Question (gain): 30 is what percent of 100 ?
Options: a ) 35 % , b ) 30 % , c ) 45 % , d ) 50 % , e ) 55 %
Rationale: 30 / 100 × 100 = 30 % answer : b
Answer: b
Question (gain): how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 31 % iodine solution ?
Options: a ) 35 , b ) 42 , c ) 100 , d ) 105 , e ) 140
Rationale: "solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 31 / 100 40 x + 700 = 31 x + 1085 9 x = 385 x = 42 lts correct option : b"
Answer: b
Question (general): if k ^ 3 is divisible by 180 , what is the least possible value of integer k ?
Options: a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: "180 = 2 ^ 2 * 3 ^ 2 * 5 therefore k must include at least 2 * 3 * 5 = 30 . the answer is b ."
Answer: b
Question (physics): a clock shows the time as 8 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 25 minutes , e ) 50 minutes
Rationale: "there are 10 hours in between 8 a . m . to 6 p . m . 10 * 5 = 50 minutes . answer : e"
Answer: e
Question (gain): a watch was sold at a loss of 12 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s . 1000 , b ) s . 875 , c ) s . 1007 , d ) s . 1006 , e ) s . 1002
Rationale: "explanation : 88 % 104 % - - - - - - - - 16 % - - - - 140 100 % - - - - ? = > rs . 875 answer : b"
Answer: b
Question (gain): a vendor bought toffees at 6 for a rupee . how many for a rupee must he sell to gain 20 % ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 9 , e ) 1
Rationale: "explanation : c . p . of 6 toffees = re . 1 s . p . of 6 toffees = 120 % of re . 1 = rs . 6 / 5 for rs . 6 / 5 , toffees sold = 6 . for re . 1 . toffees sold = 6 * 5 / 6 = 5 answer : c"
Answer: c
Question (other): ratio between rahul and deepak is 4 : 3 , after 10 years rahul age will be 26 years . what is deepak present age
Options: a ) 12 , b ) 15 , c ) 20 , d ) 22 , e ) 23
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 10 = 26 = > x = 4 so deepak age is = 3 ( 4 ) = 12 answer : option a"
Answer: a
Question (gain): a man can row downstream at the rate of 10 km / hr and upstream at 4 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 7,3 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 10 + 4 ) = 7 km / hr rate of current = 1 / 2 ( 10 - 4 ) = 3 km / hr answer : option b"
Answer: b
Question (physics): worker a takes 8 hours to do a job . worker b takes 12 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 40 days , b ) 24 / 5 days , c ) 39 / 9 days , d ) 30 / 9 days , e ) 60 / 9 days
Rationale: "a ' s one hour work = 1 / 8 . b ' s one hour work = 1 / 12 . ( a + b ) ' s one hour work = 1 / 8 + 1 / 12 = 5 / 24 . both a & b can finish the work in 24 / 5 days b"
Answer: b
Question (general): denominator of a number is 4 less than the numerator . if 6 is added to the numerator , it becomes 3 times the denominator . find the denominator .
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: let the numerator be x and denominator be y . then = > x = y + 4 and 6 + x = 3 * y = > 6 + y + 4 = 3 * y = > 2 y = 10 = > y = 5 option c
Answer: c
Question (general): if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 3 - m ) then m = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "( - 2 ) ^ ( 2 m ) = 4 ^ m and 2 ^ ( 3 - m ) = 4 ^ ( ( 3 - m ) / 2 ) therefore , m = ( 3 - m ) / 2 2 m = 3 - m m = 1 answer a"
Answer: a
Question (geometry): a rectangular paper when folded into two congruent parts had a perimeter of 34 cm foer each part folded along one set of sides and the same is 38 cm . when folded along the other set of sides . what is the area of the paper ?
Options: a ) 140
b ) 388
c ) 238
d ) 119
e ) 112
Rationale: when folded along the breadth we have 2 ( l / 2 + b ) = 34 or l + 2 b = 34 . . . . . . . . . . . ( 1 ) when folded along the length , we have 2 ( l + b / 2 ) = 38 or 2 l + b = 38 . . . . . ( 2 ) from 1 & 2 we get l = 14 and b = 10 area of the paper = 14 * 10 = 140 sq cmv answer : a
Answer: a
Question (gain): given a certain number ( x ) , find x given that 5.76 is 12 % of 40 % of x ?
Options: a ) 130 , b ) 120 , c ) 140 , d ) 100 , e ) 300
Rationale: using elimination method to pick the correct option it will be discovered that option b i . e 120 is the correct option because 40 % of 120 is 48 and 12 % of 48 is 5.76 . answer : b
Answer: b
Question (gain): a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 12.60 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 12.60 when c . p = ( 100 * 12.60 ) / 21 = 60 answer : d"
Answer: d
Question (physics): a 270 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 230 , b ) 200 , c ) 250 , d ) 300 , e ) 500
Rationale: "answer : option a explanation : relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 270 ) / 9 = 500 / 9 = > x = 230 . answer a"
Answer: a
Question (other): two numbers are in respectively 20 % and 50 % more than a third number . the ratio of the two numbers is ?
Options: a ) 2 : 5 , b ) 1 : 2 , c ) 4 : 5 , d ) 3 : 7 , e ) 5 : 6
Rationale: "let the 3 rd number be x then , first number = 120 % of x = 120 x / 100 = 6 x / 5 second number = 150 % of x = 150 x / 100 = 3 x / 2 ratio of first two numbers = 6 x / 5 : 3 x / 2 = 12 x : 15 x = 4 : 5 answer is c"
Answer: c
Question (general): a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 4 rows or 5 rows or 6 rows , then no tree will be left . find the least number of trees required
Options: a ) 22 , b ) 60 , c ) 28 , d ) 76 , e ) 21
Rationale: explanation : the least number of trees that are required = lcm ( 4 , 5 , 6 ) = 60 . answer : b
Answer: b
Question (general): a batsman ' s avg in 12 innings is 24.00 . if his avg is to be double of the no of innings ( 15 innings ) , what should he score in the remaining 3 innings ( avg ) ?
Options: a ) 143 , b ) 144 , c ) 145 , d ) 146 , e ) 147
Rationale: let total runs done by a batsman in 12 innings be x therefore , x / 12 = 24 that means x = 12 * 24 = 288 runs for 15 innings , avg was doubled i . e . . 48.00 therefore , ( x + y ) / 15 = 48 where y is the no of runs done in last 3 innings y = 432 therefore average is 432 / 3 = 144 answer : b
Answer: b
Question (physics): in what time will a railway train 80 m long moving at the rate of 40 kmph pass a telegraph post on its way ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 6.4 , e ) 7.2
Rationale: "t = 80 / 40 * 18 / 5 = 7.2 sec answer : e"
Answer: e
Question (other): the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people z who purchased only book a ?
Options: a ) 250 , b ) 500 , c ) 750 , d ) 1000 , e ) 1500
Rationale: "this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , z = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000"
Answer: d
Question (general): if the sum of two numbers is 20 and the sum of their squares is 200 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 100 , d ) 88 , e ) 48
Rationale: "according to the given conditions x + y = 20 and x ^ 2 + y ^ 2 = 200 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 20 ^ 2 = 200 + 2 xy so xy = 200 / 2 = 100 answer : c"
Answer: c
Question (general): ratio of two numbers x and y is 3 : 7 . if x is increased by 50 % and y is increased by 2 then the new ratio becomes 1 : 2 . what is the ratio 2 y : ( 2 x + 6 )
Options: a ) 16 : 15 , b ) 4 : 5 , c ) 7 : 12 , d ) 4 : 9 , e ) 6 : 5
Rationale: "let : x = 3 n y = 7 n 4.5 n / ( 7 n + 5 ) = 1 / 2 9 n = 7 n + 2 n = 1 so , x = 3 ; y = 7 2 y / ( 2 x + 6 ) = 14 / 12 = 7 : 6 answer = c"
Answer: c
Question (gain): bruce purchased 8 kg of grapes at the rate of 70 per kg and 8 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1050 , c ) c ) 1000 , d ) d ) 1065 , e ) e ) 1075
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 8 kg of mangoes = 55 × 8 = 440 . total cost he has to pay = 560 + 440 = 1000 c"
Answer: c
Question (general): the sum of the ages of 4 children born at the intervals of 3 years each is 36 years . what is the age of the youngest child ?
Options: a ) 22 , b ) 18 , c ) 4.5 , d ) 99 , e ) 38
Rationale: "let x = the youngest child . each of the other four children will then be x + 3 , x + 6 , x + 9 we know that the sum of their ages is 36 so , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) = 36 therefore the youngest child is 4.5 years old answer : c"
Answer: c
Question (general): a certain number when divided by 39 leaves a remainder 16 , what is the remainder when the same number is divided by 13 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 3
Rationale: "explanation : 39 + 16 = 55 / 13 = 3 ( remainder ) answer : e"
Answer: e
Question (physics): a pump can fill a tank with water in 4 hours . because of a leak , it took 20 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 4 , e ) 2
Rationale: p - - > pump , l - - - > leak pipe - - - - - - - - - - p - - - - - - - - - l - - - - - - - - - - - - ( p - l ) - - time - - - - - - - - - 4 - - - - - - - - - x - - - - - - - - - - - - - 20 * rate - - - - - - - - - 5 - - - - - - - - - x - - - - - - - - - - - - - 1 work - - - - - - - 20 - - - - - - - - - 20 - - - - - - - - - - - 20 time required to empty the tank if leakage present = 20 / ( ( 5 ) - 1 ) = ( 20 ) / ( 4 ) = 5 ans - c
Answer: c
Question (physics): suppose 5 monkeys take 5 minutes to eat 5 bananas . how many monkeys would it take to eat 15 bananas in 15 minutes ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 5 , e ) 13
Rationale: "one monkey takes 5 min to eat 1 banana , so in 15 mins 1 monkey will eat 3 bananas , so for 15 bananas in 15 min we need 15 / 3 = 5 monkeys answer : d"
Answer: d
Question (general): what is the decimal equivalent of ( 1 / 4 ) ^ 6 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.0002 , e ) 0.5
Rationale: "( 1 / 4 ) ^ 6 = 1 / 4096 = 0.0002 answer : d"
Answer: d
Question (physics): 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 2 men and 2 women will do that task .
Options: a ) 3 / 7 , b ) 3 / 10 , c ) 3 / 18 , d ) 3 / 16 , e ) 3 / 11
Rationale: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 2 m + 2 w = 6 w answer is 6 / 14 = 3 / 7 answer : a"
Answer: a
Question (general): what is the remainder when the number 14 ^ 2 * 15 ^ 8 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )"
Answer: a
Question (general): rahul played weel in this season . his current batting averagge is 52 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 12 , c ) 9 , d ) 6 , e ) 5
Rationale: "52 x + 78 = 54 ( x + 1 ) = > 2 x = 24 = > x = 12 answer : b"
Answer: b
Question (other): a container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 9 ounces of a solution that is 1 part alcohol to 2 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 1 : 2 , b ) 3 : 7 , c ) 3 : 5 , d ) 4 : 7 , e ) 7 : 3
Rationale: "container 1 has 12 ounces in the ratio 1 : 2 or , x + 2 x = 12 gives x ( alcohol ) = 4 and remaining water = 8 container 2 has 9 ounces in the ratio 1 : 2 or , x + 2 x = 9 gives x ( alcohol ) = 3 and remaining water = 6 mixing both we have alcohol = 4 + 3 and water = 8 + 6 ratio thus alcohol / water = 7 / 14 = 1 / 2 answer a"
Answer: a
Question (gain): some of the 50 % solution of acid was removed and this was replaced with an equal amount of 20 % solution of acid . as a result , a 35 % solution of acid was obtained . what fraction of the original solution was replaced ?
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 2 / 3 , d ) 3 / 5 , e ) 4 / 7
Rationale: let x be the fraction of the original solution that was replaced . 0.5 * ( 1 - x ) + 0.2 ( x ) = 0.35 0.3 x = 0.15 x = 1 / 2 the answer is b .
Answer: b
Question (other): there are 202 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 93 , b ) 94 , c ) 92 , d ) 96 , e ) 95
Rationale: "editing my solution : number of switches = 202 number of switches turned on by a : 3 , 6 , . . . 201 = 67 number of switches turned on by b : 5 , 10 , . . . . 200 = 40 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 67 - 6 ) + ( 40 - 6 ) = 95 answer : e"
Answer: e
Question (general): the maximum number of students among them 1048 pens and 828 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 4 , b ) 8 , c ) 16 , d ) 1911 , e ) none of these
Rationale: "explanation : required number of students = h . c . f of 1048 and 828 = 4 . answer : a"
Answer: a
Question (geometry): a 6 by 8 rectangle is inscribed in circle . what is the circumference of the circle ?
Options: a ) 5 π , b ) 10 π , c ) 15 π , d ) 20 π , e ) 25 π
Rationale: "the diagonal of the rectangle will be the diameter of the circle . and perimeter = 2 * pi * r ans : b"
Answer: b
Question (general): marts income is 40 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) b ) 120 % , c ) c ) 96 % , d ) d ) 80 % , e ) e ) 84 %
Rationale: "m = ( 140 / 100 ) t t = ( 60 / 100 ) j = > m = ( 84 / 100 ) j answer e ."
Answer: e
Question (other): if all the 6 are replaced by 9 , then the algebraic sum of all the numbers from 1 to 100 ( both inclusive ) varies by
Options: a ) 330 , b ) 340 , c ) 350 , d ) 360 , e ) 370
Rationale: 1 11 21 . . . . . . . 91 2 12 22 . . . . . . . . 92 3 13 23 . . . . . . . . 93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . there are total 20 occurrence of 6 . once place at 6 th row in every column and tens place in 6 th column and diff of 6 and 9 is 3 so 3 * 1 * 10 + 3 * 10 * 10 = 330 answer : a
Answer: a
Question (physics): a boy is travelling from his home to school at 3 km / hr and reached 7 min late . next day he traveled at 12 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 1 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "let the distance be x t 1 = x / 3 hr t 2 = x / 12 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 3 - x / 12 = 1 / 4 x / 4 = 1 / 4 x = 1 km answer is a"
Answer: a
Question (general): a gold purification process cycle , is able to remove 1 / 16 of impurities in gold . if we have a 10 grams of gold ore dust containing 16 / 24 pure gold . how much impurities would have been removed from that old after 4 cycles of purification using that method ?
Options: a ) 0.72 , b ) 0.74 , c ) 0.76 , d ) 0.78 , e ) 0.82
Rationale: x is the initial quantity of impurities in that gold . after a cycle of purification the quantity of impurities left would be x 1 = x - 1 / 16 x i . e . x 1 = 15 / 16 x same thing for x 2 , x 3 , x 4 , respectively representing the quantity of impurities left after 2 , 3 , 4 cycles of purification . so we have : x 1 = 15 / 16 x x 2 = 15 / 16 x 1 x 3 = 15 / 16 x 2 x 4 = 15 / 16 x 3 by multiplying both ends of the equations we get : x 1 * x 2 * x 3 * x 4 = ( 15 / 16 ) ^ 4 x * x 1 * x 2 * x 3 simplification leaves us with : x 4 = ( 15 / 16 ) ^ 4 x x 4 is the quantity of impurities left after four cycles . so the cumulative quantity of impurities ( q 4 ) which has been removed after 4 cycles is : q 4 = x - x 4 = x - ( 15 / 16 ) ^ 4 x i . e . q 4 = x ( 1 - ( 15 / 16 ) ^ 4 ) in this case , given x was : x = ( 1 - 16 / 24 ) * 10 g = 3.33 g ( remember we had 16 / 24 pure gold ) so we have q 4 = 3.33 * ( 1 - ( 15 / 16 ) ^ 4 ) = 3.33 * ( 1 - ( 50625 / 65536 ) ) = 3.33 * ( 14911 / 65536 ) = 0.757 rounded gives q 4 = 0.76 answer : c
Answer: c
Question (general): if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 20 , what is the value of f ( 5 ) ?
Options: a ) 104 , b ) 60 , c ) 62 , d ) 50 , e ) 25
Rationale: "f ( x ) = 2 x ^ 2 + y f ( 2 ) = 20 = > 2 * ( 2 ) ^ 2 + y = 20 = > 8 + y = 20 = > y = 12 f ( 5 ) = 2 * ( 5 ) ^ 2 + 12 = 62 answer c"
Answer: c
Question (general): in a 100 member association consisting of men and women , exactly 20 % of men and exactly 25 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 21 , b ) 47 , c ) 45 , d ) 43 , e ) 41
Rationale: "solution simple out of 100 20 % are male i . e 20 and 25 % are female i . e 25 , so total homeowner is 45 . now min number homeowner is 20 and max is 45 so question ask us to find least and 21 has least value among all option . so ans is 21 . answer : a"
Answer: a
Question (gain): of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 10 percent was planted with grapes and 80 percent of the cleared land was planted with potato . if the remaining 450 acres of cleared land was planted with tomato , how many acres did the farmer own ?
Options: a ) 3500 , b ) 4500 , c ) 5500 , d ) 5250 , e ) 5000
Rationale: 10 % od 90 % = 9 % , 80 % 0 f 90 % = 72 % so the remaining 90 - 9 - 72 = 9 % = 450 acres or 10 % of 90 % = 9 % - - > 450 / 9 * 100 = 5000 acres answer ( e )
Answer: e
Question (general): the ages of 2 persons differ by 18 years . if 12 years ago the elder one be 6 times as old as the younger one , find the present age of elder person .
Options: a ) 33.6 , b ) 47 , c ) 50.4 , d ) 52.4 , e ) 47.9
Rationale: "age of the younger person = x age of the elder person = x + 18 6 ( x - 12 ) = x + 18 - 12 x = 15.6 age of elder person = 15.6 + 18 = 33.6 answer is a"
Answer: a
Question (general): david obtained 36 , 35 , 42 , 57 and 55 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 45 , c ) 87 , d ) 165 , e ) 11
Rationale: "explanation : average = ( 36 + 35 + 42 + 57 + 55 ) / 5 = 225 / 5 = 45 . answer : b"
Answer: b
Question (general): find the smallest number of five digits exactly divisible by 32 , 40,56 and 64 .
Options: a ) 11020 , b ) 11030 , c ) 11040 , d ) 11060 , e ) 11080
Rationale: "smallest number of five digits is 10000 . required number must be divisible by l . c . m . of 32,40 , 56,64 i . e 2240 , on dividing 10000 by 2240 , we get 1200 as remainder . therefore , required number = 10000 + ( 2240 â € “ 1200 ) = 11040 . answer is c ."
Answer: c
Question (gain): find compound interest on $ 16000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 6109 , b ) 6209 , c ) 6218 , d ) 6107 , e ) 6100
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 16000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 16000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 22218 . : . c . i . = rs . ( 22218 - 16000 ) = $ 6218 answer c ."
Answer: c