regisss/math_qa huggingface dataset:
Problem: a boat covers a certain distance downstream in 1 hour , while it comes back in 11 â  „ 2 hours . if the speed of the stream be 3 kmph , what is the speed of the boat in still water ?
Options: a ) 31 kmph , b ) 16 kmph , c ) 19 kmph , d ) 15 kmph , e ) 14 kmph
Rationale: "let the speed of the water in still water = x given that speed of the stream = 3 kmph speed downstream = ( x + 3 ) kmph speed upstream = ( x â ˆ ’ 3 ) kmph he travels a certain distance downstream in 1 hour and come back in 11 â  „ 2 hour . i . e . , distance travelled downstream in 1 hour = distance travelled upstream in 11 â  „ 2 hour since distance = speed ã — time , we have ( x + 3 ) ã — 1 = ( x - 3 ) 3 / 2 2 ( x + 3 ) = 3 ( x - 3 ) 2 x + 6 = 3 x - 9 x = 6 + 9 = 15 kmph answer : d"
Answer: d
Problem: in a division , a student took 87 as divisor instead of 36 . his answer was 24 . the correct answer is -
Options: a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 58
Rationale: x / 87 = 24 . x = 24 * 87 . so correct answer would be , ( 24 * 87 ) / 36 = 58 . answer : e
Answer: e
Problem: what is the sum of all digits for the number 10 ^ 26 - 51 ?
Options: a ) 199 , b ) 209 , c ) 219 , d ) 229 , e ) 239
Rationale: "10 ^ 26 is a 27 - digit number : 1 followed by 26 zeros . 10 ^ 26 - 51 is a 26 - digit number : 24 9 ' s and 49 at the end . the sum of the digits is 24 * 9 + 4 + 9 = 229 . the answer is d ."
Answer: d
Problem: what is the measure of the angle w made by the diagonals of the any adjacent sides of a cube .
Options: a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90
Rationale: "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . c"
Answer: c
Problem: what is the compound interest paid on a sum of rs . 6000 for the period of 2 years at 10 % per annum .
Options: a ) 1260 , b ) 1320 , c ) 1200 , d ) 1250 , e ) none of these
Rationale: solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 6000 = 6000 * ( 21 / 100 ) = 1260 answer a
Answer: a
Problem: a fair 2 sided coin is flipped 8 times . what is the probability that tails will be the result at least twice , but not more than 8 times ?
Options: a ) 5 / 8 , b ) 3 / 4 , c ) 7 / 8 , d ) 157 / 64 , e ) 143 / 128
Rationale: "at least twice , but not more than 8 timesmeans exactly 2 times , 3 times , 4 times , 5 times , 6 times , 7 times , 8 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 8 c 2 / 2 ^ 8 + 8 c 3 / 2 ^ 8 + 8 c 4 / 2 ^ 8 + 8 c 5 / 2 ^ 8 + 8 c 6 / 2 ^ 8 + 8 c 7 / 2 ^ 8 = 143 / 128 option : e"
Answer: e
Problem: the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 54 . what is the rate of interest per annum ?
Options: a ) 8 , b ) 2 , c ) 9 , d ) 4 , e ) 6
Rationale: "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 54 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 54 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 54 r 2 = ( 54 * 2 ) / 3 = 36 = > r = 6 rate = 6 % answer : option e"
Answer: e
Problem: find the compound ratio of ( 1 : 2 ) , ( 2 : 3 ) and ( 3 : 4 ) is
Options: a ) 1 : 2 , b ) 3 : 5 , c ) 5 : 7 , d ) 1 : 4 , e ) 2 : 1
Rationale: "required ratio = 1 / 2 * 2 / 3 * 3 / 4 = 1 / 4 = 1 : 4 answer is d"
Answer: d
Problem: if 1 is added to the denominator of fraction , the fraction becomes 1 / 2 . if 1 is added to the numerator , the fraction becomes 1 . the fraction is
Options: a ) 4 / 7 , b ) 5 / 9 , c ) 2 / 3 , d ) 10 / 11 , e ) none of these
Rationale: explanation : let the required fraction be a / b . then ⇒ a / b + 1 = 1 / 2 ⇒ 2 a – b = 1 - - - - ( 1 ) ⇒ a + 1 / b = 1 ⇒ a – b = – 1 ⇒ a – b = – 1 - - - - - - - ( 2 ) solving ( 1 ) & ( 2 ) we get a = 2 , b = 3 fraction = a / b = 2 / 3 correct option : c
Answer: c
Problem: if the ratio of two number is 2 : 3 and lcm of the number is 120 then what is the number .
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "product of two no = lcm * hcf 2 x * 3 x = 120 * x x = 20 answer : b"
Answer: b
Problem: find out the c . i on rs . 4000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 244.83 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01
Rationale: "a = 4000 ( 51 / 50 ) 3 = 4244.832 4000 - - - - - - - - - - - 244.83 answer : a"
Answer: a
Problem: bert and rebecca were looking at the price of a condominium . the price of the condominium was 40 % more than bert had in savings , and separately , the same price was also 75 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .
Options: a ) 1 : 4 , b ) 4 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 5 : 4
Rationale: suppose bert had 100 so price becomes 140 , this 140 = 1.75 times r ' s saving . . so r ' s saving becomes 80 so required ratio is 100 : 80 = 5 : 4 answer : e
Answer: e
Problem: walking at 5 / 6 of her normal speed , a worker is 12 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: "let v be her normal speed and let t be her normal time . d = ( 5 / 6 ) v * ( t + 12 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 5 / 6 ) v * ( t + 12 ) t / 6 = 10 t = 60 the answer is e ."
Answer: e
Problem: if 12 lions can kill 12 deers in 12 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 12 minute , c ) 120 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: "we can try the logic of time and work , our work is to kill the deers so 12 ( lions ) * 12 ( min ) / 12 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 12 answer : b"
Answer: b
Problem: a man cycling along the road noticed that every 18 minutes a bus overtakes him and every 6 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes
Rationale: let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 18 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 18 , d = 18 b - 18 c ; every 6 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 6 , d = 6 b + 6 c ; d = 18 b - 18 c = 6 b + 6 c , - - > b = 2 c , - - > d = 18 b - 9 b = 9 b . interval = \ frac { d } { b } = \ frac { 9 b } { b } = 9 answer : d ( 9 minutes ) .
Answer: d
Problem: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 27000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 20 : 9 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 5 : 3
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 27000 × 9 = 45 × 12 : 27 × 9 = 15 × 12 : 9 × 9 = 20 : 9 answer is a"
Answer: a
Problem: the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 15 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 20 , b ) 55 / 4 , c ) 25 , d ) 14 , e ) 13
Rationale: "after passing the hiker the cyclist travels for 5 minutes at a rate of 15 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 4 miles . in those 5 mins the hiker travels a distance of 1 / 3 miles . so the hiker still has to cover 11 / 12 miles to meet the waiting cyclist . the hiker will need 55 / 4 mins to cover the remaining 11 / 12 miles . so the answer is b ."
Answer: b
Problem: if x + y = 10 , x - y = 18 , for integers of x and y , x = ?
Options: a ) 14 , b ) 15 , c ) 25 , d ) 13 , e ) 42
Rationale: x + y = 10 x - y = 18 2 x = 28 x = 14 answer is a
Answer: a
Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 2 / 3 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ?
Options: a ) 4 / 15 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22
Rationale: "p ( 1 and not 2 ) = 2 / 3 * ( 1 - 3 / 5 ) = 4 / 15 . answer : a ."
Answer: a
Problem: find the least number must be subtracted from 964807 so that remaining no . is divisible by 8 ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "on dividing 964807 by 15 we get the remainder 7 , so 7 should be subtracted a"
Answer: a
Problem: if 8 people take an hour to complete a piece of work , then how long should 16 people will take to complete the same piece of work ?
Options: a ) 15 min , b ) 30 min , c ) 26 min , d ) 28 min , e ) 18 min
Rationale: if 8 people take an hour to complete a piece of work , then 16 people will take 8 * 60 / 16 = 30 mins to complete the same piece of work . answer : b
Answer: b
Problem: find the area of a parallelogram with base 25 cm and height 15 cm ?
Options: a ) 295 cm 2 , b ) 385 cm 2 , c ) 275 cm 2 , d ) 375 cm 2 , e ) 285 cm 2
Rationale: "area of a parallelogram = base * height = 25 * 15 = 375 cm 2 answer : d"
Answer: d
Problem: when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 6 ] * [ 4 ] = ?
Options: a ) [ 12 ] , b ) [ 44 ] , c ) [ 45 ] , d ) [ 88 ] , e ) [ 90 ]
Rationale: "[ 6 ] * [ 4 ] = ( 6 / 2 + 1 ) ( 4 / 2 + 1 ) = [ 12 ] . ans - a"
Answer: a
Problem: in a certain company , a third of the workers do not have a retirement plan . 60 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 180 , d ) 120 , e ) 210
Rationale: "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,4 * 1 / 3 * x 120 = 12 / 30 x x = 300 300 - 120 = 180 answer c"
Answer: c
Problem: a bus started its journey from mumbai and reached pune in 65 min with its average speed of 60 km / hr . if the average speed of the bus is increased by 5 km / hr , how much time will it take to cover the same distance ?
Options: a ) 2 hrs , b ) 3 hrs , c ) 1 hrs , d ) 1 1 / 2 hrs , e ) 2 1 / 2 hrs
Rationale: sol . distance between ramgarh and devgarh = ( 60 * 65 ) / 60 = 60 average speed of the bus is increased by 5 km / hr then the speed of the bus = 60 km / hr required time = 60 / 60 = 1 hr c
Answer: c
Problem: the mean of 50 observations is 200 . but later he found that there is decrements of 47 from each observations . what is the the updated mean is ?
Options: a ) 165 , b ) 185 , c ) 153 , d ) 198 , e ) 199
Rationale: "153 answer is c"
Answer: c
Problem: a bag contains 4 red , 6 blue and 3 green balls . if 3 balls are picked at random , what is the probability that both are blue ?
Options: a ) 11 / 144 , b ) 12 / 455 , c ) 10 / 143 , d ) 11 / 125 , e ) 14 / 368
Rationale: "p ( both are red ) , = 6 c 3 / 13 c 3 = 10 / 143 c"
Answer: c
Problem: what is 120 % of 13 / 24 of 360 ?
Options: a ) 52 , b ) 117 , c ) 234 , d ) 312 , e ) 576
Rationale: "120 % * 13 / 24 * 360 = 1.2 * 13 * 15 = 234 the answer is c ."
Answer: c
Problem: if a farmer sells 10 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 15 more chickens , he will run out of feed 3 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 12 , b ) 24 , c ) 48 , d ) 35 , e ) 60
Rationale: "say farmer has n chicken and he is good for d days . : - we have 3 equations given in question : - ( n - 10 ) * d + 4 = ( n + 15 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 15 d - 3 n = 45 4 n - 10 d = 40 = > n = 35 ans d it is !"
Answer: d
Problem: how many 1 / 2 s are there in 37 1 / 2 ?
Options: a ) 75 , b ) 150 , c ) 300 , d ) 600 , e ) 700
Rationale: "required number = ( 75 / 2 ) / ( 1 / 2 ) = ( 75 / 2 x 2 / 1 ) = 75 answer : a"
Answer: a
Problem: a , b , c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 175 , then how much amount should c pay as his share of rent ?
Options: a ) 23 , b ) 45 , c ) 15 , d ) 28 , e ) 18
Rationale: a : b : c = 10 * 7 : 12 * 5 : 15 * 3 = 2 * 7 : 12 * 1 : 3 * 3 = 14 : 12 : 9 amount that c should pay = 175 * ( 9 / 35 ) = 5 * 9 = 45 answer is b
Answer: b
Problem: in a box of 12 pens , a total of 6 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 1 / 6 , b ) 5 / 22 , c ) 6 / 11 , d ) 9 / 16 , e ) 3 / 4
Rationale: "method - 1 there are 9 fine pieces of pen and 6 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 6 / 12 ) i . e . probability of second pen not being defective = ( 5 / 11 ) [ 11 pen remaining with 5 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 6 / 12 ) * ( 5 / 11 ) = 5 / 22 answer : option b"
Answer: b
Problem: a part of certain sum of money is invested at 6 % per annum and the rest at 15 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 6 , b ) 4 : 9 , c ) 4 : 3 , d ) 5 : 2 , e ) 4 : 2
Rationale: "15 : 6 = 5 : 2 answer : d"
Answer: d
Problem: if a randomly selected non - negative single digit integer is added to { 2 , 3 , 5 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ?
Options: a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6
Rationale: we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 5 ) / 2 = 4 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c .
Answer: c
Problem: on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 630 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 8 % , b ) 10 % , c ) 12 % , d ) 14 % , e ) 16 %
Rationale: "difference in c . i . and s . i for 2 years = $ 630 - $ 600 = $ 30 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 30 rate = ( 100 * 30 ) / ( 300 ) = 10 % the answer is b ."
Answer: b
Problem: there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is seven - third that of the smaller circle . find the circumference of the smaller circle .
Options: a ) 165 ∏ cm , b ) 65 ∏ cm , c ) 12 ∏ cm , d ) 14 ∏ cm , e ) 16 ∏ cm
Rationale: "let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 ∏ s = 12 ∏ cm . answer : c"
Answer: c
Problem: y and z walk around a circular track . they start at 5 a . m from the same point in the opposite directions . y and z walk at a speed of 3 rounds per hour and 4 rounds per hour respectively . how many times shall they cross each other before 7 a . m
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: explanation : relative speed = ( 3 + 4 ) = 9 rounds per hour so , they cross each other 9 times in an hour hence , they cross 18 times before 7 a . m answer : option e
Answer: e
Problem: a box contains 10 black , 5 red and 4 green marbles . 3 marbles are drawn from the box at random . what is the probability that all the three marbles are of the same color ?
Options: a ) 143 / 969 , b ) 134 / 969 , c ) 120 / 969 , d ) 19 / 969 , e ) 120 / 134
Rationale: "explanation : total marbles in a box = 10 black + 5 red + 4 green marbles = 19 marbles 3 marbles are drawn from 19 marbles at random . therefore , n ( s ) = 19 c 3 = 969 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 10 c 3 + 5 c 3 + 4 c 3 = 120 + 10 + 4 = 134 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 134 / 969 answer : b"
Answer: b
Problem: a towel , when bleached , lost 20 % of its length and 10 % of its breadth . what is the percentage decrease in area ?
Options: a ) 26 , b ) 28 , c ) 24 , d ) 20 , e ) 22
Rationale: "formula for percentage change in area is : = ( − x − y + ( xy ) / 100 ) % = ( − 20 − 10 + ( 20 × 10 ) / 100 ) % = − 28 % i . e . , area is decreased by 28 % answer is b ."
Answer: b
Problem: two numbers are respectively 35 % and 50 % more than a third number . the percentage that is first of the second is ?
Options: a ) 90 % , b ) 47 % , c ) 38 % , d ) 52 % , e ) 83 %
Rationale: "i ii iii 135 150 100 150 - - - - - - - - - - 135 100 - - - - - - - - - - - ? = > 90 % answer : a"
Answer: a
Problem: a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 272 less than the sum lent . what was the sum lent ?
Options: a ) 400 , b ) 278 , c ) 289 , d ) 500 , e ) 821
Rationale: "p - 272 = ( p * 4 * 8 ) / 100 p = 400 answer : a"
Answer: a
Problem: a marketing firm determined that , of 200 households surveyed , 80 used neither brand r nor brand b soap , 60 used only brand r soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45
Rationale: solution for soap r and soap b ( d ) 40
Answer: d
Problem: the length of the bridge , which a train 150 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 388 , b ) 267 , c ) 225 , d ) 288 , e ) 261
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 150 + x ) / 30 = 25 / 2 = = > 2 ( 150 + x ) = 750 = = > x = 225 m . answer : c"
Answer: c
Problem: if x and y are numbers such that ( x + 4 ) ( y - 4 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
Options: a ) 0 , b ) 9 , c ) 12 , d ) 16 , e ) 18
Rationale: "from ( x + 4 ) ( y - 4 ) = 0 it follows that either x = - 4 or y = 4 . thus either x ^ 2 = 16 or y ^ 2 = 16 . now , if x ^ 2 = 16 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 16 + 0 = 16 . similarly if y ^ 2 = 16 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 16 = 16 . answer : d ."
Answer: d
Problem: in the set of positive integers from 1 to 90 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 245 , c ) 320 , d ) 405 , e ) 450
Rationale: "reduce 1 - 90 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 - - 85 are valid multiples . add them - - > 405 d"
Answer: d
Problem: 1000 men have provisions for 18 days . if 400 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.8 , c ) 12.6 , d ) 12.2 , e ) 12.1
Rationale: 1000 * 18 = 1400 * x x = 12.8 answer : b
Answer: b
Problem: if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2014 ) = ?
Options: a ) 2015 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2014 ) = 2015 ans : a"
Answer: a
Problem: a , b and c can do a piece of work in 30 days , 30 days and 40 days respectively . they began the work together but c left 4 days before the completion of the work . in how many days was the work completed ?
Options: a ) 12 days , b ) 16 days , c ) 18 days , d ) 11 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 30 + 1 / 30 + 1 / 40 = 1 / 11 work done by a and b together in the last 4 days = 4 * ( 1 / 30 + 1 / 30 ) = 4 / 15 remaining work = 11 / 15 the number of days required for this initial work = 8 days . the total number of days required = 4 + 8 = 12 days . answer : a"
Answer: a
Problem: a man buys an article for $ 100 . and sells it for $ 110 . find the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 100 s . p . = $ 110 gain = $ 10 gain % = 10 / 100 * 100 = 10 % answer is a"
Answer: a
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) rs . 650 , b ) rs . 690 , c ) rs . 698 , d ) rs . 700 , e ) rs . 740
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 815 - 117 ) = rs . 698 . answer : option c"
Answer: c
Problem: if the average ( arithmetic mean ) of x + 1 , x + 5 , and x + 9 is 0 , then x =
Options: a ) – 5 , b ) – 4 , c ) – 2 , d ) – 1 , e ) 0
Rationale: "( x + 1 + x + 5 + x + 9 ) / 3 = 0 = > 3 x + 15 = 0 = > x = - 5 answer a"
Answer: a
Problem: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 14 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 14,000 imported car and ended up paying $ 1440 in taxes , what is the first tier ' s price level ?
Options: a ) $ 1600 , b ) $ 5333 , c ) $ 6050 , d ) $ 7050 , e ) $ 8000
Rationale: "let t be the tier price , p be total price = 14000 per the given conditions : 0.14 t + 0.08 ( p - t ) = 1440 - - - - > t = 5333 . b is the correct answer ."
Answer: b
Problem: what should be added to 4750 so that it may become a perfect square ?
Options: a ) 11 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "69 x 69 = 4761 4761 - 4750 = 11 if added to 11 get perfect square answer = a"
Answer: a
Problem: john makes $ 60 a week from his job . he earns a raise andnow makes $ 72 a week . what is the % increase ?
Options: a ) 20 % , b ) 16.66 % , c ) 16.56 % , d ) 17.66 % , e ) 18.1 %
Rationale: "increase = ( 12 / 60 ) * 100 = ( 1 / 5 ) * 100 = 20 % . a"
Answer: a
Problem: 50 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 23 , b ) 78 , c ) 27 , d ) 51 , e ) 81
Rationale: "explanation : 50 + 5 * 12 / ( 180 / 3 ) = 50 + 5 * 12 / ( 60 ) = 50 + ( 5 * 12 ) / 60 = 50 + 1 = 51 . answer : d"
Answer: d
Problem: find number which is 50 % less than 60 .
Options: a ) 18 , b ) 30 , c ) 32 , d ) 26 , e ) 98
Rationale: explanation : 50 % less is 50 % of the given number therefore , 50 % of 60 is 30 . answer : b
Answer: b
Problem: mark bought a set of 6 flower pots of different sizes at a total cost of $ 7.80 . each pot cost 0.25 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?
Options: a ) $ 1.75 , b ) $ 1.93 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30
Rationale: this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 7.80 ( a 25 - cent increment ) and the the difference in sequential prices of the pots is 25 cents , the largest pot probably has a price that is a 25 - cent increment . from the answer choices , i would then test answer c first ( since answers b and d are not in 25 - cent increments ) . if . . . . the largest pot = $ 1.75 the other 5 pots are . . . . 1.75 1.50 1.25 1.00 0.75 total = $ 7.80 so this must be the answer . b
Answer: b
Problem: a certain basketball team that has played 2 / 3 of its games has a record of 18 wins and 2 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "18 wins , 2 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 2 games so it can lose another 5 at most . answer ( c )"
Answer: c
Problem: a circular well with a diameter of 2 metres , is dug to a depth of 10 metres . what is the volume of the earth dug out ?
Options: a ) 32 m 3 , b ) 31.4 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) none
Rationale: "solution volume = π r 2 h ‹ = › ( 22 / 7 × 1 × 1 × 10 ) m 3 ‹ = › 31.4 m 3 . answer b"
Answer: b
Problem: a sum fetched a total simple interest of $ 4241.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8930
Rationale: "e 8930 principal = $ 100 x 4241.25 / 9 x 5 = $ 424125 / 45 = $ 8930 ."
Answer: e
Problem: the unit digit in the product ( 635 * 767 * 984 * 489 ) is :
Options: a ) 0 , b ) 8 , c ) 3 , d ) 2 , e ) 1
Rationale: "explanation : unit digit in the given product = unit digit in ( 5 * 7 * 4 * 9 ) = 0 answer : a"
Answer: a
Problem: in a survey of political preferences , 78 % of those asked were in favour of at least one of the proposals : i , ii and iii . 50 % of those asked favoured proposal i , 30 % favoured proposal ii , and 20 % favoured proposal iii . if 5 % of those asked favoured all 3 of the proposals , what x percentage of those asked favoured more than one of the 3 proposals .
Options: a ) 10 , b ) 12 , c ) 17 , d ) 22 , e ) 30
Rationale: bunuel , my answer for exactly 2 people was 17 and this was my approach : 100 % = ( a + b + c ) - ( anb + anc + bnc ) - 5 % + 22 % which leads me to x = 100 % = ( 50 + 30 + 20 ) - ( at least 2 people ) - 5 % + 22 % . c
Answer: c
Problem: a certain bag contains 60 balls — 22 white , 18 green , 2 yellow , 15 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.7 , b ) 0.15 , c ) 0.54 , d ) 0.85 , e ) 0.91
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 2 ) / 60 = 42 / 60 = 0.7 . answer : a ."
Answer: a
Problem: if the personal income tax rate is lowered from 38 % to 30 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 36500 ?
Options: a ) $ 1825 , b ) $ 5000 , c ) $ 3150 , d ) $ 7000 , e ) $ 10000
Rationale: "saving = ( 38 - 33 ) % of 36500 = 1825 . answer : a"
Answer: a
Problem: elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 48 and elvin ' s total telephone bill for february was 90 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 6 , e ) $ 28
Rationale: "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 48 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 90 i . e . x + y = 48 and 2 x + y = 90 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 90 - 48 i . e . x = 42 i . e . fixed monthly charge , y = 6 answer : option d"
Answer: d
Problem: in the recent , climate conference in new york , out of 500 men , 300 women , 500 children present inside the building premises , 10 % of the men , 60 % of the women and 70 % of the children were indians . find the percentage of people who were not indian ?
Options: a ) 59.54 % , b ) 66.25 % , c ) 55.39 % , d ) 63.21 % , e ) 64.22 %
Rationale: "solution : number of indians men present there = 500 * 10 / 100 = 50 indian women = 300 * 60 / 100 = 180 indian children = 500 * 70 / 100 = 350 . total member present in climate conference = 500 + 300 + 500 = 1300 total indian = 50 + 180 + 350 = 580 hence , % of indian present there = 580 * 100 / 1300 = 44.61 % % of people who were not indian = 100 - 44.61 = 55.39 % . answer c"
Answer: c
Problem: two numbers are in the ratio of 5 : 8 . if 30 be subtracted from each , they are in the ratio of 5 : 9 . find the numbers ?
Options: a ) 122,195 , b ) 121,199 , c ) 120,192 , d ) 102,192 , e ) 126,109
Rationale: "( 5 x - 30 ) : ( 8 x - 30 ) = 5 : 9 x = 24 = > 120,192 answer : c"
Answer: c
Problem: find k if 56 / k = 4 .
Options: a ) 16 , b ) 17 , c ) 18 , d ) 14 , e ) 13
Rationale: "since 56 / k = 4 and 56 / 14 = 4 , then k = 14 correct answer d"
Answer: d
Problem: a car traveled from san diego to san francisco at an average speed of 45 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 30 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 45 x total distance traveled = 2 * 45 x = 90 x total time taken = x + 2 x = 3 x average speed = 90 x / 3 x = 30 answer : a"
Answer: a
Problem: a 400 meter long train crosses a man standing on the platform in 10 sec . what is the speed of the train ?
Options: a ) 144 , b ) 108 , c ) 278 , d ) 126 , e ) 112
Rationale: "s = 400 / 10 * 18 / 5 = 144 kmph answer : a"
Answer: a
Problem: a man took a loan from a bank at the rate of 9 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
Options: a ) rs . 2000 , b ) rs . 10,000 , c ) rs . 15,000 , d ) rs . 20,000 , e ) none
Rationale: "solution principal = rs . ( 100 x 5400 / 9 x 3 ) = rs . 20000 . answer d"
Answer: d
Problem: what is the value of ( 44444445 * 88888885 * 44444442 + 44444438 / 44444444 ^ 2 )
Options: a ) 88888883 , b ) 88888884 , c ) 88888885 , d ) 88888886 , e ) 88888873
Rationale: "let x = 44444444 , then 44444445 = x + 1 88888885 = 2 x - 3 44444442 = x - 2 44444438 = x - 6 44444444 ^ 2 = x ^ 2 then substitute it in equation ( x + 1 ) ( 2 x - 3 ) ( x - 2 ) + ( x - 6 ) / x ^ 2 ans is 2 x - 5 i . e 88888883 answer : a"
Answer: a
Problem: jack spent 1 / 6 of his lifetime in adolescence . his facial hair started growing after 1 / 12 more of his life . he successfully married his girlfriend diana after 1 / 7 more of his life . their son was born after 5 years from then . the son lived just 1 / 2 of what jack lived . jack dies 4 years after his son died . how long did jack live ?
Options: a ) 75 , b ) 90 , c ) 45 , d ) 80 , e ) 84
Rationale: e 84 explanation : let us assume that jack lived for p years . p / 6 + p / 12 + p / 7 + 5 + p / 2 + 4 = x = > p = 84 . therefore , jack lived for 84 years .
Answer: e
Problem: if 7 a - 3 b = 10 b + 40 = - 12 b - 2 a , what is the value of 9 a + 9 b ?
Options: a ) - 5 , b ) - 3 , c ) 0 , d ) 3 , e ) 5
Rationale: ( i ) 7 a - 13 b = 40 ( ii ) 2 a + 22 b = - 40 adding ( i ) and ( ii ) : 9 a + 9 b = 0 the answer is c .
Answer: c
Problem: the price of a book is increased from $ 300 to $ 420 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "explanation : change in the price = rs 420 â € “ rs 300 = rs 120 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 120 300 ) * 100 = 40 % c"
Answer: c
Problem: a train 210 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 50 sec , c ) 44 sec , d ) 49 sec , e ) 28 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 210 + 140 = 350 m required time = 350 * 2 / 25 = 28 sec answer : e"
Answer: e
Problem: the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 1 / 8 of that total . what was the price of the basic computer ?
Options: a ) 1500 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2125
Rationale: "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 8 of that new total price : p = 1 / 8 * $ 3,000 = $ 375 . plug this value in the first equation : c + 375 = $ 2,500 - - > c = $ 2,125 . answer : e ."
Answer: e
Problem: 39 ! is divided by 41 then what is the remainder ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 7
Rationale: "substituting p = 41 in the wilson ' s theorem , we get 40 ! + 141 = 0 40 × 39 ! + 141 = 0 − 1 × 39 ! 41 = − 1 cancelling - 1 on both sides , 39 ! 41 = 1 a"
Answer: a
Problem: if x is equal to the sum of the integers from 10 to 30 , inclusive , and y is the number of even integers from 10 to 30 , inclusive , what is the value of x + y ?
Options: a ) 401 , b ) 411 , c ) 421 , d ) 431 , e ) 441
Rationale: "x = 10 + 11 + . . . + 30 = 21 ( 20 ) = 420 y = 11 x + y = 431 the answer is d ."
Answer: d
Problem: the product of two numbers is 4107 . if the h . c . f . of these numbers is 37 , then the greater number is : explanation :
Options: a ) 101 , b ) 107 , c ) 111 , d ) 117 , e ) 121
Rationale: let the numbers be 37 a and 37 b . then , 37 a x 37 b = 4107 ab = 3 . now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 x 1 , 37 x 3 ) i . e . , ( 37 , 111 ) . greater number = 111 . answer : option c
Answer: c
Problem: if 42.36 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "42.36 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.36 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.36 = km / 50 . . . . . . 36 / 100 = 3 m / 50 . . . . . . m = 6 k + m = 3 + 6 = 9 answer : d"
Answer: d
Problem: if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 14 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?
Options: a ) 6 , b ) 16 , c ) 20 , d ) 30 , e ) 174
Rationale: the number of integers that belong to set x only is 14 - 6 = 8 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 8 + 12 = 20 . answer : c .
Answer: c
Problem: how many seconds will a 700 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 287 , b ) 288 , c ) 600 , d ) 277 , e ) 121
Rationale: "let length of tunnel is x meter distance = 700 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 700 + x = ( 65 / 3 ) * 60 700 + x = 20 * 65 = 1300 x = 1300 - 700 = 600 meters answer : c"
Answer: c
Problem: a bakery has 6 employees . it pays annual salaries of $ 16,000 to each of 2 employees , $ 18,000 to 1 employee , and $ 19,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 17,200 , b ) $ 17,500 , c ) $ 17,800 , d ) $ 18,000 , e ) $ 18,400
Rationale: "average = 2 ( 16000 ) + ( 18000 ) + 3 ( 19000 ) / 6 = $ 17,833 the answer is c ."
Answer: c
Problem: find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 35 as remainder
Options: a ) 1235 , b ) 1456 , c ) 1567 , d ) 1678 , e ) 1631
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 35 5 x = 1330 x = 266 large number = 266 + 1365 = 1631 e"
Answer: e
Problem: how many odd numbers between 10 and 1400 are the squares of integers ?
Options: a ) 14 , b ) 17 , c ) 20 , d ) 23 , e ) 26
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 37 which includes 17 numbers . the answer is b ."
Answer: b
Problem: n is a whole number which when divided by 4 gives 3 as remainder . what will be the remainder when 2 * n is divided by 4 ?
Options: a ) 8 , b ) 2 , c ) 6 , d ) 7 , e ) 1
Rationale: explanation : let n = 4 * q + 3 . then , 2 * n = 8 * q + 6 = 4 ( 2 * q + 1 ) + 2 . thus when 2 * n is divided by 4 , the reminder is 2 . answer : b ) 2
Answer: b
Problem: a person want to give his money of $ 2700 to his 3 children a , b , c in the ratio 2 : 3 : 4 . what is the b ' s share ?
Options: a ) $ 200 , b ) $ 900 , c ) $ 700 , d ) $ 600 , e ) $ 400
Rationale: "b ' s share = 2700 * 3 / 9 = $ 900 answer is b"
Answer: b
Problem: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 18 . the larger of the two numbers is :
Options: a ) 276 , b ) 414 , c ) 322 , d ) 345 , e ) 355
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 18 ) . larger number = ( 23 x 18 ) = 414 . answer : option b"
Answer: b
Problem: if 6 ^ k = 4 , then 6 ^ ( 2 k + 3 ) =
Options: a ) 2925 , b ) 3456 , c ) 4581 , d ) 3683 , e ) 1308
Rationale: 6 ^ k = 4 6 ^ 2 k = 4 ^ 2 6 ^ 2 k = 16 6 ^ ( 2 k + 3 ) = 6 ^ 2 k * 6 ^ 3 = 16 * 216 = 3456 answer : b
Answer: b
Problem: a can finish a work in 18 days and b can do the same work in half the time taken by a . then , working together , what part of the same work they can finish in a day ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 1 , e ) 1 / 4
Rationale: given that b alone can complete the same work in days = half the time taken by a = 9 days a ’ s one day work = 1 / 18 b ’ s one day work = 1 / 9 ( a + b ) ’ s one day work = 1 / 18 + 1 / 9 = 1 / 6 answer : b .
Answer: b
Problem: an empty fuel tank with a capacity of 212 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 98 , c ) 100 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 212 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 212 - a gallons of fuel b is 0.16 ( 212 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 212 - a ) = 30 - - > a = 98 . answer : b ."
Answer: b
Problem: the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams r ?
Options: a ) 16 , b ) r = 32 , c ) r = 64 , d ) 128 , e ) 512
Rationale: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"
Answer: b
Problem: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 2 women and 10 children take to complete the work ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10
Rationale: "1 women ' s 1 day work = 1 / 70 1 child ' s 1 day work = 1 / 140 ( 2 women + 10 children ) ' s 1 day work = ( 2 / 70 + 10 / 140 ) = 1 / 10 2 women and 10 children will complete the work in 10 days . e"
Answer: e
Problem: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 8 , b ) 8.5 , c ) 11 , d ) 9.5 , e ) 10
Rationale: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 8 80 360 9 90 450 10 100 550 11 110 660 it takes a total of nine hours to cover the 660 mile distance . answer : c . 11
Answer: c
Problem: how many integers are divisible by 2 between 10 ! and 10 ! + 20 inclusive ?
Options: a ) 6 , b ) 7 , c ) 21 , d ) 9 , e ) 10
Rationale: "c = 21 10 ! is divisible by 2 there are 20 numbers between 10 ! and 10 ! + 20 that are divisible by 1 . hence 21"
Answer: c
Problem: ramesh purchased a refrigerator for rs . 14500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 20350 , d ) 17600 , e ) 12778
Rationale: "price at which the tv set is bought = rs . 14,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 18125 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 18125 + 375 = rs . 18500 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 18500 * 110 / 100 = rs . 20350 answer : c"
Answer: c
Problem: if equation | x / 2 | + | y / 2 | = 4 encloses a certain region on the coordinate plane , what is the area of this region ?
Options: a ) 20 , b ) 50 , c ) 108 , d ) 200 , e ) 400
Rationale: the equation can be reduced to intercept form as | x / 8 | + | y / 8 | = 1 , so these are lines in four quadrants with x and y intercept as 8 , so it is a rhombus with diagonals of 16 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 16 * 16 = 108 . answer c .
Answer: c
Problem: let f ( x ) = x ^ 2 + bx + c . if f ( 6 ) = 0 and f ( - 1 ) = 0 , then b + c =
Options: a ) 18 , b ) 15 , c ) - 15 , d ) - 11 , e ) - 24
Rationale: "f ( x ) = x ^ 2 + bx + c . if f ( 6 ) = 0 and f ( - 1 ) = 0 , then b + c = f ( 6 ) = 0 = 36 + 6 b + c - - - taking 36 to the other side - > 6 b + c = - 36 f ( - 1 ) = 0 = 1 - b + c - - - taking - b + c to the other side - > b - c = 1 when we add these 2 equations , we get 7 b = - 35 - - - > b = - 5 and while substituting b = - 5 we get c = - 6 . b + c = - 11 - - - answer d"
Answer: d
Problem: approximately how many revolutions will be made by a car tire with a 13 - inch diameter if the car travels 1 ⁄ 2 mile ?
Options: a ) 120 , b ) 180 , c ) 772 , d ) 720 , e ) 1,440
Rationale: "diameter of car tire = 13 inches radius of car tire = 6.5 inches = 6.5 * 2.54 cm = 16.51 cm circumference of the car tire = 2 * pi * 16.51 = 2 * 3.14 * 16.51 = 103.68 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 103.68 = 771.60 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer c"
Answer: c
Problem: if x / y = 2 / 5 , then ( x + y ) / ( x - y ) = ?
Options: a ) 5 , b ) 1 / 5 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 7 / 3
Rationale: any x and y satisfying x / y = 2 / 5 should give the same value for ( x + y ) / ( x - y ) . say x = 2 and y = 5 , then ( x + y ) / ( x - y ) = ( 2 + 5 ) / ( 2 - 5 ) = - 7 / 3 . answer : e .
Answer: e
Problem: if the radius of a circle is increased by 60 % then the area is increased by :
Options: a ) 44 % , b ) 120 % , c ) 156 % , d ) 40 % , e ) none of the above
Rationale: "initially a = pi * r 2 now r 2 = 160 / 100 r then area = pi * ( 160 r / 100 ) 2 area = 256 r / 100 that is area increases from 100 to 256 = increase in area = 156 % answer : c"
Answer: c
Problem: a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter )
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24
Rationale: "back - solving is the best way to solve this problem . you basically need 12 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - b"
Answer: b
Problem: 10 binders can bind 1400 books in 21 days . how many binders will be required to bind 1800 books in 20 days ?
Options: a ) 87 , b ) 18 , c ) 17 , d ) 16 , e ) 12
Rationale: "binders books days 10 1400 21 x 1600 20 x / 10 = ( 1800 / 1400 ) * ( 21 / 20 ) = > x = 12 answer : e"
Answer: e
Problem: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 27 metre of cloth ?
Options: a ) 211 seconds , b ) 195 seconds , c ) 155 seconds , d ) 115 seconds , e ) 115 seconds
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 27 : x = > x = { \ color { blue } \ frac { 27 \ times 1 } { 0.128 } } = > x = 210.94 so time will be approx 211 seconds answer : a"
Answer: a
Problem: a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 11 % below the cost price of the claimed weight .
Options: a ) 19.81 % , b ) 22.38 % , c ) 37.5 % , d ) 25 % , e ) 37.5 %
Rationale: "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while selling , he sells 20 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 80 pounds and should have got only $ 80 for it . so this is again a mark up of $ 20 on $ 80 which is 25 % . but he also sells at 11 % less ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 89 / 100 = ( 1 + p % ) profit % = 22.38 % b"
Answer: b
Problem: the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 11 kmph ?
Options: a ) 21.23 , b ) 52.85 , c ) 23.26 , d ) 41.67 , e ) 25.15
Rationale: "distance covered in 1 min = ( 66 * 1000 ) / 60 = 183.33 cm circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 183.33 / 4.4 = 41.67 answer : d"
Answer: d