Cheukting/mathqa huggingface dataset:
Question (general): the units digit of ( 3 ) ^ ( 44 ) + ( 10 ) ^ ( 46 ) is :
Options: a ) 2 , b ) 4 , c ) 1 , d ) 8 , e ) 0
Rationale: "any power of anything ending in zero always has a units digit of 0 . so the first term has a units digit of 0 . the period is 4 . this means , 3 to the power of any multiple of 4 will have a units digit of 1 . 3 ^ 44 has a units digit of 1 . of course 0 + 1 = 1 c"
Answer: c
Question (general): if a ( a + 8 ) = 9 and b ( b + 8 ) = 9 , where a ≠ b , then a + b =
Options: a ) − 8 , b ) − 2 , c ) 2 , d ) 46 , e ) 48
Rationale: "a ( a + 8 ) = 9 = > we have a = 1 or - 9 also b ( b + 8 ) = 9 = > b = 1 or - 9 given a ≠ b 1 ) when a = 1 , b = - 9 and a + b = - 8 1 ) when a = - 9 , b = 1 and a + b = - 8 answer choice a"
Answer: a
Question (general): what is the thousandths digit in the decimal equivalent of 66 / 5000 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 5 , e ) 6
Rationale: "66 / 5000 = 66 / ( 5 * 10 ^ 3 ) = ( 66 / 5 ) * 10 ^ - 3 = 13.2 * 10 ^ - 3 = . 0132 thousandths digit = 3 answer c"
Answer: c
Question (physics): a contractor undertook to do a piece of work in 6 days . he employed certain number of laboures but 7 of them were absent from the very first day and the rest could finish the work in only 10 days . find the number of men originally employed ?
Options: a ) 17.2 , b ) 16.5 , c ) 17.5 , d ) 17.9 , e ) 17.3
Rationale: "let the number of men originally employed be x . 6 x = 10 ( x â € “ 7 ) or x = 17.5 answer c"
Answer: c
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 8 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 2 : 5 , 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 8 ounces in the ratio 1 : 3 or , x + 3 x = 8 gives x ( alcohol ) = 2 and remaining water = 6 mixing both we have alcohol = 4 + 2 and water = 8 + 6 ratio thus alcohol / water = 6 / 14 = 3 / 7 answer : b"
Answer: b
Question (geometry): the inside dimensions of a rectangular wooden box are 4 meters by 5 meters by 6 meters . a cylindrical drum is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces . of all such drums that could be used , what is the volume , in cubic meters , of the one that has maximum volume ?
Options: a ) 20 π
b ) 24 π
c ) 25 π
d ) 96 π
e ) 100 π
Rationale: you have three options here . approach is to calculate volumes for all of them and see which one is greatest . 1 . cylinder ' s base rests on a 4 x 5 side of the box . so , height becomes 6 and the maximum possible radius becomes 4 / 2 . so , maximum volume = π . ( 4 / 2 ) ^ 2.6 = π 24 2 . cylinder ' s base rests on a 5 x 6 side of the box . so , height becomes 4 and the maximum possible radius becomes 5 / 2 . so , maximum volume = π . ( 5 / 2 ) ^ 2.4 = π 25 3 . cylinder ' s base rests on a 4 x 6 side of the box . so , height becomes 5 and the maximum possible radius becomes 4 / 2 . so , maximum volume = π . ( 4 / 2 ) ^ 2.5 = π 20 option 2 gives maximum value and so that should be the answer , π 25 . answer : c
Answer: c
Question (general): there are some people in party , 1 / 3 rd left the party . then 2 / 5 th of the remaining left the party , then 2 / 3 rd of the remaining left the party . at last 10 were remaining . how many people were in total ?
Options: a ) 45 , b ) 27 , c ) 28 , d ) 26 , e ) 75
Rationale: "sol : 45 if x persons were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 10 x × 2 / 3 × 3 / 5 × 1 / 3 = 10 x = 75 answer : e"
Answer: e
Question (other): the hcf of two numbers is 40 and the other two factors of their lcm are 11 and 12 . what is the largest number .
Options: a ) 462 , b ) 450 , c ) 488 , d ) 480 , e ) 555
Rationale: "explanation : hcf of the two numbers = 40 hcf will be always a factor of lcm 40 is factor of lcm other two factors are 11 & 12 then the numbers are ( 40 * 11 ) and ( 40 x 12 ) = 440 and 480 answer : option d"
Answer: d
Question (gain): bert and rebecca were looking at the price of a condominium . the price of the condominium was 110 % more than bert had in savings , and separately , the same price was also 20 % 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 : 5 , b ) 1 : 4 , c ) 2 : 3 , d ) 4 : 7 , e ) 1 : 2
Rationale: "suppose bert had 100 so price becomes 210 , this 210 = 1.2 times r ' s saving . . so r ' s saving becomes 175 so required ratio is 100 : 175 = 4 : 7 answer : d"
Answer: d
Question (gain): at what rate percent on simple interest will rs . 800 amount to rs . 950 in 5 years ?
Options: a ) 3.75 % , b ) 5.93 % , c ) 4.75 % , d ) 5.33 % , e ) 6.33 %
Rationale: "150 = ( 800 * 5 * r ) / 100 r = 3.75 % answer : a"
Answer: a
Question (general): in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 115 ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 115 5 x - 20 = 115 5 x = 135 x = 27 the answer is c ."
Answer: c
Question (general): the length of 3 ropes are in the ratio 4 : 5 : 6 . if the sum of the weights of the longest and the shortest rope is 100 metres more than the length of the third rope , what is the length of the shortest rope ?
Options: a ) 80 m , b ) 180 m , c ) 100 m , d ) 60 m , e ) of these
Rationale: let the lengths of the three ropes be 4 k , 5 k and 6 k respectively . 4 k + 6 k = 5 k + 100 = > 5 k = 100 = > k = 20 therefore the weight of the lightest boy = 4 k = 4 ( 20 ) = 80 m answer : a
Answer: a
Question (probability): on a ranch , a rancher can place a loop of rope , called a lasso , once in every 2 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 6 attempts ?
Options: a ) 3 / 4 , b ) 7 / 8 , c ) 15 / 16 , d ) 31 / 32 , e ) 63 / 64
Rationale: "p ( missing all 6 ) = ( 1 / 2 ) ^ 6 = 1 / 64 p ( success on at least one attempt ) = 1 - 1 / 64 = 63 / 64 the answer is e ."
Answer: e
Question (physics): two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 50 hr . if all pipes are opened simultaneously , then the cistern will be filled in
Options: a ) 6.12 hr , b ) 8 hr , c ) 8.5 hr , d ) 10 hr , e ) none of these
Rationale: solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 50 = 8 / 49 hence , tank will be filled in 49 / 8 = 6.12 hour option ( a )
Answer: a
Question (general): 9 people decided to split the restaurant bill evenly . if the bill was $ 514.16 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 514.16 , b ) $ 514.17 , c ) $ 514.18 , d ) $ 514.19 , e ) $ 514.20
Rationale: "this is equivalent to finding the first number that is divisible by 9 that occurs after 51416 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 51416 = 17 and 18 is divisible by 9 . hence , we need to add 1 to this number for it to be divisible by 9 correct option : b"
Answer: b
Question (physics): a certain car increased its average speed by 5 miles per hour in each successive 5 - minute interval after the first interval . if in the first 5 - minute interval its average speed was 26 miles per hour , how many miles did the car travel in the third 5 - minute interval ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: in the third time interval the average speed of the car was 22 + 5 + 5 = 36 miles per hour ; in 5 minutes ( 1 / 12 hour ) at that speed car would travel 36 * 1 / 12 = 3 miles . answer : e .
Answer: e
Question (probability): there are 13 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl & 2 boys are selected ?
Options: a ) 120 , b ) 480 , c ) 780 , d ) 720 , e ) 800
Rationale: n ( s ) = sample space = 23 c 3 = 1771 e = event that 1 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 13 and 1 girl from 10 = 13 c 2 * 10 c 1 = 780 ans - c
Answer: c
Question (general): the grade point average of the entire class is 84 . if the average of one fourth of the class is 96 , what is the average of the rest of the class ?
Options: a ) 76 , b ) 77 , c ) 78 , d ) 79 , e ) 80
Rationale: "let x be the number of students in the class . let p be the average of the rest of the class . 84 x = ( 1 / 4 ) 96 x + ( 3 / 4 ) ( p ) x 336 = 96 + 3 p 3 p = 240 p = 80 . the answer is e ."
Answer: e
Question (general): the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.2 kg . the weight of the new student is ?
Options: a ) 1 kg , b ) 10.8 kg , c ) 11 kg , d ) 14.9 kg , e ) none
Rationale: "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.2 - 19 x 15 ) kg = 1 kg . correct option : a"
Answer: a
Question (other): if a student loses 6 kilograms , he will weigh twice as much as his sister . together they now weigh 132 kilograms . what is the student ' s present weight in kilograms ?
Options: a ) 82 , b ) 84 , c ) 86 , d ) 88 , e ) 90
Rationale: "let x be the weight of the sister . then the student ' s weight is 2 x + 6 . x + ( 2 x + 6 ) = 132 3 x = 126 x = 42 kg then the student ' s weight is 90 kg . the answer is e ."
Answer: e
Question (general): an ant walks an average of 600 meters in 10 minutes . a beetle walks 25 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?
Options: a ) 2.215 . , b ) 2.5 . , c ) 2.6 , d ) 2.7 , e ) 3.5 .
Rationale: "the ant walks an average of 600 meters in 10 minutes 600 meters in 5 / 30 hours the beetle walks 25 % less distance = 600 - 150 = 450 meters in 10 minutes 0.450 km in 5 / 30 = 5 / 30 hours speed = 0.450 * 30 / 5 = 2.7 km / h i guess option d should be 2.7"
Answer: d
Question (geometry): the width of a rectangular hall is ½ of its length . if the area of the hall is 578 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m
Rationale: "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 578 = x * 1 x / 2 x ² = 1156 x = 34 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 34 / 2 = 17 m answer : e"
Answer: e
Question (physics): how long does a train 165 meters long running at the rate of 90 kmph take to cross a bridge 660 meters in length ?
Options: a ) 28 , b ) 27 , c ) 33 , d ) 18 , e ) 12
Rationale: "t = ( 660 + 165 ) / 90 * 18 / 5 t = 33 answer : c"
Answer: c
Question (physics): a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of man is
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none
Rationale: "solution volume of water displaced = ( 3 x 2 x 0.01 ) m 3 = 0.06 m 3 . mass of man = volume of water displaced × density of water = ( 0.06 × 1000 ) kg = 60 kg . answer b"
Answer: b
Question (probability): how many different pairs of numbers ( s , t ) such that s = 3 t can be obtained if s and t are selected from the set of number { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: given s = 3 t t can take 0,1 , 2,3 , 4 and so s = 0,3 , 6,9 , 12 4 such pairs can be formed . answer e
Answer: e
Question (gain): in one alloy there is 10 % chromium while in another alloy it is 8 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 9.0 % , b ) 9.4 % , c ) 9.2 % , d ) 8.8 % , e ) 8.6 %
Rationale: "the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.10 * 15 + 0.08 * 35 = 4.3 kg , so the percentage is 4.3 / 50 * 100 = 8.6 % . answer : e ."
Answer: e
Question (general): on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 80,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "x - interest rate 80.000 = 10.000 ( 1 + x ) ^ year = > 8 = ( 1 + x ) ^ year 40.000 = 10.000 . ( 1 + x ) ^ 12 = > 4 = ( 1 + x ) ^ 12 = > 2 = ( 1 + x ) ^ 6 = > 8 = ( 1 + x ) ^ 18 so , after 18 years , the total value of the investment plus interest will increase to $ 80,000 . answer : c"
Answer: c
Question (general): in a river flowing at 2 km / hr , a boat travels 32 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .
Options: a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 16 hours , e ) none of these
Rationale: "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 32 km total time taken = time taken downstream + time taken upstream = ( 32 / 8 ) + ( 32 / 4 ) = ( 32 / 8 ) + ( 64 / 8 ) = ( 96 / 8 ) = 12 hr . answer : option b"
Answer: b
Question (general): a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 66 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?
Options: a ) 16 , b ) 20 , c ) 36 , d ) 44 , e ) 48
Rationale: "lets say x ounces of p is mixed with q . = > 66 - x ounces of q is present in the mixture ( as the total = 66 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 66 - x ) = 15 = > x = 30 = > 66 - 30 = 36 ounces of q is present in the mixture . answer is c ."
Answer: c
Question (general): what is the units digit of ( 6 ! * 4 ! + 6 ! * 5 ! ) / 6 ?
Options: a ) 1 , b ) 0 , c ) 2 , d ) 3 , e ) 4
Rationale: ( 6 ! * 4 ! + 6 ! * 5 ! ) / 6 = 6 ! ( 4 ! + 5 ! ) / 6 = 720 ( 24 + 120 ) / 6 = ( 720 * 144 ) / 6 = 720 * 24 units digit of the above product will be equal to 0 answer b
Answer: b
Question (other): 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 8 integers , y consists of 10 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 ) 22 , d ) 30 , e ) 174
Rationale: "the number of integers that belong to set x only is 8 - 6 = 2 ; the number of integers that belong to set y only is 10 - 6 = 4 ; the number of integers that belong to set x or set y , but not both is 2 + 4 = 6 . answer : a ."
Answer: a
Question (general): the mean of 50 observations was 36 . it was found later that an observation 48 was wrongly taken as 21 . the corrected new mean is :
Options: a ) 36.54 , b ) 36.58 , c ) 36.23 , d ) 36.14 , e ) 36.81
Rationale: "explanation : correct sum = ( 36 * 50 + 48 - 21 ) = 1827 . correct mean = = 1827 / 50 = 36.54 answer : a ) 36.54"
Answer: a
Question (physics): if an object travels at ten feet per second , how many feet does it travel in two hours ?
Options: a ) 60000 , b ) 30000 , c ) 18000 , d ) 72000 , e ) 22200
Rationale: "if an object travels at 10 feet per second it covers 10 x 60 feet in one minute , and 10 x 60 x 2 x 60 feet in two hour . answer = 72000 answer : d"
Answer: d
Question (physics): 3 medical experts , working together at the same constant rate , can write an anatomy textbook in 24 days . how many additional experts , working together at this same constant rate , are needed to write the textbook in 18 days ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: each expert can write 1 / 72 of the book per day . to complete the book in 18 days , we need 72 / 18 = 4 experts , thus 1 more expert is needed . the answer is a .
Answer: a
Question (general): the value of ( 34.31 * 0.473 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.05 , d ) 2.15 , e ) 2.35
Rationale: "( 34.31 * 0.473 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) = 25.4303 / 11.845 = 2.15 answer : d"
Answer: d
Question (physics): the cost of carpeting a room 15 meters long with a carpet 75 cm wide at 30 paise per meter is rs . 36 . the breadth of the room is ?
Options: a ) 6 meters , b ) 7 meters , c ) 8 meters , d ) 9 meters , e ) 10 meters
Rationale: "length of carpet = total cost / rate = 3600 / 30 = 120 m area of carpet = ( 120 x 75 ) / 100 m 2 = 90 m 2 ∴ area of the room = 90 m 2 breadth of the room = area / length = 90 / 15 m = 6 m answer : a"
Answer: a
Question (physics): an aeroplane covers a certain distance of 590 kmph in 8 hours . to cover the same distance in 2 3 / 4 hours , it must travel at a speed of
Options: a ) 1780 , b ) 1716 , c ) 1890 , d ) 1980 , e ) 1450
Rationale: speed of aeroplane = 590 kmph distance travelled in 8 hours = 590 * 8 = 4720 km speed of aeroplane to acver 4720 km in 11 / 4 = 4720 * 4 / 11 = 1716 km answer b .
Answer: b
Question (physics): a work can be completed by 12 boys in 24 days and 12 girls in 12 days . in how many days would the 6 boys and 6 girls working together complete the work ?
Options: a ) 12 , b ) 18 , c ) 16 , d ) 20 , e ) 24
Rationale: in 1 day , 12 boys does 1 / 24 of the total work . = > in 1 day , 1 boy does 1 / ( 24 * 12 ) of the total work = > in 1 days , 6 boys do 6 / ( 24 * 12 ) = 1 / 48 of the total work in 1 day , 12 girls do 1 / 12 of the total work . = > in 1 day , 1 girl does 1 / ( 12 * 12 ) of the total work = > in 1 day , 6 girls do 6 / ( 12 * 12 ) = 1 / 24 of the total work in 1 day , 6 boys and 6 girls do 1 / 48 + 1 / 24 of the total work = > in 1 days , 6 boys and 6 girls do 3 / 48 = 1 / 16 of the total work so , 6 boys and 6 girls complete all work in 16 days . hence , the answer is c
Answer: c
Question (physics): walking at 75 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 72
Rationale: "speed is inversly proprtional to time walking at 75 % of speed meand 3 / 4 s takes 4 / 3 t . it takes 24 minutes extra to cover the distance . then 4 / 3 t = t + 24 4 t = 3 t + 72 t = 72 option e is correct"
Answer: e
Question (physics): anusha , banu and esha run a running race of 100 meters . anusha is the fastest followed by banu and then esha . anusha , banu and esha maintain constant speeds during the entire race . when anusha reached the goal post , banu was 10 m behind . when banu reached the goal post esha was 10 m behind . how far was behind anusha when the latter reached the goal post .
Options: a ) 22 , b ) 88 , c ) 81 , d ) 66 , e ) 22
Rationale: by that time anusha covered 100 m , bhanu covered 90 m . so ratio of their speeds = 10 : 9 by that time bhanu reached 100 m , esha covered 90 m . so ratio of their speeds = 10 : 9 ratio of the speed of all the three = 100 : 90 : 81 by that time anusha covered 100 m , esha covers only 81 . answer : c
Answer: c
Question (general): the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 30 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: "the original output increases by 10 % and then 30 % . total % change = a + b + ab / 100 total % change = 10 + 30 + 10 * 30 / 100 = 43 % now , you want to change it to 0 , so , 0 = 43 + x + 43 x / 100 x = - 43 ( 100 ) / 143 = 30 % approximately answer is c"
Answer: c
Question (gain): if the cost price is 89 % of selling price then what is the profit percentage .
Options: a ) 8.35 , b ) 9.35 , c ) 10.35 , d ) 11.35 , e ) 12.35
Rationale: "selling price = rs 100 : then cost price = rs 89 : profit = rs 11 . profit = { ( 11 / 89 ) * 100 } % = 12.35 % answer is e ."
Answer: e
Question (general): the rate of interest on a sum of money is 2 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occured on the sum for the total period of 8 years is rs . 540 / - , the sum is
Options: a ) 2,200 , b ) 2,000 , c ) 2,100 , d ) 2,250 , e ) 2,560
Rationale: "explanation : i 1 = ( p x 3 x 2 ) / 100 = 3 p / 50 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 3 p / 50 + 4 p / 25 + p / 20 = 540 the l . c . m of 50 , 25 , 20 = 100 ( 6 p + 16 p + 5 p ) / 100 = 540 27 p / 100 = 540 27 p = 54000 p = 54000 / 27 p = 2000 answer : option b"
Answer: b
Question (gain): at what rate percent per annum will the simple interest on a sum of money be 7 / 5 of the amount in 10 years ?
Options: a ) 4 % , b ) 7 % , c ) 9 % , d ) 3 % , e ) 14 %
Rationale: "let sum = x . then , s . i . = 7 x / 5 , time = 10 years . rate = ( 100 * 7 x ) / ( x * 5 * 10 ) = 14 % answer : e"
Answer: e
Question (physics): two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 2.9 km and 1.6 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 99 , b ) 277 , c ) 48 , d ) 96 , e ) 108
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 2.9 + 1.6 = 4.5 km = 4500 m . required time = 4500 * 3 / 125 = 108 sec . answer : e"
Answer: e
Question (geometry): the edge of a cube is 3 a cm . find its surface ?
Options: a ) 24 a 8 , b ) 24 a 4 , c ) 24 a 1 , d ) 54 a 2 , e ) 24 a 7
Rationale: "6 a 2 = 6 * 3 a * 3 a = 54 a 2 answer : d"
Answer: d
Question (general): how many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit ?
Options: a ) 1339 , b ) 2300 , c ) 4200 , d ) 1340 , e ) 2414
Rationale: "there is one number in hundred with 2 in th tens digit and 1 in the units digit : 21 , 121 , 221 , 321 , . . . the difference between 324,700 and 458,600 is 458,600 - 324,700 = 133,900 - one number per each hundred gives 133,900 / 100 = 1,339 numbers . answer : 1,339 a"
Answer: a
Question (other): in a graduating class of 242 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 123
Rationale: "greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 242 = 21 greatest - smallest is 144 - 21 = 123 so answer must be e . 123"
Answer: e
Question (general): the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 95 . find the number of students who wrote the exam .
Options: a ) 15 , b ) 45 , c ) 35 , d ) 25 , e ) 55
Rationale: let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 95 ( x - 5 ) 80 x - ( 5 * 20 ) = 95 ( x - 5 ) 375 = 15 x = > x = 25 answer : d
Answer: d