Cheukting/mathqa huggingface dataset:
Question (geometry): a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 7 per sq m ?
Options: a ) 4350 , b ) 4725 , c ) 4328 , d ) 4329 , e ) 4829
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 7 = rs . 4725 answer : b"
Answer: b
Question (general): of 40 applicants for a job , 24 had at least 4 years ' experience , 15 had degrees , and 4 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 3 , c ) 9 , d ) 7 , e ) 5
Rationale: "set a : people with more than 4 years exp set b : people with degree aub = total - ( less than 4 exp and no degree ) aub = 40 - 4 = 36 aub = a + b - aib aib = 15 + 24 - 36 = 3 answer b"
Answer: b
Question (general): what is the sum of all the multiples of 3 between 30 and 80 ?
Options: a ) 2103 , b ) 2106 , c ) 1053 , d ) 1252 , e ) 1535
Rationale: "you first have to know all the multiples of 3 between 30 and 80 . they are 3 , 6,9 , 12,15 , 18,21 , 24,27 , 30,33 , 36,39 , 42,45 , 48,51 , 54,57 , 60,63 , 66,69 , 72,75 , and 78 . if you add all these numbers together , you get 1053 . final answer : c"
Answer: c
Question (gain): the first half of the 20 th century , the population of a particular country increased by 200 percent . in the second half of the century , the population increased by 300 percent . what was the percent increase for the 20 th century as a whole ?
Options: a ) 500 % , b ) 600 % , c ) 800 % , d ) 1100 % , e ) 1200 %
Rationale: say initially population was 100 . what is 200 % of 100 ? it is 200 / 100 * 100 = 200 . an increase of 200 % means the new population became 100 + 200 = 300 what is 300 % of 300 ? it is 300 / 100 * 300 = 900 an increase of 300 % means the new population now is 300 + 900 = 1200 so from 100 , the population increased to 1200 i . e . an increase of 1100 . 1100 is what percent of 100 ? 1100 = x / 100 * 100 i . e . it is 1100 % d
Answer: d
Question (general): at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 60 . if the restaurant serves 120 customers today , raising the average to 70 customers per day , what is the value of x ?
Options: a ) 2 , b ) 5 , c ) 9 , d ) 15 , e ) 30
Rationale: "withoutusing the formula , we can see that today the restaurant served 50 customers above the average . the total amount above the average must equal total amount below the average . this additional 50 customers must offset the “ deficit ” below the average of 70 created on the x days the restaurant served only 60 customers per day . 50 / 10 = 5 days . choice ( a ) . withthe formula , we can set up the following : 70 = ( 60 x + 120 ) / ( x + 1 ) 70 x + 70 = 60 x + 120 10 x = 50 x = 5 answer choice ( b )"
Answer: b
Question (other): 100 students appeared in 2 tests . 60 students passed 1 st test . 40 students passed in the 2 nd test . 20 students passed in both 1 and 2 tests . what is the probability of the students who failed in both tests ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: 20 student passed both two test 40 student passed only 1 st test 20 student passed only 2 nd test so 100 - ( 20 + 40 + 20 ) = 20 student failed in both sub so ans is 20 % answer : c
Answer: c
Question (general): how many 3 - digit even numbers are possible such that if one of the digits is 5 , the next / succeeding digit to it should be 6
Options: a ) 5 , b ) 305 , c ) 365 , d ) 405 , e ) 495
Rationale: 560 , 562 , 564 , 566 , and 568 , so total 5 . hence option a .
Answer: a
Question (general): there has been successive increases of 30 % and then 20 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 20 % , b ) 24 % , c ) 28 % , d ) 32 % , e ) 36 %
Rationale: "let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.2 * 1.3 * p = x * p y = x / ( 1.2 * 1.3 ) which is about 0.64 x which is a decrease of about 36 % . the answer is e ."
Answer: e
Question (physics): a train speeds past a pole in 50 seconds and a platform 500 m long in 100 seconds . its length is :
Options: a ) 550 m . , b ) 300 m . , c ) 600 m . , d ) 400 m . , e ) 500 m .
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 50 = > y = x / 50 x + 500 / 100 = x / 50 x = 500 m . answer : option e"
Answer: e
Question (general): if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 24 - m ) then m = ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "2 m = 24 - m 3 m = 24 m = 8 the answer is b ."
Answer: b
Question (general): a seller of used cars has 16 cars to sell and each of his clients selected 2 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 24
Rationale: ifno caris selected more than once then the number of clients = 16 / 2 = 8 but since every car is being selected three times so no . of clients must be thrice as well = 8 * 3 = 24 answer : option e
Answer: e
Question (other): two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 9 : 17 . the first number is ?
Options: a ) 36 , b ) 76 , c ) 98 , d ) 27 , e ) 24
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 9 : 17 x = 12 = > 3 x = 36 answer : a"
Answer: a
Question (general): the smallest fraction , which each of 6 / 7 , 5 / 14 , 10 / 21 will divide exactly is ?
Options: a ) 30 / 7 , b ) 30 / 9 , c ) 30 / 2 , d ) 30 / 3 , e ) 30 / 6
Rationale: "required fraction = l . c . m of 6 / 7 , 5 / 14 , 10 / 21 = ( l . c . m of 6 , 5 , 10 ) / ( h . c . f of 7 , 14 , 21 ) = 30 / 7 answer : a"
Answer: a
Question (gain): a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 40 % lemonade syrup ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.14 , d ) 2.34 , e ) 2.64
Rationale: "let the total solution is 150 l with 80 l water & 70 l syrup . to make 40 % syrup solution , the result solution must have 90 l syrup and 60 l syrup . therefore we are taking 10 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 10 l syrup in 21.4 l solution we started by multiplying 10 now to get to the result we need to divide by 10 = > amount of solution to be replaced with water = ( 21.4 / 10 ) = 2.14 . correct option : c"
Answer: c
Question (gain): the length of a rectangular floor is more than its breadth by 200 % . if rs . 640 is required to paint the floor at the rate of rs . 5 per sq m , then what would be the length of the floor ?
Options: a ) 19.6 m . , b ) 20.0 m . , c ) 19.3 m . , d ) 18.5 m . , e ) 18.9 m .
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 3 b = 3 b area of the floor = 640 / 5 = 128 sq m l b = 128 i . e . , l * l / 3 = 128 l 2 = 384 = > l = 19.6 m . answer : a"
Answer: a
Question (gain): a reduction of 15 % in the price of wheat enables a house wife to obtain 3 kgs more for rs . 500 , what is the reduced price for kg ?
Options: a ) rs . 10 , b ) rs . 15 , c ) rs . 20 , d ) rs . 25 , e ) rs . 30
Rationale: explanation : 500 * ( 15 / 100 ) = 75 - - - - 3 ? - - - - 1 = > rs . 25 answer : d
Answer: d
Question (other): in a certain corporation , there are 300 male employees and 150 female employees . it is known that 20 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 7 / 15 , b ) 3 / 10 , c ) 3 / 5 , d ) 2 / 5 , e ) 3 / 4
Rationale: "p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.2 * 300 / 450 = 60 / 450 = 2 / 15 the sum of the probabilities is 7 / 15 the answer is a ."
Answer: a
Question (general): the ration of the father ’ s age to his son ’ s age is 7 : 3 . the product of their ages is 756 . the ratio of their ages after 6 years will be :
Options: a ) 5 : 2 , b ) 2 : 1 , c ) 11 : 7 , d ) 13 : 9 , e ) none of these
Rationale: solution let the present ages of the father and son be 7 x and 3 x years respectively . then , 7 x 3 x = 756 ⇔ 21 x 2 = 756 ⇔ x 2 = 36 ⇔ x = 6 . ∴ required ratio = ( 7 x + 6 ) : ( 3 x + 6 ) = 48 : 24 = 2 : 1 . answer b
Answer: b
Question (gain): at a certain university , 68 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?
Options: a ) 25 , b ) 37.5 , c ) 55 , d ) 62.5 , e ) 75
Rationale: total women = 68 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 22 % but question wants to know the percent of men that are tenured 22 % / 40 % = 55 % c
Answer: c
Question (physics): how many times are the hands of a clock at right angles in a day ?
Options: a ) 42 , b ) 44 , c ) 49 , d ) 41 , e ) 47
Rationale: in 12 hours , they are at right angles 22 times . = = > in 24 hours , they are at right angles 44 times . answer is b .
Answer: b
Question (physics): a cyclist traveled for two days . on the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day . if during the two days she traveled a total of 240 miles and spent a total of 12 hours traveling , what was her average speed on the second day ?
Options: a ) 5 mph , b ) 10 mph , c ) 20 mph , d ) 30 mph , e ) 40 mph
Rationale: solution : d = 280 mi t = 12 hrs đ â y 1 time = t 1 d â y 2 time = t 2 t 2 - t 1 = 4 hrs - - - - - ( i ) t 1 + t 2 = 12 hrs - - - - - ( ii ) adding i and ii , t 2 = 8 hrs and t 1 = 4 hrs d à y 1 rate = r 1 d â y 2 rate = r 2 r 1 - r 2 = 10 mph í . ẹ . r 1 = 10 + r 2 280 = 8 r 2 + 4 r 1 í . ẹ . 280 = 8 r 2 + 4 ( 10 + r 2 ) í . ẹ . r 2 = 20 mph answer : b
Answer: b
Question (physics): a is twice as good as workman as b and together they finish a piece of work in 18 days . in how many days will b alone finish the work .
Options: a ) 27 days , b ) 54 days , c ) 56 days , d ) 68 days , e ) none of these
Rationale: explanation : as per question , a do twice the work as done by b . so a : b = 2 : 1 also ( a + b ) one day work = 1 / 18 to get days in which b will finish the work , lets calculate work done by b in 1 day = = ( 118 ∗ 13 ) = 154 [ please note we multiplied by 1 / 3 as per b share and total of ra ɵ o is 1 / 3 ] so b will finish the work in 54 days answer : b
Answer: b
Question (general): in the xy - coordinate system , what is the slope of the line that goes through the origin and is equidistant from the two points p = ( 4 , 6 ) and q = ( 6 , 2 ) ?
Options: a ) 0.8 , b ) 1.0 , c ) 1.2 , d ) 1.4 , e ) 1.6
Rationale: first , get the middle coordinate between ( 46 ) and ( 62 ) . x = 4 + ( 6 - 4 ) / 2 = 5 y = 2 + ( 6 - 2 ) / 2 = 4 second , get the slope of ( 54 ) and ( 00 ) . m = 4 - 0 / 5 - 0 = 4 / 5 = 0.8 answer : a
Answer: a
Question (gain): an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 15 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 80.00
Rationale: "without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 23 % , thus he must pay slightly more than $ 77 . answer : e ."
Answer: e
Question (geometry): the perimeter of a rectangle is 60 mete ( 132 ) 7 × ( 132 ) ? = ( 132 ) 11.5 .
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "7 + x = 11.5 x = 11.5 - 7 x = 4.5 answer : d"
Answer: d
Question (general): the youngest of 4 children has siblings who are 3 , 5 , and 8 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 21 , what is the age of the youngest sibling ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 21 , e ) 22
Rationale: "total age of the 4 sibling is 21 x 4 = 84 years . . we already have the total age of all the children is 4 y + 16 so , 4 y + 16 = 84 or , 4 y = 68 or , y = 17 so , age of the youngest child is 17 years . answer : a"
Answer: a
Question (physics): a can do a piece of work in 15 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 2 days and b leaves after 4 days from the beginning . how long will work lost ?
Options: a ) 15 , b ) 10 , c ) 12 , d ) 11 , e ) 13
Rationale: "2 / 15 + 4 / 15 + x / 20 = 1 x = 12 answer : c"
Answer: c
Question (physics): the speed of a boat in still water is 36 kmph . what is the speed of the stream if the boat can cover 80 km downstream or 40 km upstream in the same time ?
Options: a ) 10 kmph , b ) 14 kmph , c ) 12 kmph , d ) 16 kmph , e ) 15 kmph
Rationale: "x = the speed of the stream ( 36 + x ) / ( 36 - x ) = 2 / 1 36 + x = 72 - 2 x 3 x = 36 x = 12 km / hour if the speed of the stream is 12 km / hour , then the ' downstream ' speed of the boat is 36 + 12 = 48 km / hour and the ' upstream ' speed of the boat is 36 - 12 = 24 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 48 = 96 km downstream and 2 x 24 = 48 km / hour upstream . answer : c"
Answer: c
Question (gain): a man buys a cycle for rs . 1800 and sells it at a loss of 10 % . what is the selling price of the cycle ?
Options: a ) 1410 , b ) 1620 , c ) 1430 , d ) 1440 , e ) 1540
Rationale: "s . p . = 90 % of rs . 1800 = 90 / 100 x 1800 = rs . 1620 answer : b"
Answer: b
Question (general): if n divided by 11 has a remainder of 1 , what is the remainder when 5 times n is divided by 11 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 9 , e ) 5
Rationale: "as per question = > n = 11 p + 1 for some integer p hence 5 n = > 55 q + 5 = > remainder = > 5 for some integer q hence e"
Answer: e
Question (geometry): an artist wishes to paint a circular region on a square poster that is 3.4 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ?
Options: a ) 1 / pi
b ) sqrt ( 2 / pi )
c ) 1
d ) 2 / sqrt ( pi )
e ) sqrt ( 5.78 / pi )
Rationale: area of the poster is 3.4 x 3.4 = 11.56 1 / 2 the area = 5.78 pi * r ^ 2 = 5.78 r ^ 2 = 5.78 / pi r = sqrt ( 5.78 / pi ) answer ( e )
Answer: e
Question (general): the value of ( 34.31 * 0.473 * 1.567 ) / ( 0.0673 * 23.5 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.05 , d ) 2.12 , e ) 2.35
Rationale: "( 34.31 * 0.473 * 1.567 ) / ( 0.0673 * 23.5 * 7.57 ) = 25.4303 / 11.972 = 2.12 answer : d"
Answer: d
Question (general): a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 47 , then how old is b ?
Options: a ) 17 years , b ) 19 years , c ) 18 years , d ) 10 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 47 5 x = 45 = > x = 9 hence , b ' s age = 2 x = 18 years . answer : c"
Answer: c
Question (general): find the value of 658217 x 99999 = m ?
Options: a ) 65842158943 , b ) 65839570421 , c ) 65821141683 , d ) 66821785904 , e ) 65821041783
Rationale: "658217 x 99999 = 658217 x ( 100000 - 1 ) = 658217 x 100000 - 658217 x 1 = 65821700000 - 658217 = 65821041783 e"
Answer: e
Question (general): a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1251 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 139
Rationale: "let the required number be x . then , 43 x – 34 x = 1251 or 9 x = 1251 or x = 139 . required number = 139 . answer : e"
Answer: e
Question (general): calculate the largest 6 digit number which is exactly divisible by 55 ?
Options: a ) 999955 , b ) 999900 , c ) 999845 , d ) 999790 , e ) 999735
Rationale: "largest 4 digit number is 999999 after doing 999999 ÷ 55 we get remainder 44 hence largest 4 digit number exactly divisible by 88 = 999999 - 44 = 999955 a"
Answer: a
Question (general): 10 years ago , the age of peter was one - third the age of jacob at that time . the present age of jacob is 12 years more than the present age of peter . find the present age of peter ?
Options: a ) 15 , b ) 11 , c ) 18 , d ) 16 , e ) 20
Rationale: d 16 let the present ages of peter and jacob be ' a ' and ' b ' respectively . a - 10 = 1 / 3 ( b - 10 ) - - - ( 1 ) b = a + 12 substituting b = a + 12 in first equation , a - 10 = 1 / 3 ( a + 2 ) = > 3 a - 30 = a + 2 = > 2 a = 32 = > a = 16 .
Answer: d
Question (general): at a supermarket , john spent 1 / 2 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 8 on candy , how much did john spend at the supermarket ?
Options: a ) $ 60 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 180
Rationale: let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 2 of his money on fresh fruits and vegetables , or ( 1 / 2 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 8 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 2 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 8 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 240 = 30 t 28 t + 240 = 30 t 240 = 2 t t = 120 john spent $ 90 at the supermarket . answer : d
Answer: d
Question (general): tough and tricky questions : exponents . if 5 ^ ( x + 1 ) * 4 ^ ( y - 1 ) = 25 ^ x * 64 ^ y , then x + y =
Options: a ) 3 / 2 , b ) - 1 / 2 , c ) - 1 , d ) 1 / 2 , e ) 2 / 3
Rationale: here is my solution . 5 ^ ( x + 1 ) * 4 ^ ( y - 1 ) = 25 ^ x * 64 ^ y here rhs 25 ^ x * 64 ^ y = 5 ^ ( 2 x ) * 4 ^ ( 3 y ) equating powers on both sides - - > x + 1 = 2 x , thus x = 1 and 2 y - 1 = 3 y giving y = - 1 / 2 so , x + y = 1 / 2 option : d
Answer: d
Question (general): what is the remainder of e = 3 ^ 19 when divided by 10 ?
Options: a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9
Rationale: i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , e = when divided by 10 , the remainder must be 7 . d
Answer: d
Question (geometry): what no should be subtracted from 92555 to make it a perfect square ?
Options: a ) 128
b ) 158
c ) 178
d ) 139
e ) 140
Rationale: root 92555 = 304.228 and 304 ^ 2 = 92416 92555 - 92416 = 139 should be subtracted from 92555 to make it a perfect square answer : d
Answer: d
Question (geometry): a hall is 6 meters long and 6 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?
Options: a ) 96 , b ) 100 , c ) 104 , d ) 108 , e ) 112
Rationale: "2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 108 the answer is d ."
Answer: d
Question (gain): the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 6 . the true discount is
Options: a ) rs . 72 , b ) rs . 36 , c ) rs . 54 , d ) rs . 50 , e ) none
Rationale: "solution t . d = [ b . g x 100 / r x t ] = rs . ( 6 x 100 / 12 x 1 ) = rs . 50 . answer d"
Answer: d
Question (general): a line has a slope of 3 / 4 and intersects the point q ( - 12 , - 39 ) . at which point does this line intersect the x - axis ?
Options: a ) ( 40,0 ) , b ) ( 30,0 ) , c ) ( 0,40 ) , d ) ( 40,30 ) , e ) ( 0,30 )
Rationale: "assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point q of intersection is ( 40,0 ) . a is the correct answer ."
Answer: a
Question (general): a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 80 points . to the nearest tenth of a point , what was the student ’ s average grade for the entire two - year period ?
Options: a ) 79 , b ) 89 , c ) 95 , d ) 90.91 , e ) 97.2
Rationale: let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 80 * 5 = 400 student ' s average = ( 600 + 400 ) / 11 = 90.91 answer d
Answer: d
Question (general): 8.008 / 2.002
Options: a ) 0.004 , b ) 0.04 , c ) 4 , d ) 40 , e ) 400
Rationale: "answer is 4 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 8008 / 2002 = 4 answer c"
Answer: c
Question (geometry): the number 86 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "7 ^ 2 + 6 ^ 2 + 1 ^ 2 = 49 + 36 + 1 = 86 7 + 6 + 1 = 14 hence answer is d"
Answer: d
Question (physics): a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 50 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 54 , e ) 60
Rationale: "a - b = 120 miles b - c = 60 miles avg speed = 50 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 50 = 180 / 4 t t = 54 b - c = 54 mph answer d"
Answer: d
Question (gain): a 14 % stock yielding 10 % is quoted at :
Options: a ) 83.33 , b ) 110 , c ) 112 , d ) 140 , e ) 160
Rationale: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 14 , money invested = rs . ( 100 / 10 x 14 ) = rs . 140 . â ˆ ´ market value of rs . 100 stock = rs . 140 answer d"
Answer: d
Question (general): subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 30 pages .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 30 / 2.5 ) = 12 hrs answer : c"
Answer: c
Question (gain): a 25 % stock yielding 20 % is quoted at :
Options: a ) s . 83.33 , b ) s . 110 , c ) s . 112 , d ) s . 125 , e ) s . 140
Rationale: "income of rs 20 on investment of rs 100 income of rs 25 on investment of ? = ( 25 * 100 ) / 20 = 125 answer : d"
Answer: d