Cheukting/mathqa huggingface dataset:
Question (physics): how many bricks , each measuring 25 cm x 11 cm x 6 cm , will be needed to build a wall of 8 m x 1 m x 5 cm ?
Options: a ) 5600 , b ) 6000 , c ) 242 , d ) 7200 , e ) 8600
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 100 x 5 ) / ( 25 x 11 x 6 ) = 242 . answer : option c"
Answer: c
Question (geometry): the breadth of a rectangular field is 60 % of its length . if the perimeter of the field is 800 m , find out the area of the field .
Options: a ) 37500 , b ) 38000 , c ) 38500 , d ) 39000 , e ) 39500
Rationale: "given that breadth of the rectangular field is 60 % of its length . ⇒ b = 60 l 100 = 3 l 5 perimeter of the field = 800 m ⇒ 2 ( l + b ) = 800 ⇒ 2 ( l + 3 l 5 ) = 800 ⇒ l + 3 l 5 = 400 ⇒ 8 l 5 = 400 ⇒ l 5 = 50 ⇒ l = 5 × 50 = 250 m b = 3 l 5 = 3 × 2505 = 3 × 50 = 150 m area = lb = 250 × 150 = 37500 m 2 answer is a ."
Answer: a
Question (general): if the number is divided by 3 , it reduced by 30 . the number is
Options: a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 40 , e ) e ) 36
Rationale: "explanation : let the number be x . then , x - ( x / 3 ) = 30 = > 2 x / 3 = 30 = > x = 45 answer : option c"
Answer: c
Question (other): among 400 students , 51 % study sociology , 46 % study mathematics and 40 % study biology . if 34 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 30 , b ) 90 , c ) 148 , d ) 172 , e ) 188
Rationale: i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 136 using your analysis : we see that the total number of students who study either maths or sociology = 184 + 204 - 136 = 252 so , in the image we know that the number of students in the zone with the black boundary = 252 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 400 , we can write : 252 + b + w = 400 or , b + w = 400 - 252 = 148 that is , b = 148 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 148 c
Answer: c
Question (other): in the third grade of windblown school there are 102 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .
Rationale: "total = 102 failed in math = 102 / 3 = 34 failed in literature = 108 / 6 = 17 the least failed in both can be 0 while max can be 17 answer a"
Answer: a
Question (gain): the principal that amounts to rs . 5913 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) s . 3096 , b ) s . 4076 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096
Rationale: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 5913 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 5096 . answer : e"
Answer: e
Question (general): if 2805 / 2.55 = 1100 , then 280.5 / 25.5 is equal to ?
Options: a ) 1.01 , b ) 1.1 , c ) 0.11 , d ) 11 , e ) none
Rationale: "answer given expression 280.5 / 25.5 = 2805 / 255 = 2805 / ( 2.55 x 100 ) = 1100 / 100 = 11 correct option : d"
Answer: d
Question (physics): a and b complete a work in 50 days . a alone can do it in 40 days . if both together can do the work in how many days ?
Options: a ) 1.075 days , b ) 0.185 days , c ) 0.065 days , d ) 0.045 days , e ) 0.0775 days
Rationale: "1 / 50 + 1 / 40 = 0.045 days answer : d"
Answer: d
Question (gain): a sum of rs . 2769 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1642 , b ) 1640 , c ) 1632 , d ) 2789 , e ) 1704
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2769 - x ) * 3 * 5 ) / 100 24 x / 100 = 41535 / 100 - 15 x / 100 39 x = 41535 = > x = 1065 second sum = 2769 – 1065 = 1704 answer : e"
Answer: e
Question (general): ( 0.0077 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.007 ) =
Options: a ) 0.099 , b ) 0.0099 , c ) 9.9 , d ) 990 , e ) 99
Rationale: "( 0.0077 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.007 ) = 0.0077 * 360 / 4 * ( 0.1 ) ( 0.007 ) = 0.077 * 90 / 1 * 0.007 = 77 * 90 / 7 = 11 * 90 = 990 answer : d"
Answer: d
Question (gain): in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 12 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24 % , d ) 25 % , e ) 34 %
Rationale: "since 12 % of the customers who sample the candy are not caught , then 88 % of the customers who sample the candy are caught : { % of customers who sample candy } * 0.88 = 0.22 ; { % of customers who sample candy } = 0.25 . answer : d ."
Answer: d
Question (gain): a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 1760 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 8 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 1760 100 r + 120 r = 1760 r = 8 % answer : e"
Answer: e
Question (general): out of 4 numbers , the average of first 3 is 20 and that of the last 3 is 15 . if the last number is 18 , the first number is :
Options: a ) 22 , b ) 33 , c ) 77 , d ) 99 , e ) 27
Rationale: explanation : let the numbers be a , b , c , d given , a + b + c = 60 , b + c + d = 45 now , d = 18 thus , b + c + 18 = 45 ⇒ b + c = 27 putting the value of b + c in a + b + c = 60 a + 27 = 60 ⇒ a = 33 answer : b
Answer: b
Question (general): 4 car rental agencies a , b , c and d rented a plot for parking their cars during the night . a parked 15 cars for 12 days , b parked 12 cars for 20 days , c parked 18 cars for 18 days and d parked 16 cars for 15 days . if a paid rs . 1125 as rent for parking his cars , what is the total rent paid by all the 4 agencies ?
Options: a ) rs . 6152 , b ) rs . 6159 , c ) rs . 6156 , d ) rs . 6150 , e ) rs . 6196
Rationale: the ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15 = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60 let us consider the four amounts to be 45 k , 60 k , 81 k and 60 k respectively . the total rent paid by the four agencies = 45 k + 60 k + 81 k + 60 k = 246 k it is given that a paid rs . 1125 45 k = 1125 = > k = 25 246 k = 246 ( 25 ) = rs . 6150 thus the total rent paid by all the four agencies is rs . 6150 . answer : d
Answer: d
Question (physics): harry started a 7 - mile hike with a full 9 - cup canteen of water and finished the hike in 2 hours with 3 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 2 cups of water during the last mile , how many cups did he drink per mile during the first 6 miles of the hike ?
Options: a ) 1 / 6 , b ) 2 / 6 , c ) 3 / 6 , d ) 4 / 6 , e ) 5 / 6
Rationale: "no of cups leaked during the trip = 2 cups . no of cups harry drank = 6 cups . no of cups harry drank during the first 6 miles = 4 . drink / mile = 4 / 6 answer d"
Answer: d
Question (gain): the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 900 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 2150 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 900 × 100 ) / ( 6 × 12 ) = rs . 1250 bg = bd – td = > 900 = bd - 1250 = > bd = 2150 answer : option d"
Answer: d
Question (general): 8 ^ 100 is divisible by 17 . find the remainder for this ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 17 , e ) 19
Rationale: "this is an extremely difficult problem to solve with out fermat ' s little theorem . by applying fermat ' s little theorem , we know that 816 when divided by 17 , the remainder is 1 . so divide 100 by 16 and find the remainder . remainder = 4 therefore , 100 = ( 16 × 6 ) + 4 now this problem can be written as 810017 = 816 × 6 + 417 = ( 816 ) 6 × 8417 now this problem simply boils down to ( 1 ) 6 × 8417 = 8417 84 = 82 × 82 , we need to find the remainder when 64 × 64 is divisible by 17 . or 13 × 13 = 169 . when 169 is divided by 17 , remainder is 16 . c"
Answer: c
Question (gain): a shopkeeper sold an book offering a discount of 5 % and earned a profit of 42.5 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 140 , b ) 120 , c ) 130 , d ) 110 , e ) 150
Rationale: "let c . p . be $ 100 . then , s . p . = $ 142.50 let marked price be $ x . then , 95 / 100 x = 142.5 x = 14250 / 95 = $ 150 now , s . p . = $ 150 , c . p . = $ 100 profit % = 50 % . e"
Answer: e
Question (general): a driver would have reduced the time it took to drive from home to the store by 1 / 4 if the average speed had been increased by 10 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 4 would give us : d = ( r ) ( t ) = ( 3 t / 4 ) ( x * r ) x = 4 / 3 since ( 3 t / 4 ) ( 4 r / 3 ) = ( r ) ( t ) = d 4 r / 3 = r + 10 r / 3 = 10 r = 30 the answer is e .
Answer: e
Question (physics): a can do a job in 15 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 14 days , b ) 16 days , c ) 20 days , d ) 11 days , e ) 19 days
Rationale: "c 1 / 15 + 1 / 30 = 1 / 10 10 * 2 = 20 days"
Answer: c
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 $ 10 on candy , how much did john spend at the supermarket ?
Options: a ) $ 60 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 150
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 $ 10 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 + 10 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 300 = 30 t 28 t + 300 = 30 t 300 = 2 t t = 150 john spent $ 90 at the supermarket . answer : e"
Answer: e
Question (physics): the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 120 , find the other ?
Options: a ) 100 , b ) 60 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 120 = 60 answer is b"
Answer: b
Question (gain): 66.2 is what percent of 1000 ?
Options: a ) 6.62 , b ) 66.2 , c ) 662 , d ) 0.662 , e ) 0.0662
Rationale: "we assume that 1000 is 100 % assume ' x ' is value we looking for here , 1000 = 100 % and x % = 66.2 therefore , 100 / x = 1000 / 66.2 100 / x = 15.105 x = 6.62 a"
Answer: a
Question (general): if the sum and difference of two numbers are 5 and 10 respectively , then the difference of their square is :
Options: a ) 50 , b ) 28 , c ) 160 , d ) 180 , e ) 18
Rationale: "let the numbers be x and y . then , x + y = 5 and x - y = 10 x 2 - y 2 = ( x + y ) ( x - y ) = 5 * 10 = 50 . answer : a"
Answer: a
Question (general): find the least number which when divided by 56 , 78 leaves a remainder 3 but when divided by 9 leaves no remainder
Options: a ) 9632 , b ) 7896 , c ) 8741 , d ) 1683 , e ) 8523
Rationale: l . c . m of 5,6 , 7,8 = 840 required number is of the form of 840 k + 3 least value of k for which ( 840 k + 3 ) is divided by 9 is k = 2 required number = ( 840 * 2 + 3 ) = 1683 answer ( d )
Answer: d
Question (general): what is the average of first 21 multiples of 8 ?
Options: a ) a ) 70 , b ) b ) 77 , c ) c ) 79 , d ) d ) 81 , e ) e ) 88
Rationale: "required average = 8 ( 1 + 2 + . . . . + 21 ) / 21 ( 8 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 88 e"
Answer: e
Question (gain): a invested $ 150 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 20 , d ) $ 120 , e ) $ 60
Rationale: "a : b = 150 * 12 : 200 * 6 a : b = 3 : 2 a ' s share = 100 * 3 / 5 = $ 60 answer is e"
Answer: e
Question (general): for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 9.2 – 9.2 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: "since y * is defined as the greatest positive even integer less than or equal to y , then 9.2 * = 8 ( the greatest positive even integer less than or equal to 9.2 is 4 ) . hence , 9.2 – 9.2 * = 9.2 - 8 = 1.2 answer : b ."
Answer: b
Question (physics): the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.40 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 399 , b ) 272 , c ) 932.4 , d ) 277 , e ) 311
Rationale: "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1.4 = 932.4 answer : c"
Answer: c
Question (general): $ 400 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is
Options: a ) $ 100 , b ) $ 150 , c ) $ 160 , d ) $ 200 , e ) $ 250
Rationale: "a : ( b + c ) = 2 : 3 a ' s share = 400 * 2 / 5 = $ 160 answer is c"
Answer: c
Question (general): 2 . the value of x + x ( xx ) when x = 2 is :
Options: a ) 5 , b ) 10 , c ) 8 , d ) 15 , e ) 20
Rationale: x + x ( xx ) put the value of x = 2 in the above expression we get , 2 + 2 ( 22 ) = 2 + 2 ( 2 × 2 ) = 2 + 2 ( 4 ) = 2 + 8 = 10 answer : b
Answer: b
Question (general): find the value of x from the below equation ? : x ^ 2 + 5 x + 25 = 0
Options: a ) no answer , b ) 25 , c ) 1 , d ) 0 , e ) - 2
Rationale: "a = 1 , b = 5 , c = 25 x 1,2 = ( - 5 â ± â ˆ š ( 5 ^ 2 - 4 ã — 1 ã — 25 ) ) / ( 2 ã — 1 ) = ( - 5 â ± â ˆ š ( 25 - 100 ) ) / 2 = ( - 5 â ± â ˆ š - 75 ) / 2 no real roots a"
Answer: a
Question (gain): a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 75 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 20 %
Rationale: "typical dosage is dose : weight : : 2 : 15 . now if weight is 75 : ( 75 / 15 ) ) then typical dosage would be 2 * 5 = 10 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 10 ) * 100 = 20 % e is the answer ."
Answer: e
Question (general): if two positive numbers are in the ratio 1 / 7 : 1 / 5 , then by what percent is the second number more than the first ?
Options: a ) 70 % , b ) 90 % , c ) 60 % , d ) 40 % , e ) 65 %
Rationale: "given ratio = 1 / 7 : 1 / 5 = 5 : 7 let first number be 5 x and the second number be 7 x . the second number is more than first number by 2 x . required percentage = 2 x / 5 x * 100 = 40 % . answer : d"
Answer: d
Question (gain): 30.5 % of 2000
Options: a ) 556 , b ) 612.5 , c ) 756.8 , d ) 610 , e ) 820
Rationale: 1 % of 2000 = 20 30 % of 2000 = 30 * 20 = 600 0.5 % of 2000 = 0.5 * 2000 = 10 total = 610 answer : d
Answer: d
Question (general): if the operation x is defined by a x b = ( b - a ) ^ 2 / a ^ 2 for all numbers a and b , and a ≠ 0 , then − 1 x ( 1 x − 1 ) =
Options: a ) − 1 , b ) 0 , c ) 1 , d ) 25 , e ) 29
Rationale: on solving the inner bracket we get 4 . then we get equation as - 1 x 4 where b = 4 and a = - 1 answer d
Answer: d
Question (general): the two lines y = x and x = - 3 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length of a cube whose surface area is equal to 6 z ?
Options: a ) 16 , b ) 3 / √ 2 , c ) 8 , d ) 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: 800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 3 , - 3 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 3 × 3 ) = 9 / 2 ; so z = 9 / 2 . the next step requires us to find the length of a side of a cube that has a face area equal to 9 / 2 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 9 / 2 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 9 / 2 . clearly s = √ 9 / 2 = 3 / √ 2 , oranswer choice ( b ) .
Answer: b
Question (general): subtracting 4 % of a from a is equivalent to multiplying a by how much ?
Options: a ) 0.96 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none
Rationale: "answer let a - 4 % of a = ab . ⇒ ( 96 x a ) / 100 = ab ∴ b = 0.96 correct option : a"
Answer: a
Question (gain): each of the integers from 0 to 9 , inclusive , is written on a separate slip of blank paper and the ten slips are dropped into a hat . if 5 of the slips are the drawn , without replacement , what is the probability that all 5 have a even number written on it ?
Options: a ) 1 / 252 , b ) 1 / 10 , c ) 1 / 8 , d ) 1 / 2 , e ) 5 / 9
Rationale: "key is that there is no replacement , so each successive choice will become more skewed towards picking a neg ( i . e . the pool of positives decreases , while the pool of negatives stay the same ) p ( + on 1 st pick ) = 5 / 10 p ( + on 2 nd pick ) = 4 / 9 p ( + on 3 rd pick ) = 3 / 8 p ( + on 4 rd pick ) = 2 / 7 p ( + on 5 rd pick ) = 1 / 6 5 / 10 * 4 / 9 * 3 / 8 * 2 / 7 * 1 / 6 = 1 / 252 a"
Answer: a
Question (general): if a and b are integers and ( a * b ) ^ 5 = 32 y , y could be :
Options: a ) 16 , b ) 1 , c ) 8 , d ) 12 , e ) 24
Rationale: "distribute the exponent . a ^ 5 * b ^ 5 = 32 y find the prime factorization of 32 . this is 2 ^ 5 * 1 . we need 1 the answer is b ."
Answer: b
Question (physics): it was calculated that 100 men could complete a piece of work in 20 days . when work was scheduled to commence , it was found necessary to send 50 men to another project . how much longer will it take to complete the work ?
Options: a ) 45 days . , b ) 40 days . , c ) 38 days . , d ) 35 days . , e ) 30 days .
Rationale: one day work = 1 / 20 one man ’ s one day work = 1 / ( 20 * 100 ) now : no . of workers = 50 one day work = 50 * 1 / ( 20 * 100 ) the total no . of days required to complete the work = ( 100 * 20 ) / 50 = 40 answer : b
Answer: b
Question (physics): if a is thrice as fast as b and together can do a work in 15 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 20 , c ) 28 , d ) 54 , e ) 45
Rationale: "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 15 = 3 + 1 / 3 x = 4 / 3 x = 1 / 15 x = 15 * 4 / 3 = 20 answer : b"
Answer: b
Question (general): average of 5 numbers is - 10 , and the sum of 3 of the numbers is 16 , wat is the average of the other 2 numbers ?
Options: a ) - 33 , b ) 33 , c ) 35 , d ) 36 , e ) - 35
Rationale: let the five numbers be a , b , c , d , e . then their average is ( a + b + c + d + e 5 ) = 10 . ( a + b + c + d + e 5 ) = 10 . now three of the numbers have a sum of 16 , say , a + b + c = 16 a + b + c = 16 . so substitute 16 for a + b + ca + b + c in the average above : ( 16 + d + e 5 ) = 10 . ( 16 + d + e 5 ) = 10 . solving this equation for d + ed + e gives d + e = − 66 d + e = − 66 . finally , dividing by 2 ( to form the average ) gives ( d + e 2 ) = − 33 . ( d + e 2 ) = − 33 . hence , the answer is a : - 33
Answer: a
Question (general): a number when divided by 296 leaves 75 as remainder when the same number is divided by 37 then the remainder will be ?
Options: a ) 2 , b ) 9 , c ) 6 , d ) 5 , e ) 1
Rationale: "let x = 296 q + 75 = ( 37 * 8 q + 37 * 2 ) + 1 37 * ( 8 q + 2 ) + 1 thus when the number is divided by 37 the remainder is 1 answer ( e )"
Answer: e
Question (general): if | 4 x + 6 | = 50 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 2 , c ) 4 , d ) - 3 , e ) 6
Rationale: "there will be two cases 4 x + 6 = 50 or 4 x + 6 = - 50 = > x = 11 or x = - 14 sum of both the values will be - 14 + 11 = - 3 answer is d"
Answer: d
Question (gain): a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent e of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "let the market price of the product is mp . let the original cost price of the product is cp . selling price ( discounted price ) = 100 % of mp - 20 % mp = 80 % of mp . - - - - - - - - - - - - - - - - ( 1 ) profit made by selling at discounted price = 20 % of cp - - - - - - - - - - - - - - ( 2 ) apply the formula : profit e = selling price - original cost price = > 20 % of cp = 80 % of mp - 100 % cp = > mp = 120 cp / 80 = 3 / 2 ( cp ) now if product is sold without any discount , then , profit = selling price ( without discount ) - original cost price = market price - original cost price = mp - cp = 3 / 2 cp - cp = 1 / 2 cp = 50 % of cp thus , answer should bec ."
Answer: c
Question (geometry): the width of a rectangle is 10 meter and its area is 150 square meter . if length of the rectangle is increased then its new area is 4 / 3 times of the original area . what is the new perimeter of the rectangle ?
Options: a ) 48 m
b ) 52 m
c ) 54 m
d ) 60 m
e ) none of these
Rationale: let length of new rectangle be x m then x × 10 = 150 × 4 / 3 = 200 or , x = 20 m hence new perimeter = 2 ( 10 + 20 ) = 60 m answer : d
Answer: d
Question (gain): the cost price of a radio is rs . 2300 and it was sold for rs . 1800 , find the loss % ?
Options: a ) 18 , b ) 99 , c ) 27 , d ) 26 , e ) 21
Rationale: "2300 - - - - 500 100 - - - - ? = > 21 % answer : e"
Answer: e
Question (physics): a and b can finish a work 30 days if they work together . they worked together for 20 days and then b left . a finished the remaining work in another 20 days . in how many days a alone can finish the work ?
Options: a ) 30 , b ) 60 , c ) 40 , d ) 20 , e ) 50
Rationale: amount of work done by a and b in 1 day = 1 / 30 amount of work done by a and b in 20 days = 20 × ( 1 / 30 ) = 20 / 30 = 2 / 3 remaining work – 1 – 2 / 3 = 1 / 3 a completes 1 / 3 work in 20 days amount of work a can do in 1 day = ( 1 / 3 ) / 20 = 1 / 60 = > a can complete the work in 60 days answer is b .
Answer: b
Question (general): 0.0004 ? = 0.01
Options: a ) 4 , b ) 0.4 , c ) 0.04 , d ) 40 , e ) none of these
Rationale: "explanation : required answer = 0.0004 / 0.01 = 0.04 / 1 = 0.04 . answer : option c"
Answer: c
Question (general): 860 % of 50 + 50 % of 860 = ?
Options: a ) 430 , b ) 516 , c ) 660 , d ) 860 , e ) none
Rationale: "solution given expression = [ 860 / 100 x 50 + 50 / 100 x 860 ] = 430 + 430 = 860 . answer d"
Answer: d
Question (physics): in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 39 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
Options: a ) 36 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47
Rationale: "working backward from the day it ' s covered : day 39 : fully covered day 38 : half covered so 38 days answer : d"
Answer: d