Cheukting/mathqa huggingface dataset:
Question (general): set a : { 1 , 3 , 4 , 6 , 9 , 12 , 15 } if 3 numbers are randomly selected from set a without replacement , what is the probability that the sum of the 3 numbers is divisible by 3 ?
Options: a ) 3 / 14 , b ) 2 / 7 , c ) 9 / 14 , d ) 5 / 7 , e ) 11 / 14
Rationale: probability of an event = ( # of favorable outcomes ) / ( total # of outcomes ) . there are 5 numbers you can choose from ( 3 , 6 , 9 , 12 , 15 ) so that the sum to be divisible by 3 and there are total of 7 numbers so p = c 35 c 37 = 27 p = c 53 c 73 = 27 . answer : b .
Answer: b
Question (geometry): in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 1,3 ) , ( 5,3 ) , ( 2,6 ) , ( 6,6 ) ?
Options: a ) 21 . , b ) 12 . , c ) 35 . , d ) 49 . , e ) 52 .
Rationale: "delta x will give us the dimension of one side of the parallelogram = 5 - 1 = 4 unit delta y will give us the dimension of the other side of parallelogram = 6 - 3 = 3 unit area of parallelogram = 4 * 3 = 12 answer is b"
Answer: b
Question (gain): the banker ' s gain on a sum due 3 years hence at 12 % per year is rs . 270 . the banker ' s discount is :
Options: a ) 960 , b ) 840 , c ) 1020 , d ) 760 , e ) 920
Rationale: "t . d . = ( b . g . x 100 / r x t ) = rs . ( 270 x 100 / 12 x 3 ) = rs . 750 . therefore , b . d . = rs . ( 750 + 270 ) = rs . 1020 . answer is c"
Answer: c
Question (physics): convert the 12 / 43 m / s into kilometers per hour ?
Options: a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1 kmph . , d ) 1.5 kmph . , e ) 1.9 kmph .
Rationale: "12 / 43 m / s = 12 / 43 * 18 / 5 = 1 ( 1 / 250 ) = 1 kmph . answer : c"
Answer: c
Question (geometry): a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 4 per sq m ?
Options: a ) 2288 , b ) 2779 , c ) 2779 , d ) 5200 , e ) 2781
Rationale: "area = ( l + b â € “ d ) d ( 80 + 60 â € “ 10 ) 10 = > 1300 m 2 1300 * 4 = rs . 5200 answer : d"
Answer: d
Question (geometry): a 45 ° - 45 ° - 90 ° right triangle has hypotenuse of length h . what is the area of the triangle r in terms of h ?
Options: a ) h / √ 2
b ) h / 2
c ) h / 4
d ) ( h ) ^ 2
e ) ( h ) ^ 2 / 4
Rationale: if . . . each of the two shorter sides = 3 , then the hypotenuse = h = 3 ( root 2 ) . the area r = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 3 ) ( 3 ) = 9 / 2 . so we ' re looking for an answer that = 9 / 2 when h = 3 ( root 2 ) . there ' s only one answer that matches . . . e
Answer: e
Question (general): - 88 * 49 + 100 = ?
Options: a ) - 4212 , b ) 4601 , c ) - 4801 , d ) - 3471 , e ) none of these
Rationale: "= > - 88 * ( 50 - 1 ) + 100 ; = > - ( 88 * 50 ) + 88 + 100 ; = > - 4400 + 188 = - 4212 . correct option : a"
Answer: a
Question (general): how many digits 2 ^ 200 has ?
Options: a ) 31 , b ) 61 , c ) 50 , d ) 99 , e ) 101
Rationale: "2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 60 therefore 61 digits would be my best guess b"
Answer: b
Question (physics): in an intercollegiate competition that lasted for 3 days , 175 students took part on day 1 , 210 on day 2 and 150 on day 3 . if 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days , how many students took part only on day 1 ?
Options: a ) 25 , b ) 45 , c ) 55 , d ) 70 , e ) 30
Rationale: day 1 & 2 = 80 ; only day 1 & 2 ( 80 - 20 ) = 60 , day 2 & 3 = 70 ; only day 2 & 3 ( 70 - 20 ) = 50 , only day 1 = 175 - ( 60 + 50 + 20 ) = 45 answer : b
Answer: b
Question (gain): rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 75 . how much was lent at 5 % ?
Options: a ) 388 , b ) 1500 , c ) 277 , d ) 500 , e ) 271
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 75 5 x / 100 + 90 – 6 x / 100 = 75 x / 100 = 15 = > x = 1500 . answer : b"
Answer: b
Question (gain): a sum of money at simple interest amounts to $ 980 in 3 years and to $ 1024 in 4 years . the sum is :
Options: a ) $ 153 , b ) $ 848 , c ) $ 398 , d ) $ 549 , e ) $ 675
Rationale: "b $ 848 s . i . for 1 year = $ ( 1024 - 980 ) = $ 44 . s . i . for 3 years = $ ( 44 x 3 ) = $ 132 . principal = $ ( 980 - 132 ) = $ 848 ."
Answer: b
Question (geometry): the perimeter of a rectangular yard is completely surrounded by a fence that measures 18 meters . what is the length of the yard if the area of the yard is 20 meters squared ?
Options: a ) 8 , b ) 2 , c ) 7 , d ) 5 , e ) 1
Rationale: "perimeter of rectangular yard = 2 ( l + b ) = 18 - - > l + b = 9 area = l * b = 20 b = 9 - l l ( 9 - l ) = 20 29 l - l ^ 2 = 20 l ^ 2 - 9 l + 20 = 0 upon simplifying we get l = 5 or 4 . only 5 is there in the answer choice . answer : d"
Answer: d
Question (general): the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 68 % of the required amount . what is the net difference in the expenditure on that product ?
Options: a ) 12.5 % , b ) 13 % , c ) 16 % , d ) 15 % , e ) 19 %
Rationale: "quantity x rate = price 1 x 1 = 1 0.68 x 1.25 = 0.85 decrease in price = ( 0.15 / 1 ) × 100 = 15 % d )"
Answer: d
Question (gain): a store reduced the price of all items in the store by 10 % on the first day and by another 14 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?
Options: a ) 80.0 , b ) 80.9 , c ) 77.4 , d ) 81.1 , e ) 81.9
Rationale: "consider price of the all items as $ 100 after a initial reduction of 10 % price becomes = 0.9 * 100 = $ 90 after the final reduction of 14 % price becomes = 0.86 * 90 = $ 77.4 price of all items on second day is 77.4 % of price on first day correct answer option c"
Answer: c
Question (general): if 25 % of ( x - y ) = 15 % of ( x + y ) , then what percent of x is y ?
Options: a ) 20 % , b ) 15 % , c ) 30 % , d ) 25 % , e ) none of these
Rationale: "explanation : solution : 25 % of ( x - y ) = 15 % of ( x + y ) 25 ( x - y ) / 100 = 15 ( x + y ) / 100 5 ( x - y ) = 3 ( x + y ) x = 4 y . . ' . required percentage = ( y * 100 / x ) % = y * 100 / 4 y = 25 % answer : d"
Answer: d
Question (general): the average weight of 3 men a , b and c is 84 kg . the average weight becomes 80 kg when d joins them . if e whose weight is 3 kg more than d joins the group replacing a , then the average weight of b , c , d and e becomes 79 kg . the weight of a is :
Options: a ) 65 kg , b ) 70 kg , c ) 75 kg , d ) 80 kg , e ) 85 kg
Rationale: wt of abc = 84 * 3 = 252 kg wt of abcd = 80 * 4 = 320 kg wt of d = 68 kg wt of e = 71 kg wt of abcde = 320 + 71 = 391 kg wt of bcde = 79 * 4 = 316 kg wt of a = 391 - 316 = 75 kg answer : c
Answer: c
Question (other): the ratio of the present ages of two friends is 2 : 3 and 6 years back , the ratio was 1 : 3 . what will be the ratio of their ages after 4 years ?
Options: a ) 1 : 4 , b ) 3 : 4 , c ) 1 : 2 , d ) 3 : 1 , e ) 3 : 2
Rationale: let the ages be 2 x , 3 x 6 yrs back , so 2 x - 6 / 3 x - 6 = 1 / 3 x = 4 after 4 yrs 2 x + 43 x + 4 2 ( 4 ) + 43 ( 4 ) + 4 12 : 16 3 : 4 answer : b
Answer: b
Question (geometry): the perimeter of a triangle is 24 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 30 cm 2 , b ) 85 cm 2 , c ) 65 cm 2 , d ) 45 cm 2 , e ) 35 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 24 / 2 = 30 cm 2 answer : a"
Answer: a
Question (gain): if 85 % of the population of an ant colony is red , and of these 45 % are females , then what % of the total ant population are male red ants ?
Options: a ) 46.75 , b ) 40 , c ) 33.66 , d ) 66.66 , e ) 66.86
Rationale: 55 % are males percentage of male red ants is 55 * . 85 = 46.75 answer : a
Answer: a
Question (general): if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 54 / r years . if pat ' s parents invested $ 6,000 in a long - term bond that pays 6 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 54 / r years , then for r = 6 it ' ll double in 54 / 6 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 18 years investment will become $ 6,000 * 2 = $ 12,000 . answer : c ."
Answer: c
Question (physics): a train 210 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options: a ) 28 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 40 sec
Rationale: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 210 × 2 / 15 ) sec = 28 sec answer : a"
Answer: a
Question (general): in 3 annual examinations , of which the aggregate marks of each was 500 , a student secured average marks 45 % and 55 % in the first and the second yearly examinations respectively . to secure 40 % average total marks , it is necessary for him in third yearly examination to secure marks :
Options: a ) 100 , b ) 350 , c ) 400 , d ) 450 , e ) 500
Rationale: total marks : 1500 for three exams 40 % of 1500 = 600 first exam marks = 45 % of 500 = 225 second exam marks = 55 % of 500 = 275 let x be the third exam marks 225 + 275 + x = 600 x = 100 answer : a
Answer: a
Question (general): a man has some hens and cows . if the number of heads be 46 and the number of feet equals 140 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 24 , d ) 26 , e ) 28
Rationale: "let hens be x and cows be y now , feet : x * 2 + y * 4 = 140 heads : x * 1 + y * 1 = 46 implies , 2 x + 4 y = 140 and x + y = 46 solving these two equations , we get x = 22 and y = 24 therefore , hens are 22 . answer : a"
Answer: a
Question (general): two negative numbers are multiplied to give a product of 48 . if the lesser number is 10 less than thrice the greater number , what is the greater number ?
Options: a ) - 6 , b ) - 8 , c ) - 5 , d ) - 9 , e ) - 10
Rationale: test the options . the options give you the greater number . ( a ) - 6 triple of - 6 is - 18 and 10 less is - 8 . - 8 * - 6 = 48 ( correct ) correct answer ( a )
Answer: a
Question (gain): yesterday ' s closing prices of 2,860 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
Options: a ) 484 , b ) 726 , c ) 1,100 , d ) 1,320 , e ) 1,560
Rationale: "lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 2860 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 1560 . e is my answer ."
Answer: e
Question (geometry): from a square piece of a paper having each side equal to 10 cm , the largest possible circle is being cut out . the ratio of the area of the circle to the area of the original square is nearly :
Options: a ) 4 ⁄ 5
b ) 3 ⁄ 5
c ) 5 ⁄ 6
d ) 6 ⁄ 7
e ) none of these
Rationale: area of the square = ( 10 ) 2 = 100 cm 2 area of the circle = 22 ⁄ 7 × ( 5 ) 2 = 22 × 25 / 7 required ratio = 22 × 25 / 7 × 100 = 22 / 28 = 11 / 14 = 0.785 ≈ 0.8 = 4 ⁄ 5 answer a
Answer: a
Question (physics): light glows for every 13 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 381 , b ) 382 , c ) 383 , d ) 384 , e ) 385
Rationale: the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 13 = 382 . so total 383 times light ll glow answer : c
Answer: c
Question (physics): if 7 men and 2 boys working together , can do 6 times as much work per hour as a man and a boy together . find the ratio of the work done by a man and that of a boy for a given time ?
Options: a ) 2 : 5 , b ) 2 : 3 , c ) 1 : 8 , d ) 4 : 1 , e ) 3 : 2
Rationale: 7 m + 2 b = 6 ( 1 m + 1 b ) 7 m + 2 b = 6 m + 6 b 1 m = 4 b the required ratio of work done by a man and a boy = 4 : 1 answer : d
Answer: d
Question (general): if x is 20 percent greater than 52 , then x =
Options: a ) 68 , b ) 62.4 , c ) 86 , d ) 72.8 , e ) 108
Rationale: "x is 20 % greater than 52 means x is 1.2 times 52 ( in other words 52 + 20 / 100 * 52 = 1.2 * 52 ) therefore , x = 1.2 * 88 = 62.4 answer : b"
Answer: b
Question (physics): two stations p and q are 245 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ?
Options: a ) 10 am , b ) 12 am , c ) 10.30 am , d ) 12.30 am , e ) 1 pm
Rationale: "assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 245 = > 20 x + 25 ( x - 1 ) = 245 = > 45 x = 270 = > x = 6 means , they meet after 6 hours after 7 am , ie , they meet at 1 pm answer is 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 1215 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 135 , d ) 136 , e ) 138
Rationale: let the required number be x . then , 43 x – 34 x = 1215 or 9 x = 1215 or x = 135 . required number = 135 answer : c
Answer: c
Question (gain): there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 64 %
Options: a ) 18.75 , b ) 19.75 , c ) 20.75 , d ) 21.75 , e ) 22.75
Rationale: "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 64 / 100 = 50.40 so x = 18.75 answer : a"
Answer: a
Question (general): if x + y = - 10 , and x = 25 / y , what is the value of x ^ 2 + y ^ 2 ?
Options: a ) 55 , b ) 65 , c ) 50 , d ) 75 , e ) 85
Rationale: "x ^ 2 + y ^ 2 should make you think of these formulas : ( x + y ) ( x + y ) = x ^ 2 + y ^ 2 + 2 xy we already know ( x + y ) = - 10 and x * y = 25 ( x + y ) ( x + y ) = ( - 10 ) ( - 10 ) = x ^ 2 + y ^ 2 + 2 * ( 25 ) x ^ 2 + y ^ 2 = 100 - 50 = 50 answer : c"
Answer: c
Question (physics): a type r machine can complete a job in 5 hours and a type b machine can complete the job in 7 hours . how many hours will it take 2 type r machines and 3 type b machines working together and independently to complete the job ?
Options: a ) 1 / 5 , b ) 29 / 35 , c ) 5 / 6 , d ) 35 / 29 , e ) 35 / 12
Rationale: now d should be the answer . r need 5 hours to complete and b needs 7 hours to compete so 2 r + 3 b will complete 2 / 5 + 3 / 7 or 29 / 35 portion of the job in 1 hour so the whole job will take 35 / 29 hours . . . . = d
Answer: d
Question (physics): the speed of a boat in still water in 42 km / hr and the rate of current is 6 km / hr . the distance travelled downstream in 44 minutes is :
Options: a ) 86.6 km , b ) 46.6 km , c ) 35.2 km , d ) 35.6 km , e ) 26.6 km
Rationale: "speed downstream = ( 42 + 6 ) = 48 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 48 = 35.2 km answer : c"
Answer: c
Question (general): a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points l that an individual player might have scored ?
Options: a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23
Rationale: "general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points l for 12 th player is 100 - 77 = 23 . answer : e ."
Answer: e
Question (general): find the value of log y ( x 4 ) if logx ( y 3 ) = 2
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: logx ( y 3 ) = 2 : given x 2 = y 3 : rewrite in exponential form x 4 = y 6 : square both sides x 4 = y 6 : rewrite the above using the log base y logy ( x 4 ) = logy ( y 6 ) = 6 correct answer c
Answer: c
Question (physics): arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 70 days .
Options: a ) 16 days . , b ) 17 days . , c ) 18 days . , d ) 19 days . , e ) 42 days .
Rationale: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 70 * 6 / 10 = 42 days . answer : e"
Answer: e
Question (general): a 100 - litre mixture of milk and water contains 36 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 16 % . what is the value of x ?
Options: a ) 37.5 litres , b ) 36.67 litres , c ) 37.67 litres , d ) 36.5 litres , e ) 33.33 litres
Rationale: "working formula . . . initial concentration * initial volume = final concentration * final volume . let x is the part removed from 100 lts . 36 % ( 1 - x / 100 ) ^ 2 = 16 % * 100 % ( 1 - x / 100 ) ^ 2 = 16 / 36 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 4 / 6 ) ^ 2 100 - x = 400 / 6 x = 33.33 . . . ans e"
Answer: e
Question (general): a man â € ™ s current age is ( 2 / 5 ) of the age of his father . after 5 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?
Options: a ) 40 , b ) 25 , c ) 38 , d ) 50 , e ) 39
Rationale: "let , father â € ™ s current age is a years . then , man â € ™ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 5 ] = ( 1 / 2 ) ( a + 5 ) 2 ( 2 a + 25 ) = 5 ( a + 8 ) a = 25 b"
Answer: b
Question (physics): after an ice began to melt out from the freezer , in the first hour lost 3 / 4 , in the second hour lost 3 / 4 of its remaining . if after two hours , the volume is 0.75 cubic inches , what is the original volume of the cubic ice , in cubic inches ?
Options: a ) 2.5 , b ) 3.0 , c ) 4.0 , d ) 6.5 , e ) 12.0
Rationale: "let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.75 x = 12 alternate solution : try to backsolve . initial volume = 12 after one hour - - > ( 1 / 4 ) 12 = 3 after two hours - - > ( 1 / 4 ) 3 = 0.75 answer : e"
Answer: e
Question (general): the average height of 20 girls out of a class of 50 is 142 cm . and that of the remaining girls is 149 cm . the average height of the whole class is :
Options: a ) 146.2 cms , b ) 146.5 cms , c ) 146.9 cms , d ) 142.2 cms , e ) 136.2 cms
Rationale: "explanation : average height of the whole class = ( 20 × 142 + 30 × 149 / 50 ) = 146.2 cms answer a"
Answer: a
Question (gain): a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 3 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 89.8 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 3 % of 400 = 12 therefore , total number of rotten fruits = 90 + 12 = 102 therefore number of fruits in good condition = 1000 - 102 = 898 therefore percentage of fruits in good condition = ( 898 / 1000 × 100 ) % = ( 89800 / 1000 ) % = 89.8 % answer : b
Answer: b
Question (general): if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.40 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was
Options: a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.20 , e ) $ 6.60
Rationale: "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.4 ) = $ 5.6 ( as the charge is 0.4 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 5.6 = 6.6 answer is e ."
Answer: e
Question (gain): bruce purchased 9 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1050 , c ) c ) 1055 , d ) d ) 1065 , e ) e ) 1125
Rationale: "cost of 9 kg grapes = 70 × 9 = 630 . cost of 9 kg of mangoes = 55 × 9 = 495 total cost he has to pay = 630 + 495 = 1125 e"
Answer: e
Question (general): sum of two numbers is 35 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) a ) 5 , b ) b ) 9 , c ) c ) 11 , d ) d ) 22 , e ) e ) 15
Rationale: "explanation : x + y = 35 2 x – 3 y = 5 x = 22 y = 13 d )"
Answer: d
Question (general): the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 180 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 194 , c ) 269 , d ) 177 , e ) 191
Rationale: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 180 x + ( x - 180 ) = 208 2 x = 388 x = 194 runs answer : b"
Answer: b
Question (general): the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.8 kg . the weight of the new student is ?
Options: a ) 10.6 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 14.8 - 19 x 15 ) kg = 11 kg . correct option : c
Answer: c
Question (general): john has $ 1,600 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1,200
Rationale: "let the money spent be x money he is left with after spending = x - 800 total money - - > x + ( x - 800 ) = 1600 solving for x will give x = 1200 , therefore the money he is left with = x - 800 = 1200 - 800 = 400 answer : b"
Answer: b
Question (general): how many 3 digit number contain number 4 ?
Options: a ) 352 , b ) 268 , c ) 236 , d ) 252 , e ) 354
Rationale: "total 3 digit no . = 9 * 10 * 10 = 900 not containing 4 = 8 * 9 * 9 = 648 total 3 digit number contain 4 = 900 - 648 = 252 answer : d"
Answer: d
Question (general): the total age of a and b is 16 years more than the total age of b and c . c is how many year younger than a
Options: a ) 11 , b ) 16 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : given that a + b = 16 + b + c = > a ? c = 16 + b ? b = 16 = > c is younger than a by 16 years answer : option b"
Answer: b
Question (general): how many positive integers less than 14 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?
Options: a ) 14 , b ) 13 , c ) 12 , d ) 11 , e ) 8
Rationale: "the number = 2 a + 3 b < 20 when a = 1 , b = 1 , 2 , 3 , 4 , 5 - > 2 a = 2 ; 3 b = 3 , 6 , 9 - > the number = 5 , 8 , 11 - - > 3 numbers when a = 2 , b = 1 , 2,3 - > . . . . - - > 3 numbers when a = 3 , b = 1,2 , 3,4 - - > . . . . - - > 2 numbers total number is already 8 . look at the answer there is no number greater than 8 - - > we dont need to try any more answer must be e"
Answer: e