regisss/math_qa huggingface dataset:
Problem: find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 9 cm and 6 cm ?
Options: a ) 225 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 177 cm 2 , e ) 187 cm 2
Rationale: "1 / 2 * 30 ( 9 + 6 ) = 225 cm 2 answer : a"
Answer: a
Problem: a cricketer scored 138 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 46.2 % , b ) 54.54 % , c ) 63 % , d ) 56.52 % , e ) none of these
Rationale: explanation : number of runs made by running = 138 - ( 12 x 4 + 2 x 6 ) = 138 - ( 60 ) = 78 now , we need to calculate 72 is what percent of 138 . = > 78 / 138 * 100 = 56.52 % answer : d
Answer: d
Problem: if the height of a triangle is decreased by 40 % , land its base is increased by 40 % , what will be the effect on its area ?
Options: a ) no change
b ) 16 % increase
c ) 8 % decrease
d ) 16 % decrease
e ) none of thes
Rationale: regd effect = ∣ ∣ 40 − 40 − 40 × 40100 ∣ ∣ % = − 16 % | 40 − 40 − 40 × 40100 | % = − 16 % i . e . , the area will decrease by 16 % answer d
Answer: d
Problem: p and q invested in a shop . the profits were divided in the ratio of 2 : 3 respectively . if p invested rs . 40,000 , the amount invested by q is :
Options: a ) 35000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) none
Rationale: "suppose q invested rs . y . then , 40000 / y = 2 / 3 or y = [ 40000 x 3 / 2 ] = 60000 . answer d"
Answer: d
Problem: if taxi fares were $ 8.00 for the first 1 / 5 mile and $ 0.8 for each 1 / 5 mile there after , then the taxi fare for a 8 - mile ride was
Options: a ) $ 39.00 , b ) $ 39.10 , c ) $ 39.25 , d ) $ 39.30 , e ) $ 39.20
Rationale: in 8 miles , initial 1 / 5 mile charge is $ 8 rest of the distance = 8 - ( 1 / 5 ) = 39 / 5 rest of the distance charge = 39 ( 0.8 ) = $ 31.2 ( as the charge is 0.8 for every 1 / 5 mile ) = > total charge for 4 miles = 8 + 31.2 = 39.2 answer is e
Answer: e
Problem: with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity q of the pool ?
Options: a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
Rationale: "d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters ."
Answer: d
Problem: how many diagonals does a 63 - sided convex polygon have ?
Options: a ) 1890 , b ) 1953 , c ) 3780 , d ) 3843 , e ) 3906
Rationale: "a 63 - sided convex polygon has 63 vertices . if we examine a single vertex , we can see that we can connect it with 60 other vertices to create a diagonal . note : there are 60 options because we ca n ' t connect the vertex to itself , and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 63 vertices can be connected with 60 vertices to create a diagonal then . . . . . . the total number of diagonals = ( 63 ) ( 60 ) = 3780 however , before we select answer choice c , we must recognize that we have counted every diagonal twice . for example , we might connect vertex a with vertex f and count that as 1 diagonal , and at the same time we connect vertex f with vertex a and count that as 1 diagonal . of course these diagonals are the same . to account for counting each diagonal twice , we must divide 3780 by 2 to get : 1890 answer : a"
Answer: a
Problem: in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students t in the class ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 20 , e ) e ) 25
Rationale: the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )
Answer: c
Problem: uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 20 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 10 % chocolate ?
Options: a ) 18 , b ) 20 , c ) 16 , d ) 22 , e ) 24
Rationale: "first , you must find the total weight of the mixture given that 80 % of it will be dough . 90 % * total = 36 = > ( 9 / 10 ) total = 36 = > total = 360 / 9 = > total = 40 oz , from there , you must find 10 % of the total 40 oz of the mixture . 10 % * total = > ( 1 / 10 ) ( 40 ) = 4 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 20 - 4 = 16 oz chocolate left over . answer : c"
Answer: c
Problem: the area of one square is x ^ 2 + 10 x + 25 and the area of another square is 4 x ^ 2 − 12 x + 9 . if the sum of the perimeters of both squares is 64 , what is the value of x ?
Options: a ) 0 , b ) 2 , c ) 4.8 , d ) 4.67 , e ) 10
Rationale: "spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 5 ) ^ 2 a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 5 l 2 = 2 x - 3 p 1 = 4 ( x + 5 ) p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 64 4 ( x + 5 ) + 4 ( 2 x - 3 ) = 64 . . . . . . . . . . . . > x = 4.8 answer : c"
Answer: c
Problem: how long does a train 100 m long traveling at 72 kmph takes to cross a tunnel of 1400 m in length ?
Options: a ) 70 sec , b ) 60 sec , c ) 82 sec , d ) 75 sec , e ) 62 sec
Rationale: d = 1400 + 100 = 1500 m s = 72 * 5 / 18 = 20 t = 1500 * 1 / 20 = 75 sec answer : d
Answer: d
Problem: a person walks from one end to the other of a 60 - meter long moving walkway at a constant rate in 30 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 48 , b ) 60 , c ) 72 , d ) 84 , e ) 96
Rationale: "let v be the speed of the person and let x be the speed of the walkway . 30 ( v + x ) = 60 then 120 ( v + x ) = 240 120 ( v - x ) = 60 when we add the two equations : 240 v = 300 v = 5 / 4 time = 60 / ( 5 / 4 ) = 48 seconds the answer is a ."
Answer: a
Problem: mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 22 miles , how many miles was mike ' s ride ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 54
Rationale: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 22 ) = $ 13 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 13 0.25 * x = 10.5 x = 42 miles the answer is c ."
Answer: c
Problem: if g and d are both integers , g > d , and - 3 g > 19 , then the largest value of d would be ?
Options: a ) - 5 , b ) - 6 , c ) - 7 , d ) - 8 , e ) - 10
Rationale: no , your thinking is incorrect . when we know that g > d and g < - 6.33 , the largest value of g can be - 7 while if g = - 7 , then largest value of d < - 7 will be - 8 . for negative numbers , - 7 > - 8 and - 8 > - 10 . you are right in saying that d can take any value less than - 7 - - - > d could be - 8 , - 9 , - 10 . . . . and out of all these values , - 8 is the greatest . look at the numbers on the number line . for any 2 numbers , the ones on the right are greater than the ones on the left : . . . . . . . - 11 - 10 - 9 - 8 - 7 - 6 - 5 . . . . . 0 1 2 3 4 5 6 . . . ( - 11 < - 10 , - 10 < - 8 , 4 < 5 etc ) . so , as per the question if d < g and g = - 7 , then d ' s largest ' possible ' value has to be - 8 . - 10 is smaller than - 8 = d
Answer: d
Problem: what is the dividend from tony ' s stock , if he invested rs . 3200 at 85 to obtain an income of rs . 250 .
Options: a ) 4 , b ) 7.6 , c ) 6.6 , d ) 7.6 , e ) 9.6
Rationale: by investing rs . 3200 , income = rs . 250 by investing rs . 85 , income = 250 ã — 85 / 3200 = 6.6 ie , dividend = 6.6 % answer is c .
Answer: c
Problem: a is twice as good a workman as b and together they finish a piece of work in 14 days . the number of days taken by a alone to finish the work is :
Options: a ) 11 , b ) 21 , c ) 28 , d ) 42 , e ) none of these
Rationale: "( a ' s 1 day ' s work ) : ( b ' s 1 day ' s work ) = 2 : 1 ( a + b ) ' s 1 day ' s work = 1 / 14 divide 1 / 14 in the ratio 2 : 1 a ' s 1 day ' s work = ( 1 / 14 x 2 / 3 ) = 1 / 21 hence , a alone can finish the work in 21 days . correct option : b"
Answer: b
Problem: a test has 160 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain group of test - takers attempted different numbers of questions , but each test - taker still received the same net score of 40 . what is the maximum possible number of such test - takers ?
Options: a ) 23 , b ) 25 , c ) 27 , d ) 29 , e ) 31
Rationale: a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 160 . thus 5 c < = 320 and so c < = 64 . then 40 < = c < = 64 and c can have 25 possible values . the answer is b .
Answer: b
Problem: a glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution . if 65 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ?
Options: a ) 7.50
b ) 8.75
c ) 7.75
d ) 9.50
e ) 9.75
Rationale: we are given that a glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of glucose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of glucose would be in the container when we have 45 cubic centimeters of solution , we can set up a proportion . we can say : “ 15 grams of glucose is to 100 cubic centimeters of solution as x grams of glucose is to 65 cubic centimeters of solution . ” let ’ s now set up the proportion and solve for x . 15 / 100 = x / 65 when we cross multiply we obtain : ( 15 ) ( 65 ) = 100 x 975 = 100 x 9.75 = x there are 9.75 grams of glucose in the solution in the container . the answer is e .
Answer: e
Problem: the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 150 , by what percent is the price to be reduced ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 150 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 150 ) * 100 / 500 = 30 % answer : option e"
Answer: e
Problem: if a man lost 4 % by selling oranges at the rate of 60 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 11 , b ) 28 , c ) 39 , d ) 40 , e ) 43
Rationale: "96 % - - - - 60 144 % - - - - ? 96 / 144 * 60 = 40 answer : d"
Answer: d
Problem: a man can row 9 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 6.24 km , b ) 6 km , c ) 8.84 km , d ) 5.66 km , e ) 10 km
Rationale: "m = 9 s = 1.2 ds = 10.2 us = 7.8 x / 10.2 + x / 7.8 = 1 x = 4.42 d = 4.42 * 2 = 8.84 answer : c"
Answer: c
Problem: a train speeds past a pole in 15 sec and a platform 100 m long in 25 sec , its length is ?
Options: a ) 158 m , b ) 150 m , c ) 110 m , d ) 130 m , e ) 157 m
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 100 ) / 25 = x / 15 = > x = 150 m . answer : b"
Answer: b
Problem: two trains 300 m and 450 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.6 , b ) 27 , c ) 10.4 , d ) 10.8 , e ) 10.1
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 300 + 450 = 750 m . required time = 700 * 9 / 250 = 27 sec . answer : b"
Answer: b
Problem: a shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 3 a rupee . find his net profit or loss percent ?
Options: a ) 33 4 / 3 % , b ) 33 1 / 7 % , c ) 50 % , d ) 32 1 / 3 % , e ) 60 %
Rationale: the total number of mangoes bought by the shopkeeper be 18 . if he buys 6 a rupee , his cp = 3 he selling at 3 a rupee , his sp = 6 profit = sp - cp = 6 - 3 = 3 profit percent = 3 / 6 * 100 = 50 % answer : c
Answer: c
Problem: what percent of 180 is 45 ?
Options: a ) 0.25 % , b ) 4 % , c ) 25 % , d ) 40 % , e ) 250 %
Rationale: "here ' s an algebraic approach . let p = the required percent . this means p / 100 = the percent as a fraction . so , ` ` what percent of 180 is 45 ? ' ' becomes ` ` ( p / 100 ) of 180 = 45 or : ( p / 100 ) ( 180 ) = 45 divide both sides by 180 to get : p / 100 = 45 / 180 simplify right side : p / 100 = 1 / 4 multiply both sides by 100 to get : p = 25 answer : c"
Answer: c
Problem: if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 15 men in 3 days ?
Options: a ) 65 mtr . , b ) 52 mtr , c ) 70 mtr . , d ) 78 mtr . , e ) 42 mtr .
Rationale: "20 men is 6 days can build 112 metres 15 men in 3 days can build = 112 * ( 15 / 20 ) x ( 3 / 6 ) = 42 meters answer : e ."
Answer: e
Problem: b completes a work in 3 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 2.31 days , b ) 4.31 days , c ) 5.31 days , d ) 6.31 days , e ) 7.31 days
Rationale: 1 / 3 + 1 / 10 = 13 / 30 30 / 13 = 2.31 days answer : a
Answer: a
Problem: a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 20,000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,000 , e ) s . 7,500
Rationale: a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 20000 x 3 / 10 = rs . 6,000 . d
Answer: d
Problem: nick took a bus from home to market , that travels at 80 kmph . while walking back at 8 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 60 kmph . find the average speed .
Options: a ) 49.5 kmph , b ) 49.0 kmph , c ) 48.5 kmph , d ) 48.0 kmph , e ) none of these
Rationale: let the distance be 2 x ( one way ) time taken by bus = 2 x / 80 , by walking = x / 8 , by cycling = x / 60 hours : . average speed = total distance / total time = 8 x / x / 40 + x / 8 + x / 60 = 8 * 60 / 1.5 + 7.5 + 1 = 12.0 answer : d
Answer: d
Problem: a boat having a length 6 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 100 kg , b ) 120 kg , c ) 89 kg , d ) 180 kg , e ) 110 kg
Rationale: "volume of water displaced = ( 6 x 3 x 0.01 ) m 3 = 0.18 m 3 . mass of man = volume of water displaced x density of water = ( 0.18 x 1000 ) kg = 180 kg . answer : d"
Answer: d
Problem: a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 1551 , what is the value of n ?
Options: a ) 22 , b ) 38 , c ) 62 , d ) 94 , e ) 672
Rationale: "factorise 1551 . . 3 * 11 * 47 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 47 = 94 . . ans : d"
Answer: d
Problem: 0.999999 + 0.111111 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.111 , e ) 1.11111
Rationale: "0.999999 + 0.111111 = 0.999999 + 0.11111 + 0.000001 = ( 0.999999 + 0.000001 ) + 0.11111 = 1 + 0.11111 = 1.11111 e"
Answer: e
Problem: if the cost price of 10 articles is same as the selling price of 25 articles . find the gain or loss percentage ?
Options: a ) 30 % gain , b ) 30 % loss , c ) 40 % gain , d ) 60 % loss , e ) 50 % loss
Rationale: "explanation : 10 cp = 25 sp cost price cp = 25 selling price sp = 10 formula = ( sp - cp ) / cp * 100 = ( 10 - 25 ) / 25 * 100 = 60 % loss answer : option d"
Answer: d
Problem: what is the unit digit in 7 ^ 105 ?
Options: a ) 9 , b ) 7 , c ) 3 , d ) 8 , e ) 5
Rationale: "unit digit in 7 ^ 105 = unit digit in [ ( 7 ^ 4 ) ^ 26 x 7 ] but , unit digit in ( 7 ^ 4 ) ^ 26 = 1 unit digit in 7 ^ 105 = ( 1 x 7 ) = 7 . answer b ) 7 ."
Answer: b
Problem: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 112 and $ 120 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
Options: a ) 600 , b ) 784 , c ) 1080 , d ) 1200 , e ) 1440
Rationale: $ 112 for 2 years = $ 56 per year . extra $ 8 yearned with the compound interest is the percent yearned on percent . so , $ 8 is yearned on $ 56 , which means that the interest = 7 % . this on the other hand means that half of the savings = 56 * 7 = $ 392 . twice of that = $ 784 . answer : b .
Answer: b
Problem: if 70 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?
Options: a ) 2.5 % , b ) 40 % , c ) 5 % , d ) 15 % , e ) 25 %
Rationale: "70 % of ( x - y ) = 30 % of ( x + y ) ( 70 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 7 ( x - y ) = 3 ( x + y ) 4 x = 10 y x = 5 / 2 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / ( 5 / 2 ) y ) x 100 ) = 40 % answer is b ."
Answer: b
Problem: a man spends 1 / 3 rd of his salary on food . he spends 1 / 4 th on rent and 1 / 5 th on cloths . if he is left with 1760 , then who much salary does he earn .
Options: a ) 8120 , b ) 8123 , c ) 8222 , d ) 8322 , e ) 8422
Rationale: "let salary be x total spent = ( x / 3 + x / 4 + x / 5 ) = ( 47 / 60 ) * x left = ( x - 47 x / 60 ) = ( 13 / 60 ) * x given , ( 13 / 60 ) * x = 1760 x = ( 1760 * 60 ) / 13 = 8123.077 = 8123 ( approax ) answer : b"
Answer: b
Problem: what is the least value of x , so that 2 x 5476 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 9 , d ) 3 , e ) 2
Rationale: "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 5 + 4 + 7 + 6 = 24 + x least value of x may be ' 3 ' , so that the total 24 + 3 = 27 is divisible by 9 . answer : option d"
Answer: d
Problem: the length of the ribbon was originally 55 cm . it was reduced in the ratio 11 : 7 . what is its length now ?
Options: a ) 6 cm , b ) 12 cm , c ) 35 cm , d ) 44 cm , e ) none of these
Rationale: explanation : length of ribbon originally = 55 cm let the original length be 11 x and reduced length be 7 x . but 11 x = 55 cm x = 55 / 11 cm = 5 cm therefore , reduced length = 7 x cm = 7 5 cm = 35 cm answer : c
Answer: c
Problem: at 12.00 hours , j starts to walk from his house at 6 kmph . at 13.30 , p follows him from j ' s house on his bicycle at 8 kmph . when will j be 3 km behind p ?
Options: a ) 19.39 , b ) 19.3 , c ) 19.32 , d ) 19.33 , e ) 19.36
Rationale: by the time p starts j is 1.5 hr x 6 = 9 km away from his house . j is 3 km behind when p is 3 km ahead of him . ie . , p has to cover 12 km . so he takes 12 / ( 8 - 6 ) = 6 hrs after 13.30 . so the required time is 19.30 hrs answer : b
Answer: b
Problem: how many seconds will a 800 m long train take to cross a man walking with a speed of 5 km / hr in the direction of the moving train if the speed of the train is 65 km / hr ?
Options: a ) 30 , b ) 50 , c ) 66 , d ) 44 , e ) 48
Rationale: "speed of train relative to man = 65 - 5 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 800 * 3 / 50 = 48 sec . answer : e"
Answer: e
Problem: the sum of five consecutive even numbers is 500 . find the middle number of the five ?
Options: a ) 140 , b ) 66 , c ) 100 , d ) 99 , e ) 120
Rationale: "middle number = 500 / 5 = 100 ans c"
Answer: c
Problem: a and b together can do a piece of work in 6 days and a alone can do it in 14 days . in how many days can b alone can do it ?
Options: a ) 12 days , b ) 15 days , c ) 21 / 2 days , d ) 21 days , e ) 22 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 14 work in 1 day b alone can do ( 1 / 6 - 1 / 14 ) = 2 / 21 work in 1 day = > complete work can be done in 21 / 2 days by b answer : option c"
Answer: c
Problem: triathlete dan runs along a 2 - mile stretch of river and then swims back along the same route . if dan runs at a rate of 8 miles per hour and swims at a rate of 6 miles per hour , what is his average rate for the entire trip in miles per minute ?
Options: a ) 1 / 9 , b ) 2 / 15 , c ) 3 / 15 , d ) 1 / 4 , e ) 3 / 8
Rationale: "dan travels 4 miles round trip . running part : ( 2 / 8 = 1 / 4 * 60 = 15 minutes ) swimming part : ( 2 / 6 = 1 / 3 * 60 = 20 minutes ) 4 miles in ( 15 + 20 ) minutes 4 / 35 = 1 / 9 mile per minute answer : 1 / 9 mile per minute"
Answer: a
Problem: a man engaged a servant on the condition that he would pay him rs . 600 and a uniform after one year service . he served only for 9 months and received uniform and rs . 400 , find the price of the uniform ?
Options: a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 100 , e ) s . 200
Rationale: 9 / 12 = 3 / 4 * 600 = 450 400 - - - - - - - - - - - - - 50 1 / 4 - - - - - - - - 50 1 - - - - - - - - - ? = > rs . 200 answer : e
Answer: e
Problem: find the value of y from ( 12 ) ^ 1 x 6 ^ 4 ÷ 432 = y ?
Options: a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 36
Rationale: "36 e"
Answer: e
Problem: find the least number which when divided by 20 , 25,35 and 40 leaves remainders 14 , 19,29 and 34 respectively .
Options: a ) 1394 , b ) 1294 , c ) 1194 , d ) 1094 , e ) none of them
Rationale: "here , ( 20 - 14 ) = 6 , ( 25 – 19 ) = 6 , ( 35 - 29 ) = 6 and ( 40 - 34 ) = 6 . therefore , required number = ( l . c . m . of 20,25 , 35,40 ) – 6 = 1394 . answer is a ."
Answer: a
Problem: if 1 / 8 of a pencil is black , 1 / 2 of the remaining is white and the remaining 3 1 / 2 cm is blue , find the total length of the pencil .
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 5
Rationale: let the total length of the pencil be x cm . black part is 1 / 8 of the length so x / 8 . so the remaining part is x - x / 8 = = > 8 x / 8 - x / 8 = = > 7 x / 8 cm . white part = 1 / 2 * 7 x / 8 = 7 x / 16 cm . so the remaining part is 7 x / 8 - 7 x / 16 = = > 14 x / 16 - 7 x / 16 = 7 x / 16 which is equal to 3 1 / 2 . 7 x / 16 = 7 / 2 cross multiply and we get x = 16 / 2 = 8 cm . so the total length of the pencil is 8 cm . the correct answer is option c ) 8 .
Answer: c
Problem: marcella has 25 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 21 , b ) 20 , c ) 19 , d ) 16 , e ) 15
Rationale: "greatest number of paired shoes means greatest number of lost pairs 9 shoes have 4 pairs and 1 extra shoes of a pair . so a otal of 5 pairs she loses leftover pair = 20 answer : b"
Answer: b
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 180 resolutions ?
Options: a ) 724 m , b ) 704 m , c ) 287 m , d ) 278 m , e ) 253.4 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 180 resolutions . = 180 * 2 * 22 / 7 * 22.4 = 25344 cm = 253.4 m answer : e"
Answer: e
Problem: if a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster , he would have covered 80 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 150 , e ) 160
Rationale: "case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 80 ) = ( r + 5 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 2 ) x = 160 ans e"
Answer: e
Problem: a reduction of 20 % in the price of oil enables a house wife to obtain 10 kgs more for rs . 1500 , what is the reduced price for kg ?
Options: a ) rs . 20 , b ) rs . 25 , c ) rs . 30 , d ) rs . 35 , e ) rs . 40
Rationale: "explanation : 1500 * ( 20 / 100 ) = 300 - - - - 10 ? - - - - 1 = > rs . 30 answer : c"
Answer: c
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 99 km / hr . what is the length of the platform ?
Options: a ) 440 , b ) 488 , c ) 477 , d ) 426 , e ) 422
Rationale: "speed = 99 * 5 / 18 = 27.5 m / sec . length of the train = 27.5 * 20 = 550 m . let the length of the platform be x m . then , ( x + 550 ) / 36 = 27.5 = > x = 440 m . answer : a"
Answer: a
Problem: 100 white and black tiles will be used to form a 20 x 20 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ?
Options: a ) 75 , b ) 70 , c ) 85 , d ) 90 , e ) 95
Rationale: "answer = b please refer diagram below 90 - 20 = 70"
Answer: b
Problem: two numbers a and b are such that the sum of 6 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 3 , b ) 1 : 2 , c ) 4 : 3 , d ) 1 : 1 , e ) 3 : 2
Rationale: "explanation : 6 % of a + 4 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 6 a / 100 + 4 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 6 a + 4 b = 2 / 3 ( 6 a + 8 b ) ⇒ 18 a + 12 b = 12 a + 16 b ⇒ 6 a = 4 b ⇒ ab = 4 / 6 = 2 / 3 ⇒ a : b = 2 : 3 answer : option a"
Answer: a
Problem: if the sum of the first n positive integers is s , what is the sum of the first n negative even integers , in terms of s ?
Options: a ) s / 2 , b ) s , c ) 2 s , d ) 2 s + 2 , e ) 4 s
Rationale: answer is c given sum of - 1 - 2 - 3 . . . . . - n = s sum of - 2 , - 4 , - 6 . . . . - 2 n = 2 [ sum ( - 1 - 2 - 3 . . . . n ) ] = 2 s
Answer: c
Problem: if you add all the numbers on your mobile phone except 9 , what is the answer ?
Options: a ) 45 , b ) 28 , c ) 65 , d ) 36 , e ) 42
Rationale: "we have to add 0 to 8 to find the answer . therefore 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 answer is d"
Answer: d
Problem: a fruit drink is made of orange , watermelon , and grape juice , where 25 percent of the drink is orange juice and 40 percent is watermelon juice . if the drink is made with 70 ounces of grape juice , how many ounces is the drink total ?
Options: a ) 125 , b ) 160 , c ) 200 , d ) 250 , e ) 320
Rationale: "let the total number of ounces in the drink be x . % of orange = 25 % % of watermelon = 40 % % of grape = 100 % - 65 % = 35 % 0.35 x = 70 x = 200 therefore there are a total of 200 ounces in the drink . the answer is c ."
Answer: c
Problem: the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
Options: a ) 18.75 % , b ) 23 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: let wage of erica = 10 wage of robin = 1.3 * 10 = 13 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 13 ) / 13 * 100 % = 3 / 13 * 100 % = 23 % answer b
Answer: b
Problem: find the surface area of a cuboid 12 m long , 14 m broad and 7 m high
Options: a ) 868 sq . cm
b ) 600 sq . cm
c ) 700 sq . cm
d ) 900 sq . cm
e ) none of these
Rationale: explanation : surface area = [ 2 ( 12 x 14 + 14 x 7 + 12 x 7 ) ] cm 2 = ( 2 x 350 ) cm 2 = 700 cm 2 . answer : c
Answer: c
Problem: the speed of a boat in still water in 42 km / hr and the rate of current is 7 km / hr . the distance travelled downstream in 44 minutes is :
Options: a ) 86.6 km , b ) 46.6 km , c ) 35.9 km , d ) 35.6 km , e ) 26.6 km
Rationale: "speed downstream = ( 42 + 7 ) = 49 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 49 = 35.9 km answer : c"
Answer: c
Problem: what is the remainder when 750 * 810 * 830 * 790 is divided by 13 ?
Options: a ) 4 , b ) 9 , c ) 10 , d ) 8 , e ) 6
Rationale: "oa is ' c ' . oe : take the remainder from each of 750 / 15 , 810 / 15 and so on . . 750 / 13 gives remainder = 9 810 / 13 gives remainder = 4 830 / 13 gives remainder = 11 790 / 13 gives remainder = 10 the net remainder is the product of above individual remainders . i . e = 9 * 4 * 11 * 10 break them into pairs 9 * 4 / 13 gives remainder 10 and 11 * 10 / 13 gives remainder 6 so 10 * 6 / 13 gives remainder 8 . answer : c"
Answer: c
Problem: sides of a rectangular park are in the ratio 2 : 5 and its area is 3750 sq m , the cost of fencing it at 50 ps per meter is ?
Options: a ) s . 122 , b ) s . 129 , c ) s . 125 , d ) s . 120 , e ) s . 130.64
Rationale: "2 x * 5 x = 3750 = > x = 19.36 2 ( 80.64 + 50 ) = 261.28 m 261.28 * 1 / 2 = rs . 130.64 answer : e"
Answer: e
Problem: the sum of ages of 5 children born at the intervals of 3 years each is 60 years . what is the age of the youngest child ?
Options: a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 60 5 x = 30 x = 6 . age of the youngest child = x = 6 years . c )"
Answer: c
Problem: 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 9 % . what is the value of x ?
Options: a ) 57.5 litres , b ) 56.67 litres , c ) 57.67 litres , d ) 56.5 litres , e ) 50 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 = 9 % * 100 % ( 1 - x / 100 ) ^ 2 = 9 / 36 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 3 / 6 ) ^ 2 100 - x = 300 / 6 x = 50 ans e"
Answer: e
Problem: the length of each side of an equilateral triangle having an area of 4 √ 3 cm 2 is ?
Options: a ) 3 : 4
b ) 3 : 9
c ) 3 : 7
d ) 3 : 1
e ) 3 : 2
Rationale: let the speed of the train be x km / hr and that of the car be y km / hr . then , 120 / x + 480 / y = 8 or 1 / x + 4 / y = 1 / 15 - - - ( i ) and , 200 / x + 400 / y = 25 / 3 or 1 / x + 2 / y = 1 / 24 - - - ( ii ) solving ( i ) and ( ii ) , we get x = 60 and y = 80 ratio of speeds = 60 : 80 = 3 : 4 answer : a
Answer: a
Problem: length of a rectangular plot is 24 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 52 m , b ) 62 m , c ) 72 m , d ) 82 m , e ) 92 m
Rationale: "let breadth = x metres . then , length = ( x + 24 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 24 ) + x ] = 200 2 x + 24 = 100 2 x = 76 x = 38 . hence , length = x + 24 = 62 m b"
Answer: b
Problem: if x is real , find the maximum value of the expression - 2 x ^ 2 + 7 x + 9 .
Options: a ) 6.125 , b ) 9.125 , c ) 12.125 , d ) 15.125 , e ) 18.125
Rationale: "this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 7 x + 9 = ( - 2 x + 9 ) ( x + 1 ) the roots are 9 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 1.75 the maximum value is - 2 ( 1.75 ) ^ 2 + 7 ( 1.75 ) + 9 = 15.125 the answer is d ."
Answer: d
Problem: the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 150 . what is the manager ' s monthly salary ?
Options: a ) rs . 6003 , b ) rs . 6029 , c ) rs . 4650 , d ) rs . 6108 , e ) rs . 6011
Rationale: "explanation : manager ' s monthly salary rs . ( 1650 * 21 - 1500 * 20 ) = rs . 4650 . answer : c"
Answer: c
Problem: the probability of two events a and b are 0.25 and 0.30 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________
Options: a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6
Rationale: we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 30 - . 15 = . 40 but the probability of neither a nor b = 1 - . 40 = 0.60 answer : e
Answer: e
Problem: the size of a flat - screen tablet is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 6 - inch flat - screen tablet than a square 5 - inch flat - screen tablet ?
Options: a ) 5.0
b ) 6.0
c ) 6.8
d ) 5.8
e ) 5.5
Rationale: if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 6 - inch flat - screen television the diagonal ( hypotenuse ) = 6 so , we can apply the pythagorean theorem to get x ² + x ² = 6 ² simplify : 2 x ² = 6 ² divide both sides by 2 to get : x ² = 6 ² / 2 since the area of the square = x ² , we can see that the area of this square is 6 ² / 2 square 5 - inch flat - screen television the diagonal ( hypotenuse ) = 5 so , we can apply the pythagorean theorem to get x ² + x ² = 5 ² simplify : 2 x ² = 5 ² divide both sides by 2 to get : x ² = 5 ² / 2 since the area of the square = x ² , we can see that the area of this square is 5 ² / 2 difference in areas = 6 ² / 2 - 5 ² / 2 = ( 6 ² - 5 ² ) / 2 = ( 36 - 25 ) / 2 = 11 / 2 = 5.5 e
Answer: e
Problem: the sum of 4 consecutive even numbers is 140 . what would be the largest number ?
Options: a ) 33 , b ) 38 , c ) 70 , d ) 123 , e ) 12
Rationale: let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 ( x + 1 ) = 38 . answer : b
Answer: b
Problem: in a sample of college students , 50 percent are third year students and 70 percent are not second - year students . what fraction of those students who are not third - year students are second - year students ?
Options: a ) 2 / 3 , b ) 1 / 4 , c ) 2 / 5 , d ) 3 / 7 , e ) 2 / 9
Rationale: required answer = 40 / 60 . = 2 / 3 answer is a
Answer: a
Problem: a camera lens filter kit containing 5 filters sells for $ 75.50 . if the filters are purchased individually , 3 of them are priced at $ 7.35 each , 3 at $ 12.05 each , 1 at $ 12.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 5.35 % , b ) 6.35 % , c ) 7.35 % , d ) 8.35 % , e ) 9.35 %
Rationale: "cost of kit = $ 75.50 if filters are purchased individually - $ 7.35 * 3 + $ 12.05 * 3 + $ 12.50 = $ 70.70 amount saved = $ 75.50 - $ 70.70 = $ 4.80 required % age = ( $ 4.80 / $ 75.50 ) * 100 = 6.35 % so , the correct answer is b ."
Answer: b
Problem: if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability e that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability e = 1 / 24 . answer c ."
Answer: c
Problem: when positive integer n is divided by positive integer j , the remainder is 16 . if n / j = 204.04 , what is value of j ?
Options: a ) 100 , b ) 120 , c ) 400 , d ) 260 , e ) 380
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.04 here 204 is the quotient . given that remainder = 16 so , 204.04 = 204 + 16 / j so , j = 400 answer : c"
Answer: c
Problem: find the lowest common multiple of 24 , 36 and 40 .
Options: a ) 360 , b ) 420 , c ) 510 , d ) 320 , e ) 280
Rationale: "lcm = 2 * 2 * 2 * 3 * 3 * 5 = 360 . answer is a"
Answer: a
Problem: 14 is what percent of 70 ?
Options: a ) 0.2 % , b ) 2 % , c ) 5 % , d ) 20 % , e ) 500 %
Rationale: "14 = x * 70 / 100 x = 20 % ans ; d"
Answer: d
Problem: the perimeter of a semi circle is 140 cm then the radius is ?
Options: a ) 27 , b ) 28 , c ) 19 , d ) 11 , e ) 12
Rationale: "36 / 7 r = 140 = > r = 27 answer : a"
Answer: a
Problem: among the members of the malmo family , there are 3 times as many members who do not wear glasses as members who do . half of the malmo family members have blue eyes , and 4 / 5 of the family members who have blue eyes do not wear glasses . what percent of the malmo family members wear glasses and do not have blue eyes ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 35
Rationale: number in black are given and in red are calculated . now , since x + 3 x = 100 , then x = 25 and therefore = 25 − 10 = 15 answer : b .
Answer: b
Problem: a train passes a station platform in 20 sec and a man standing on the platform in 12 sec . if the speed of the train is 72 km / hr . what is the length of the platform ?
Options: a ) 227 , b ) 140 , c ) 160 , d ) 120 , e ) 171
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . length of the train = 20 * 12 = 240 m . let the length of the platform be x m . then , ( x + 240 ) / 20 = 20 = > x = 160 m . answer : c"
Answer: c
Problem: the distance between two cities a and b is 870 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 09 pm , b ) 07 pm , c ) 03 pm , d ) 05 am , e ) 03 am
Rationale: "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 870 . therefore , 60 x + 75 ( x - 1 ) = 870 . = > x = 7 . so , they meet at ( 8 + 7 ) i . e , 15 = > 3 pm answer : c )"
Answer: c
Problem: apple , orange , mango . mango + apple = 12 . mango + orange = 10 . mango + apple + orange = 38 . calculate the no of mango ?
Options: a ) - 8 , b ) - 9 , c ) - 10 , d ) - 12 , e ) - 16
Rationale: mango + apple = 12 . . . . . . . . . . . . . ( a ) mango + orange = 10 . . . . . . . . . . ( b ) adding a and b 2 mango + apple + orange = 22 but mango + apple + orange = 38 . . . . given which is not possible . in this case , no of mangoes is negative ( - 16 ) answer : d
Answer: d
Problem: a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 360 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 110 , c ) 120 , d ) 140 , e ) 220
Rationale: "orchestra seats - a balcony seats - b a + b = 360 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 360 = 3320 - 2880 = 440 i . e . a = 110 and b = 360 - 110 = 250 more seats in balcony than orchestra = b - a = 250 - 110 = 140 answer : option d"
Answer: d
Problem: a train running at the speed of 36 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 180 metres , c ) 324 metres , d ) 90 metres , e ) 100 meters
Rationale: "speed = 36 x 5 / 18 m / sec = 30 / 3 m / sec . length of the train = ( speed x time ) . length of the train = 30 / 3 x 9 m = 90 m . answer : d"
Answer: d
Problem: tough and tricky questions : arithmetic . ( 56 ^ 2 + 56 ^ 2 ) / 28 ^ 2 =
Options: a ) 4 , b ) 18 , c ) 29 , d ) 8 , e ) 116
Rationale: ans is 8 my approach was : ( 56 ^ 2 + 56 ^ 2 ) / 28 ^ 2 = 56 ( 56 + 56 ) / 28 * 28 = 56 * 112 / 28 * 28 = 2 * 4 = 8 d
Answer: d
Problem: a boy has rs . 480 in the denominations of one - rupee notes , 5 - rupee notes and 10 - rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ?
Options: a ) 90 , b ) 110 , c ) 140 , d ) 130 , e ) 120
Rationale: let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 . a
Answer: a
Problem: glen and hannah drive at constant speeds toward each other on a highway . glen drives at a constant speed of 37 km per hour . at a certain time they pass by each other , and then keep driving away from each other , maintaining their constant speeds . if glen is 130 km away from hannah at 6 am , and also 130 km away from hannah at 11 am , then how fast is hannah driving ( in kilometers per hour ) ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: glen and hannah complete 260 km / 5 hours = 52 km / hour hannah ' s speed is 52 - 37 = 15 km / hour the answer is d .
Answer: d
Problem: 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 20 % . 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: "let initial output is o then after 10 % increase it will be 1.1 o and after 20 % increase on this new output the latest output will be 1.1 o * 1.20 = 1.32 o now we have to decrease the output by some percentage so that the new output is same as the starting output ( o ) so , 1.32 o * ( 1 - x / 100 ) = o = > x = 24.24 % so , answer will be b"
Answer: b
Problem: integer d is the product of the integers a , b , and c and 1 < a < b < c . if the remainder when 233 is divided by d is 79 , what is the value of a + c ?
Options: a ) 7 , b ) 9 , c ) 13 , d ) 14 , e ) 18
Rationale: 79 is the remainder , therefore the number ( a * b * c ) or multiple of the number we need is 79 less than 233 hence 233 - 79 = 154 therefore , 154 is either a number we want or it is a multiple of the number we want but the largest factor of 154 is 77 because 77 * 2 = 154 but 77 is less than 79 hence it can not be a number thus 154 is the number we want a * b * c = 154 now factorize 154 = 1 * 2 * 7 * 11 all are prime also we know 1 < a < b < c thus a = 2 and c = 11 therefore a + c = 2 + 11 = 13 answer : c
Answer: c
Problem: each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 20 boxes , 4 are 10 - pound boxes and 16 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 15 , the ratio of 10 - pound boxes : 20 - pound boxes should be 1 : 1 . the number of 10 pound boxes remains the same so we still have 4 of them . to get a ratio of 1 : 1 , the number of 20 - pound boxes must be 4 . we need to remove 12 of the 20 - pound boxes . the answer is b ."
Answer: b
Problem: the monthly rent of a shop of dimension 18 feet × 20 feet is rs . 3600 . what is the annual rent per square foot of the shop ?
Options: a ) 120 , b ) 56 , c ) 68 , d ) 87 , e ) 92
Rationale: "sol . monthly rent per square feet = 3600 / ( 18 * 20 ) = 10 & annual rent per square feet = 12 * 10 = 120 answer : a"
Answer: a
Problem: a van takes 6 hours to cover a distance of 378 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 70 kmph , d ) 42 kmph , e ) 90 kmph
Rationale: "time = 6 distence = 378 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 378 / 9 = 42 kmph d"
Answer: d
Problem: country x taxes each of its citizens an amount equal to 14 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 52,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.14 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 5,600 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,400 - - > x = 52,000 . answer : b ."
Answer: b
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 18.75 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 23 % , c ) 25 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 118.75 let marked price be rs . x . then , 95 / 100 x = 118.75 x = 11875 / 95 = rs . 125 now , s . p . = rs . 125 , c . p . = rs . 100 profit % = 25 % . answer : c"
Answer: c
Problem: a sum of 15,600 amounts to 21,200 in 5 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 2 % , b ) 1 % , c ) 7 % , d ) 5 % , e ) 8 %
Rationale: "c 7 % s . i . = ( 21200 - 15600 ) = 5600 . rate = ( 100 x 5600 ) / ( 15600 x 5 ) % = 7 %"
Answer: c