regisss/math_qa huggingface dataset:
Problem: if an article is sold at 19 % profit instead of 12 % profit , then the profit would be $ 84 more . what is the cost price ?
Options: a ) $ 900 , b ) $ 1200 , c ) $ 1500 , d ) $ 1800 , e ) $ 2100
Rationale: "7 % * cost price = $ 84 1 % * cost price = $ 84 / 7 = $ 12 the cost price is $ 1200 . the answer is b ."
Answer: b
Problem: if 213 × 16 = 3408 , then 16 × 21.3 is equal to :
Options: a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these
Rationale: "solution 16 × 21.3 = ( 16 x 213 / 10 ) = ( 16 x 213 / 10 ) = 3408 / 10 = 340.8 . answer d"
Answer: d
Problem: a , b and c invest in a partnership in the ratio : 7 / 24 / 36 / 5 . after 4 months , a increases his share 50 % . if the total profit at the end of one year is rs . 21600 , then what is b ' s share in the profit ?
Options: a ) 1000 , b ) 2000 , c ) 3000 , d ) 4000 , e ) 5000
Rationale: ratio of the initial investment = 7 / 2 : 4 / 3 : 6 / 5 = 105 : 40 : 36 therefore , let the initial investments of a , b and c be 105 x , 40 x and 36 x respectively a increases his share 50 % after 4 months . hence the ratio of their investments = ( 105 x × 4 ) + ( 105 x × 150 / 100 × 8 ) : 40 x × 12 : 36 x × 12 = 105 + ( 105 × 3 / 2 × 2 ) : 40 × 3 : 36 × 3 = 105 × 4 : 40 × 3 : 36 × 3 = 35 × 4 : 40 : 36 = 35 : 10 : 9 b ' s share = total profit × 10 / 54 = 21600 × 10 / 54 = 4000 answer is d .
Answer: d
Problem: if x and y are numbers such that ( x + 3 ) ( y - 3 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
Options: a ) 0 , b ) 3 , c ) 6 , d ) 9 , e ) 12
Rationale: "from ( x + 3 ) ( y - 3 ) = 0 it follows that either x = - 3 or y = 3 . thus either x ^ 2 = 9 or y ^ 2 = 9 . now , if x ^ 2 = 9 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 9 + 0 = 9 . similarly if y ^ 2 = 9 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 9 = 9 . answer : d ."
Answer: d
Problem: a bag contains 6 black and 3 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 1 / 3 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 3 ) = 9 . number of white balls = 3 . p ( drawing a white ball ) = 3 / 9 = 1 / 3 . option b ."
Answer: b
Problem: find large number from below question the difference of two numbers is 1200 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1437 , b ) 1250 , c ) 1540 , d ) 1600 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1200 = 6 x + 15 5 x = 1185 x = 237 large number = 237 + 1365 = 1437 a"
Answer: a
Problem: due to construction , the speed limit along an 8 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 4.99 , b ) b ) 8 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 8 miles stretch = 8 * 60 / 55 = 8 * 12 / 11 = 8.72 new time in minutes to cross 8 miles stretch = 8 * 60 / 35 = 8 * 12 / 7 = 13.71 time difference = 4.99 ans : a"
Answer: a
Problem: set a consists of all the prime numbers between 2 and 13 . what is the range of set a ?
Options: a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 8
Rationale: "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 11 lowest number = 3 range = highest - lowest = 11 - 3 = 8 option e"
Answer: e
Problem: if the sum of a number and its square is 210 , what is the number ?
Options: a ) 16 , b ) 14 , c ) 25 , d ) 87 , e ) 171
Rationale: "explanation : let the integer be x . then , x + x 2 = 210 x 2 + x - 210 = 0 ( x + 15 ) ( x – 14 ) = 0 x = 14 answer : b"
Answer: b
Problem: a train of length 240 m crosses a bridge of length 150 m in 20 seconds . what is the speed of train ?
Options: a ) 33 , b ) 27 , c ) 25 , d ) 70.2 , e ) 72
Rationale: "sol : ( length of train + length of bridge ) = speed of train x time ( 240 + 150 ) = 20 x speed speed = 390 / 20 = 19.5 m / s = 70.2 km / h answer = d"
Answer: d
Problem: three interviewers , a , b , and c are interviewing 50 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer a admitted 20 applicants , b admitted 22 applicants , and c admitted 20 applicants , at least how many applicants get the admission ?
Options: a ) 4 , b ) 0 , c ) 6 , d ) 8 , e ) 12
Rationale: "if a admitted 20 are overlapping with b admission of 22 but c does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : b"
Answer: b
Problem: find the sum of first 100 odd numbers
Options: a ) 5500 , b ) 2005 , c ) 10000 , d ) 5800 , e ) 4960
Rationale: "explanation : n 2 = 1002 = 10000 answer : option c"
Answer: c
Problem: a man â € ™ s current age is ( 2 / 5 ) of the age of his father . after 6 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?
Options: a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 30
Rationale: "let , father â € ™ s current age is a years . then , man â € ™ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 6 ] = ( 1 / 2 ) ( a + 6 ) 2 ( 2 a + 30 ) = 5 ( a + 6 ) a = 30 e"
Answer: e
Problem: the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 1.50 + 1.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?
Options: a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 6.00 , e ) $ 5.00
Rationale: "number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 1.50 + 1.50 ( x − 2 ) = 1.50 + 1.5 * 3 = 1.5 + 4.5 = 6 $ answer d"
Answer: d
Problem: a fraction in reduced form is such that when it is squared and then its numerator is reduced by 33 ( 1 / 3 ) % and denominator is reduced to 20 % , its result is twice the original fraction . the sum of numerator and denominator is :
Options: a ) 8 , b ) 13 , c ) 17 , d ) 15 , e ) none of these
Rationale: solution : let the fraction be x / y . when fraction is squared its numerator is reduced by 33 ( 1 / 3 ) and denominator is reduced by 20 % . according to question , ( x / y ) 2 * 33 ( 1 / 3 ) % / 20 % = 2 ( x / y ) . or , ( x / y ) 2 * ( 2 / 3 ) / ( 1 / 5 ) = 2 ( x / y ) . or , x / y = 3 / 5 . sum of numerator and denominator is , ( x + y ) = 3 + 5 = 8 . answer : option a
Answer: a
Problem: car a is 24 miles behind car b , which is traveling in the same direction along the same route as car a . car a is traveling at a constant speed of 58 miles per hour and car bis traveling at a constant speed of 50 miles per hour . how many hours will it take for car a to overtake and drive 8 miles ahead of car b ?
Options: a ) 1.5 , b ) 2.0 , c ) 2.5 , d ) 3.0 , e ) 4.0
Rationale: "relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 24 miles and drive 8 miles ahead so to drive 32 miles it ' ll need 32 / 8 = 4 hours . answer : e ."
Answer: e
Problem: a rainstorm increased the amount of water stored in state j reservoirs from 180 billion gallons to 200 billion gallons . if the storm increased the amount of water in the reservoirs to 60 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 90 , b ) 114 , c ) 125 , d ) 130 , e ) 144
Rationale: after the reservoir is filled to 200 gallons the amount of water is at 60 % - which means that 40 % of the reservoir is empty . to figure out what that 40 % is approximate : 200 gallons / 60 percent = x gallons / 40 percent , therefore , x = 133.33 gallons , answer choices a , b , c , d are below 133.33 . we know that the reservoir must be short more than 133.33 gallons , therefore , the only possible choice is e .
Answer: e
Problem: find the simple interest for rs . 2000 at 8 % p / a for 2 years .
Options: a ) rs . 300 , b ) 3 rs . 20 , c ) rs . 420 , d ) rs . 520 , e ) rs . 460
Rationale: "s . i = ( 2000 * 8 * 2 ) / 100 p = 320 answer : b"
Answer: b
Problem: 16 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 232 , d ) 90 , e ) 45
Rationale: "there are 16 business exec and in each handshake 2 business execs are involved . hence 16 c 2 = 120 also , each of 16 exec will shake hand with every 7 other chairmen for total of 112 handshake . total = 120 + 112 = 232 ans : c"
Answer: c
Problem: if two trains are 120 miles apart and are traveling toward each other at constant rate of 30 miles per hour and 40 miles per hour , respectively , how far apart will they be 1 hour before they meet ?
Options: a ) 10 , b ) 30 , c ) 40 , d ) 50 , e ) 70
Rationale: they would meet in 120 / 70 = 12 / 7 hours 1 hour earlier 5 / 7 hours distance between trains = total distance - ( distance covered by train a + distance covered by train b ) = 120 - ( 5 / 7 ( 40 + 30 ) ) [ distance of a = 5 / 7 * 40 ; like wise distance by b ] = 70 km answer : e
Answer: e
Problem: a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 2211 , what is the value of n ?
Options: a ) 22 , b ) 134 , c ) 62 , d ) 122 , e ) 672
Rationale: "factorise 2211 . . 3 * 11 * 67 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 61 = 134 . . ans : b"
Answer: b
Problem: if 30 honey bees make 30 grams of honey in 30 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 30 , d ) 49 , e ) 30
Rationale: "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 30 : : 30 : x honey 30 : 1 = > 1 x 30 x x = 30 x 1 x 30 = > x = 30 . answer : c"
Answer: c
Problem: a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many q apples did each person get before 45 people joined the feast ?
Options: a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .
Rationale: "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons q = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c"
Answer: c
Problem: if the sides of a triangle are 9 cm , 16 cm and 19 cm , what is its area ?
Options: a ) 69 , b ) 72 , c ) 75 , d ) 89 , e ) 93
Rationale: "the triangle with sides 9 cm , 16 cm and 19 cm is right angled , where the hypotenuse is 19 cm . area of the triangle = 1 / 2 * 9 * 16 = 72 cm 2 answer : option b"
Answer: b
Problem: the number of positive integers valued pairs ( x , y ) satisfying 4 x - 17 y = 1 and x < = 1000 ( x is less than or equal to 1000 ) is
Options: a ) 59 , b ) 57 , c ) 55 , d ) 58 , e ) 60
Rationale: "we are asked to find integer solutions for x , y . there is no need to apply euclidian algorithm here , we can get particular solutions simply by plugging in some values . as y reaches 3 we get : y ’ = 3 and x ’ = 13 . we need only to solve for x . general solution for x will be : x = x ’ + bn = 13 + 17 n hence lower limit for n is n ≥ 0 . now we ’ ll find upper limit using given restriction x ≤ 1000 . plugging in general solution we ’ ll get : 13 + 17 n ≤ 1000 17 n ≤ 987 n ≤ 58 and our list of possible values of n has following representation : 0 , 1,2 , 3 , … . . , 58 total number of elements is 59 . answer : a"
Answer: a
Problem: a monkey ascends a greased pole 20 meters high . he ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute . if this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
Options: a ) 30 th minute , b ) 31 st minute , c ) 37 th minute , d ) 32 nd minute , e ) 33 th minute
Rationale: "the money is climbing 1 meter in 2 min . this pattern will go on till he reaches 10 meters . i mean this will continue for first 18 * 2 = 36 mins . he would have reached 18 meters . after that he will climb 2 meters and he will reach the pole . so total time taken = 36 + 1 = 37 mins . so , asnwer will be c"
Answer: c
Problem: a retailer sells 10 shirts . the first 3 he sells for $ 20 , $ 22 and $ 25 . if the retailer wishes to sell the 10 shirts for an overall average price of over $ 20 , what must be the minimum average price of the remaining 7 shirts ?
Options: a ) $ 14.00 , b ) $ 16.00 , c ) $ 17.00 , d ) $ 19.00 , e ) $ 23.00
Rationale: "first 3 shirts are sold for $ 20 , $ 22 and $ 25 = $ 67 . to get average price of $ 20 , total sale should be 10 * $ 20 = $ 200 so remaining 7 shirts to be sold for $ 200 - $ 67 = $ 133 answer should be 133 / 7 = $ 19.00 that is d"
Answer: d
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum z of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: "i would solve it in a different way . first of all , total number of even integers between 99 and 301 are , ( 301 - 99 ) / 2 = 202 / 2 = 101 average = ( 301 + 99 ) / 2 = 400 / 2 = 200 sum z = average * total count = 200 * 101 = 20,200 answer is b"
Answer: b
Problem: there are 300 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of managers to 98 % ?
Options: a ) 200 , b ) 175 , c ) 150 , d ) 125 , e ) 100
Rationale: there are 297 managers and 3 others . the 3 others would compose 2 % of the total number of people if there were 150 people in the room . thus 150 managers must leave . the answer is c .
Answer: c
Problem: the ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8 . if there are 75 black cars in the lot , how many red cars are there in the lot ?
Options: a ) 11 , b ) 28 , c ) 24 , d ) 29 , e ) 32
Rationale: "b is correct r / b = 3 / 8 and b = 75 r = 75 * 3 / 8 = 28"
Answer: b
Problem: a total of 50 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 20 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]
Options: a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 8 / 7
Rationale: let ' take the number of geese to be 100 . male = 50 . female = 50 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 20 % are male i . e 20 / 100 * 20 = 4 geese ( males ) and now we know out of the total 20 geese , 4 are male , then 16 have to be female . now the ratio part , male geese ratios = 4 / 50 = 2 / 25 . - a female geese ratios = 16 / 50 = 8 / 25 - b cross multiply equations a and b and you get = 1 / 4 . ans a
Answer: a
Problem: mukesh weight 56.7 kg . if he reduces his weight in the ratio 7 : 6 . new weight of mukesh is ?
Options: a ) 47.6 , b ) 48.6 , c ) 49.6 , d ) 50.6 , e ) 51.6
Rationale: given ratio is 7 : 6 ; let weight before and after reduction be 7 x and 6 x respectively . a / q 7 x = 56.7 = > x = 56.7 / 7 = > x = 8.1 reduced weight = 6 x = 6 * 8.1 = 48.6 ; hence reduced weight = 48.6 answer : b
Answer: b
Problem: a shopkeeper fixes the marked price of an item 30 % above its cost price . the percentage of discount allowed to gain 8 % is
Options: a ) 15.92 % , b ) 16.92 % , c ) 17.92 % , d ) 18.92 % , e ) none of these
Rationale: "explanation : let the cost price = rs 100 then , marked price = rs 130 required gain = 8 % , so selling price = rs 108 discount = 130 - 108 = 22 discount % = ( 22 / 130 ) * 100 = 16.92 % option b"
Answer: b
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 36 kilometers , maxwell ' s walking speed is 3 km / h , and brad ' s running speed is 6 km / h . what is the distance traveled by maxwell when they meet in the middle ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 13 , e ) 11
Rationale: consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 3 xt = 36 - 6 xt ( i . e distance = speed x time ) = > 9 t = 36 hence t = 4 oa = 3 x 4 = 12 km answer : a
Answer: a
Problem: a meal cost $ 32.50 and there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 40 - 42 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: "10 % ( 32.5 ) = 3.25 15 % ( 32.5 ) = 4.875 total amount could have been 32.5 + 3.25 and 32.5 + 4.875 = > could have been between 35.75 and 37.375 = > approximately between 36 and 37 answer is e ."
Answer: e
Problem: stacy and heather are 15 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ? .
Options: a ) 6.5 mile , b ) 5.7 mile , c ) 7.0 mile , d ) 8.0 mile , e ) 12 mile
Rationale: "ss - stacy ' s speed = 6 m / hr sh - heather ' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 15 - 2.4 = 12.6 time taken = distance / speed = 12.6 / 11 = 1.145 hrs heather will cover = 5 * 1.145 = 5.72 miles . answer b"
Answer: b
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 13.69 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 37 , d ) 87 , e ) 97
Rationale: "money collected = ( 13.69 x 100 ) paise = 1369 paise numbers of members = 1369 squareroot = 37 answer c"
Answer: c
Problem: find the area of trapezium whose parallel sides are 10 cm and 18 cm long , and the distance between them is 15 cm .
Options: a ) 287 cm 2 , b ) 785 cm 2 , c ) 285 cm 2 , d ) 785 cm 2 , e ) 210 cm 2
Rationale: "explanation : area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 10 + 18 ) * ( 15 ) = 210 cm 2 answer : option e"
Answer: e
Problem: how many paying stones , each measuring 2 1 / 2 m * 2 m are required to pave a rectangular court yard 40 m long and 16 1 / 2 m board ?
Options: a ) 99 , b ) 132 , c ) 16 , d ) 10 , e ) 15
Rationale: "40 * 33 / 2 = 5 / 2 * 2 * x = > x = 132 answer : b"
Answer: b
Problem: when a number is divided by 13 , the remainder is 11 . when the same number is divided by 17 , the remainder is 9 . what is the number ?
Options: a ) 389 , b ) 356 , c ) 380 , d ) 350 , e ) 349
Rationale: "x = 13 p + 11 and x = 17 q + 9 13 q + 11 = 17 q + 9 17 q - 13 q = 2 q = 2 + 13 q / 17 the least value of p for which q = 2 + 13 q / 17 is a whole number is p = 26 x = ( 13 * 26 * 11 ) = ( 338 + 11 ) = 349 . answer is e"
Answer: e
Problem: if 1 / ( x + 5 ) + 1 / ( x - 5 ) = 1 / ( x - 5 ) , what is the value of x ?
Options: a ) - 1 , b ) 3 , c ) 1 , d ) 2 , e ) 5
Rationale: "if we solve the question , we get x = 5 . option : e"
Answer: e
Problem: how many liters of water must be added to 20 liters of milk and water containing 10 % water to make it 60 % water ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 22 , e ) 25
Rationale: "by rule of alligation : 60 % - 10 % = 50 % 100 % - 60 % = 40 % quantity of pure water : quantity of the mixture = 5 : 4 there are 20 liters of mixture , so we need to add 25 liters of pure water . the answer is e ."
Answer: e
Problem: the value of a machine depreciates at 20 % per annum . if its present value is $ 1 , 50,000 , at what price should it be sold after two years such that a profit of $ 24,000 is made ?
Options: a ) $ 250000 , b ) $ 430000 , c ) $ 120000 , d ) $ 170000 , e ) $ 150000
Rationale: "c $ 1 , 20,000 the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = $ 96,000 sp such that a profit of $ 24,000 is made = 96,000 + 24,000 = $ 1 , 20,000"
Answer: c
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 12 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 165 , e ) 462
Rationale: "ans : 462 7 c 1 * 12 c 2 answer e )"
Answer: e
Problem: an inspector rejects 10 % of the meters as defective . how many will he examine to reject 20 ?
Options: a ) a ) 100 , b ) b ) 120 , c ) c ) 250 , d ) d ) 200 , e ) e ) 160
Rationale: "then , 10 % of x = 20 ( 10 / 100 ) x = 20 x = ( 20 * 100 * ) / 10 = 200 answer is d"
Answer: d
Problem: pipe a can fill a tank in 3 hours . due to a leak at the bottom , it takes 6 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 67 , b ) 88 , c ) 4.5 , d ) 26 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 3 - 1 / x = 1 / 6 = > 1 / x = 1 / 2 - 1 / 6 = 1 / 4.5 = > x = 4.5 answer : c"
Answer: c
Problem: the area of a rectangular field is equal to 200 square meters . its perimeter is equal to 60 meters . find the width of this rectangle .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "l * w = 200 : area , l is the length and w is the width . 2 l + 2 w = 60 : perimeter l = 30 - w : solve for l ( 30 - w ) * w = 200 : substitute in the area equation w = 10 and l = 20 : correct answer b"
Answer: b
Problem: carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 2 inches tall . how tall are the sculpture andbase together ?
Options: a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.0 feet , e ) 3.5 feet
Rationale: "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 2 = 36 36 / 12 = 3.0 feet answer : d"
Answer: d
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 56 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) s . 57.40 , b ) s . 57.22 , c ) s . 51.219 , d ) s . 56.18 , e ) s . 53.11
Rationale: "explanation : sum = ( 56 * 100 ) / ( 2 * 5 ) = rs . 560 amount = [ 560 * ( 1 + 5 / 100 ) 2 ] = rs . 617.4 c . i . = ( 617.4 - 560 ) = rs . 57.4 . answer : a"
Answer: a
Problem: 18 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) 22 , b ) 66 , c ) 88 , d ) 100 , e ) 281
Rationale: "( 18 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 40 40 – 18 = 22 answer : a"
Answer: a
Problem: the perimeter of a rectangle is equal to 280 meters . the ratio of its length to its width is 5 : 2 . find the area of the rectangle .
Options: a ) 400 square meters
b ) 4000 square meters
c ) 20 square meters
d ) 2000 square meters
e ) 1000 square meters
Rationale: solution if the ratio of the length to the width is 5 : 2 , then the measure l of the length and and the measure w of the with can be written as l = 5 x and w = 2 x we now use the perimeter to write 280 = 2 ( 2 l + 2 w ) = 2 ( 5 x + 2 x ) = 14 x solve for x 280 = 14 x x = 280 / 14 = 20 the area a of the rectangle is given by a = l × w = 5 x × 2 x = 10 x ^ 2 = 10 × 20 ^ 2 = 4000 square meters answer is b
Answer: b
Problem: at the end of year x , automobile installment credit accounted for 36 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 35 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 291.67 , b ) 105 , c ) 301.05 , d ) 288 , e ) 249.55
Rationale: "system of equations a = ( 36 / 100 ) c ( 1 / 3 ) a = 35 - - > a = 105 substitution 105 = ( 36 / 100 ) c c = ( 100 / 36 ) 105 - you can do the ugly calculation 105 / 36 * 100 the correct answer is a . the correct answer is 291.67"
Answer: a
Problem: the cross - section of a tunnel is a trapezium in shape . if the tunnel is 15 m wide at the top and 5 m wide at the bottom and the area of cross - section is 400 sq m , the depth of tunnel is ?
Options: a ) 200 m , b ) 600 m , c ) 400 m , d ) 800 m , e ) 900 m
Rationale: 1 / 2 * d ( 15 + 5 ) = 400 d = 400 answer : c
Answer: c
Problem: if j is the least positive integer that is divisible by every integer from 10 to 15 inclusive , then j / 26 is =
Options: a ) 1155 , b ) 2310 , c ) 4620 , d ) 30030 , e ) 60060
Rationale: the integer should be divisible by : 10 , 11 , 12 , 13 , 14 and 15 , that is 5 * 211 , 3 * 2 ^ 2 , 13 , 2 * 7 , and 3 * 5 . the least common multiple of these integers is the product of 13 , 11 , 7 , 5 , 3 and 2 ^ 2 . then , r / 26 is ( 13 * 11 * 7 * 5 * 3 * 2 ^ 2 ) / 2 * 13 = 11 * 7 * 5 * 3 * 2 = 2310 . answer : b .
Answer: b
Problem: john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 4 % and the mobile phone at a profit of 20 % . overall how much he make aprofit .
Options: a ) s . 190 , b ) s . 1120 , c ) s . 1200 , d ) s . 1250 , e ) s . 1290
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 20 / 100 ) = 8000 + 1600 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 1600 = rs . 1200 as this is positive , an overall profit of rs . 1200 was made . c"
Answer: c
Problem: the area of sector of a circle whose radius is 18 metro and whose angle at the center is 42 â ° is ?
Options: a ) 52.6 , b ) 52.9 , c ) 52.8 , d ) 118.8 , e ) 52.2
Rationale: "42 / 360 * 22 / 7 * 18 * 18 = 118.8 m 2 answer : d"
Answer: d
Problem: the amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5 . if they worked a combined total of 120 hours , how many hours did the secretary who worked the longest spend on the project ?
Options: a ) 80 , b ) 70 , c ) 75 , d ) 16 , e ) 14
Rationale: "8 x = 120 = > x = 15 therefore the secretary who worked the longest spent 15 x 5 = 75 hours on the project option ( c )"
Answer: c
Problem: a number of 44 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?
Options: a ) 10 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "to maximize # of boxes we should minimize marbles per box : 13 * 3 + 1 * 5 = 44 - - > 13 + 1 = 14 . answer b"
Answer: b
Problem: danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 192 , what is the area of the side face of the box ?
Options: a ) 13 , b ) 16 , c ) 18 , d ) 29 , e ) 32
Rationale: "lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 192 l * 1.5 l * 2 l = 192 l = 4 side face area = l * d = l * 2 l = 4 * 2 * 4 = 32 e is the answer"
Answer: e
Problem: diana is painting statues . she has 1 / 2 of a gallon of paint remaining . each statue requires 1 / 4 gallon of paint . how many statues can she paint ?
Options: a ) 2 , b ) 20 , c ) 28 , d ) 14 , e ) 19
Rationale: "number of statues = all the paint ÷ amount used per statue = 1 / 2 ÷ 1 / 4 = 1 / 2 * 4 / 1 = 2 answer is a"
Answer: a
Problem: find the average of first 15 natural numbers .
Options: a ) 10 , b ) 120 , c ) 15 , d ) 8 , e ) 16
Rationale: explanation : sum of first n natural numbers = n ( n + 1 ) / 2 hence , sum of first 15 natural numbers = ( 15 x 16 ) / 2 = 120 therefore , required average of = 120 / 15 = 8 answer : d
Answer: d
Problem: the “ a - number ” of a number x is defined as the ones digit of 2 ^ x . antony rolls a die with 6 sides labeled with the integers from 1 to 6 , each of which has an equal probability of landing face - up . he then takes 3 ^ a , where a is the a - number of the result of his die roll , and plots 3 ^ a on a number line as the point a . finally , he repeats this entire process , this time plotting the result as the point b . what is the probability that the distance between a and b is greater than the value of b ?
Options: a ) 3 / 8 , b ) 13 / 36 , c ) 17 / 36 , d ) 19 / 36 , e ) 23 / 36
Rationale: if you calculate 3 ^ a for 1 st roll , all 6 results will be 9 , 81 , 6561 , 729 , 9 , 81 . this result is the same for 2 nd roll . 9 , 81 , 6561 , 729 , 9 , 81 . about distance : if the first result is 9 and the second is also 9 , the distance is 9 - 9 = 0 which is smaller than 9 . if the first result is 9 and the second is 81 , the distance is 81 - 9 = 72 which is also smaller than b which has the value of 81 . if the first result is 81 and the second is 9 , the distance will be greater than b . distance 81 - 9 = 72 > 9 . on the first roll , the probability of getting result 9 is 2 / 6 . in this case no other alternative values for second roll which would make the distance greater than b . so probability is 0 . so next estimations are : probability of getting 81 on the first roll ( 2 / 6 ) * probability of getting 9 on the second roll ( 2 / 6 ) = 1 / 9 probability of getting 729 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 on the second roll ( 4 / 6 ) = 1 / 9 probability of getting 6561 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 , 729 on the first roll ( 5 / 6 ) = 5 / 36 all together : 1 / 9 + 1 / 9 + 5 / 36 = 13 / 36 = b
Answer: b
Problem: you and your friend spent a total of $ 17 for lunch . your friend spent $ 3 more than you . how much did your friend spend on their lunch ?
Options: a ) $ 9 , b ) $ 3 , c ) $ 4 , d ) $ 10 , e ) $ 5
Rationale: "my lunch = l , my friends lunch = l + 3 ( l ) + ( l + 3 ) = 17 l + l + 3 - 3 = 17 - 3 2 l = 14 l = 7 my friends lunch l + 3 = 7 + 3 = $ 10 , the answer is d"
Answer: d
Problem: a man buy a book in rs 50 & sale it rs 60 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: "cp = 50 sp = 60 profit = 60 - 50 = 10 % = 10 / 50 * 100 = 20 % answer : b"
Answer: b
Problem: a man complete a journey in 1010 hours . he travels first half of the journey at the rate of 2121 km / hr and second half at the rate of 2424 km / hr . find the total journey in km .
Options: a ) 121 km , b ) 242 km , c ) 224 km , d ) 112 km , e ) 110 km
Rationale: "solution 1 average speed = 2 ã — 21 ã — 2421 + 24 = 22.4 km / hr = 2 ã — 21 ã — 2421 + 24 = 22.4 km / hr total distance = 22.4 ã — 10 = 224 km answer is c"
Answer: c
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 20 months , find for how much time did q invest the money ?
Options: a ) 11 , b ) 40 , c ) 18 , d ) 16 , e ) 12
Rationale: "7 * 5 : 20 * x = 7 : 10 x = 40 answer : b"
Answer: b
Problem: pipe a fills a tank in 56 minutes . pipe b can fill the same tank 7 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: a ' s rate is 1 / 56 and b ' s rate is 1 / 8 . the combined rate is 1 / 56 + 1 / 8 = 1 / 7 the pipes will fill the tank in 7 minutes . the answer is d .
Answer: d
Problem: a contractor undertakes to built a walls in 50 days . he employs 20 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 30 , e ) none of these
Rationale: 20 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 20 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 20 × 25 × 0.6 / 25 × 0.4 = 30 men answerd
Answer: d
Problem: find the value for m ? 19 ( m + n ) + 17 = 19 ( - m + n ) - 135
Options: a ) 0 , b ) - 1 , c ) 1 , d ) 2 , e ) - 4
Rationale: 19 m + 19 n + 17 = - 19 m + 19 n - 135 38 m = - 152 = > m = - 4 e
Answer: e
Problem: there are 720 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 320 , b ) 345 , c ) 450 , d ) 380 , e ) 400
Rationale: "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 720 . hence 3 x + 5 x = 720 solve for x 8 x = 720 x = 90 number of boys 3 x = 3 × 90 = 270 number of girls 5 x = 5 × 90 = 450 c"
Answer: c
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 2500 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 200
Rationale: "given that the area of the square = 2500 sq . units = > side of square = √ 2500 = 50 units the radius of the circle = side of the square = 50 units length of the rectangle = 2 / 5 * 50 = 20 units given that breadth = 10 units area of the rectangle = lb = 20 * 10 = 200 sq . units answer : option e"
Answer: e
Problem: convert 1.6 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .
Rationale: "1.6 hectares in ares 1 hectare = 100 ares therefore , 1.6 hectares = 1.6 × 100 ares = 160 ares . answer - b"
Answer: b
Problem: the average of 7 numbers is 15 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) a ) 110 , b ) b ) 122 , c ) c ) 90 , d ) d ) 85 , e ) e ) 75
Rationale: explanation : average of new numbers = 15 * 5 = 75 answer : option e
Answer: e
Problem: calculate the speed of a boat in still water ( in km / hr ) if in one hour , the boat goes 15 km / hr downstream and 7 km / hr upstream .
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 11 kmph
Rationale: "speed in still water = ( 15 + 7 ) 1 / 2 kmph = 11 kmph . answer : e"
Answer: e
Problem: a and b go around a circular track of length 400 m on a cycle at speeds of 36 kmph and 36 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 40 sec , b ) 198 sec , c ) 178 sec , d ) 665 sec , e ) 276 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 400 / ( 36 * 5 / 18 ) , 400 / ( 36 * 5 / 18 ) } = lcm ( 40 , 40 ) = 40 sec . answer : a"
Answer: a
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 9 % microphotonics ; 14 % home electronics ; 10 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 108 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "9 % microphotonics ; 14 % home electronics ; 10 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 9 + 14 + 10 + 29 + 8 ) = 30 % basic astrophysics . 30 % of 360 ° is 108 ° . answer : a ."
Answer: a
Problem: a mixture of 40 liters of milk and water contains 10 % water . how much water should be added to this so that water may be 20 % in the new mixture ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: 4 ltr - water 36 ltr - milk let x water be added then the new mixture must have 20 % water then 4 + x = 20 / 100 ( 40 + x ) x = 5 answer : c
Answer: c
Problem: in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 50 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 20 , d ) 15 , e ) 25
Rationale: "you should notice that 50 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 4 = 20 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : c . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . c"
Answer: c
Problem: a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 5 x km .
Options: a ) 16 , b ) 18 , c ) 24 , d ) 40 , e ) 12
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 5 x / ( x / 8 ) = 40 kmph answer : d"
Answer: d
Problem: riya and priya set on a journey . riya moves eastward at a speed of 21 kmph and priya moves westward at a speed of 22 kmph . how far will be priya from riya after 60 minutes
Options: a ) 43 kms , b ) 45 kms , c ) 50 kms , d ) 30 kms , e ) 40 kms
Rationale: "total eastward distance = 21 kmph * 1 hr = 21 km total westward distance = 22 kmph * 1 hr = 22 km total distn betn them = 21 + 22 = 43 km ans 43 km answer : a"
Answer: a
Problem: a family had dinner in a restaurant and paid $ 30 for food . they also had to pay 9.5 % sale tax and 10 % for the tip . how much did they pay for the dinner ?
Options: a ) $ 35.83 , b ) $ 35.84 , c ) $ 35.85 , d ) $ 35.86 , e ) $ 35.87
Rationale: solution they paid for food , sales tax and tip , hence total paid = $ 30 + 9.5 % * 30 + 10 % * 30 = $ 35.85 answer c
Answer: c
Problem: a man is 26 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
Options: a ) 78 years , b ) 22 years , c ) 88 years , d ) 66 years , e ) 24 years
Rationale: "let ' s son age is x , then father age is x + 26 . = > 2 ( x + 2 ) = ( x + 26 + 2 ) = > 2 x + 4 = x + 28 = > x = 24 years answer : e"
Answer: e
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 40 cm and breadth 20 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 47.14 , b ) 45.15 , c ) 43.23 , d ) 41.44 , e ) 41.51
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 40 + 20 ) = 120 cm parameter of the square = 120 cm i . e . 4 a = 120 a = 30 diameter of the semicircle = 30 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 30 ) = 1 / 2 ( 22 / 7 ) ( 30 ) = 660 / 14 = 47.14 cm to two decimal places answer : a"
Answer: a
Problem: two trains 200 m and 300 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 ) 18 , b ) 10.9 , 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 = 200 + 300 = 500 m . required time = 500 * 9 / 250 = 18 secs answer : a"
Answer: a
Problem: the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 35 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 23.3 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres
Rationale: "262.85 ( 35 ) + 3 , 104.35 x = 1 , 399.45 ( 35 + x ) solve the equation . 262.85 ( 35 ) + 3 , 104.35 x = 1 , 399.45 ( 35 + x ) 9 , 199.75 + 3 , 104.35 x = 48980.75 + 1 , 399.45 x 9 , 199.75 + 1 , 704.9 x = 48980.75 1 , 704.9 x = 39,781 x ≈ 23.3 answer is b ."
Answer: b
Problem: when n is divided by 15 , the remainder is 8 . what is the remainder when 5 n is divided by 6 ?
Options: a ) 2 , b ) 6 , c ) 3 , d ) 4 , e ) 1
Rationale: "let n = 8 ( leaves a remainder of 8 when divided by 48 ) 5 n = 5 ( 8 ) = 40 , which leaves a remainder of 4 when divided by 6 . answer d"
Answer: d
Problem: a number x is 18 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 87.5 % , c ) 80 % , d ) 94.4 % , e ) 1 %
Rationale: "say y = 1 and x = 18 . then y = 1 is less than x = 18 by ( 18 - 1 ) / 18 * 100 = 17 / 18 * 100 = 94.4 % . answer : d ."
Answer: d
Problem: a dozen eggs and 5 pounds of oranges are currently at the same price . if the price of a dozen eggs rises by 3 percent and the price of oranges rises by 6 % . how much more will it cost to buy a dozen eggs and 10 pounds of oranges .
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 5 %
Rationale: say currently both a dozen eggs and 5 pounds of oranges cost $ 100 ( they are at the same price ) . so , to buy a dozen eggs and 5 pounds of oranges we need $ 100 . after the increase , the price of a dozen eggs will be $ 103 and the price of 5 pounds of oranges will be $ 106 . so after the increase , to buy a dozen eggs and 5 pounds of oranges we ' ll need $ 209 . increase = 9 % . answer : b .
Answer: b
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "clearly d a number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a . 96 has more number of smaller prime factor thats the clue ! ! = d"
Answer: d
Problem: the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.60 per metre .
Options: a ) 2399 , b ) 3888 , c ) 2999 , d ) 5808 , e ) 6072
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.60 ) = rs . 6072 . answer : e ) 6072"
Answer: e
Problem: 3 years ago the average age of a class of 6 members was 19 years . a boy have been added , the average age of the class is the same today . what is the age of the boy ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 6 * 22 = 132 7 * 19 = 133 ` 1 a
Answer: a
Problem: find the number of shares that can be bought for rs . 8200 if the market value is rs . 28 each with brokerage being 2.5 % .
Options: a ) 237 , b ) 270 , c ) 177 , d ) 285.7 , e ) 111
Rationale: "explanation : cost of each share = ( 28 + 2.5 % of 28 ) = rs . 28.7 therefore , number of shares = 8200 / 28.7 = 285.7 answer : d"
Answer: d
Problem: if ( x + 3 ) ^ 2 / ( 3 x + 29 ) = 2 , then the difference between the two possible values of x is :
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "( x + 3 ) ^ 2 / ( 3 x + 29 ) = 2 ( x + 3 ) ^ 2 = 2 ( 3 x + 29 ) x ^ 2 + 6 x + 9 = 6 x + 58 x ^ 2 - 49 = 0 ( x - 7 ) ( x + 7 ) = 0 x = 7 or x = - 7 the answer is d ."
Answer: d
Problem: a train 710 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 2898 , b ) 277 , c ) 500 , d ) 297 , e ) 590
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 710 + x ) / 60 = 65 / 3 x = 590 m . answer : e"
Answer: e
Problem: in a certain corporation , there are 300 male employees and 100 female employees . it is known that 20 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 400 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 1 / 20 , b ) 1 / 10 , c ) 1 / 5 , d ) 2 / 5 , e ) 3 / 4
Rationale: "in this corporation , there are 400 total employees . there are 100 women . of the 300 men , 20 % have advanced degrees — - 10 % of 300 must be 30 , so 20 % of 300 must be 60 . add the women and the men with advanced degrees : 100 + 60 = 160 . this is the or region , full set of individuals that satisfy the condition “ has an advanced degree or is female . ” of the 400 employees , what ’ s the probability of picking one of the 160 in this particular group ? p = 160 / 400 = 16 / 40 = 4 / 10 = 2 / 5 answer = d"
Answer: d
Problem: the price of 24 apples is equal to that of 28 oranges . the price of 45 apples and 60 oranges together is rs . 1350 . the total price of 30 apples and 40 oranges is
Options: a ) 850 , b ) 900 , c ) 750 , d ) 950 , e ) 800
Rationale: let the price of one apple = a and price of one orange = b price of 24 apples is equal to that of 28 oranges 24 a = 28 b = > 6 a = 7 b ⇒ b = 6 a / 7 - - - - - ( equation 1 ) price of 45 apples and 60 oranges together is rs . 1350 = > 45 a + 60 b = 1350 = > 3 a + 4 b = 90 ⇒ 3 a + 4 ( 6 a ) / 7 = 90 ( ∵ substituted the value of b from equation 1 ) ⇒ a + 4 ( 2 a ) / 7 = 30 = > 7 a + 8 a = 30 × 7 = 210 = > 15 a = 210 ⇒ a = 21015 = 423 = 14 b = 6 a 7 = ( 6 × 14 ) / 7 = 6 × 2 = 12 total price of 30 apples and 40 oranges = 30 a + 45 b = ( 30 × 14 ) + ( 40 × 12 ) = 420 + 480 = 900 answer is b .
Answer: b
Problem: rhoda tosses a coin 5 times . find the probability of getting exactly 4 heads .
Options: a ) 5 / 32 , b ) 6 / 32 , c ) 5 / 16 , d ) 4 / 32 , e ) 8 / 32
Rationale: exactly 4 heads out of 5 would be : hhhht , hhthh , or many other combinations . therefore , no . of possible combinations are 5 ! / 4 ! * 1 ! = 5 probability = 5 / 2 ^ 5 = 5 / 32 answer : a
Answer: a
Problem: if two of the 4 expressions x + y , x + 5 y , x - y , and 5 x - y are chosen at random , what is the probability r that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) r = 1 / 6
Rationale: only ( x + y ) ( x - y ) pair will give the form x ^ 2 - ( by ) ^ 2 the probability of selecting these two pairs are 1 / 4 * 1 / 3 = 1 / 12 , assuming x + y is picked first , then x - y , but x - y can be picked first followed by x + y . so the probability r = 1 / 12 * 2 = 1 / 6 ans e
Answer: e
Problem: 25 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 87 , b ) 18 , c ) 17 , d ) 16 , e ) 30
Rationale: "binders books days 25 1400 21 x 1600 20 x / 25 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 30 answer : e"
Answer: e
Problem: the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 3 years is
Options: a ) rs . 9621 , b ) rs . 6921 , c ) rs . 9261 , d ) rs . 6261 , e ) rs . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 3 = 8000 ( 21 / 20 * 21 / 20 * 21 / 20 ) = rs 9261 answer : c"
Answer: c
Problem: the ratio of the capacity to do work of a and b is 3 : 2 . if they together can complete a work in 18 days , then how long does a take to complete the work alone ?
Options: a ) 45 , b ) 30 , c ) 24 , d ) 40 , e ) none of these
Rationale: llet a and b take 3 x and 2 x days to complete the work 1 / 3 x + 1 / 2 x = 1 / 18 ⇒ x = 15 so a will take 45 days . answer : a
Answer: a