regisss/math_qa huggingface dataset:
Problem: lionel left his house and walked towards walt ' s house , 48 miles away . two hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 3 miles per hour and walt ' s 3 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 27 , e ) 28
Rationale: "in the first 2 hours lionel at the rate of 3 miles per hour covered distance = rate * time = 3 * 2 = 6 miles . so , the distance between him and walt was 48 - 6 = 42 miles when walt left his house . now , their combined rate to cover this distance was 3 + 3 = 6 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 42 / 6 = 7 hours . total time that lionel was walking is 2 + 7 = 9 hours , which means that he covered in that time interval distance = rate * time = 3 * 9 = 27 miles . answer : d ."
Answer: d
Problem: calculate the value of y : 5 y ^ 2 - 8 y + 55 = 59
Options: a ) 7 , b ) 1 , c ) 2 , d ) 9 , e ) 8
Rationale: using the elimination method substitute options for x and find the correct option . answer : c
Answer: c
Problem: the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 85 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 20
Rationale: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 85 thus m = 680 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 680 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 20 ans : e"
Answer: e
Problem: a pipe can fill a cistern in 55 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 5 min , b ) 2 min , c ) 3 min , d ) 1 min , e ) 10 min
Rationale: "full cistern filled in = 55 minutes 1 / 11 part filled in = 55 * 1 / 11 = 5 minutes answer is a"
Answer: a
Problem: if the perimeter of a rectangular garden is 600 m , its length when its breadth is 95 m is ?
Options: a ) 286 m
b ) 899 m
c ) 200 m
d ) 205 m
e ) 187 m
Rationale: 2 ( l + 95 ) = 600 = > l = 205 m answer : d
Answer: d
Problem: two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 72 sec . the length of each train is ?
Options: a ) 50 , b ) 26 , c ) 27 , d ) 28 , e ) 100
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 72 = 25 / 9 = > x = 100 . answer : e"
Answer: e
Problem: 6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days d do they need to finish the same job ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time d = 3 days to finish the task imo a"
Answer: a
Problem: what is the ratio between perimeters of two squares one having 11 times the diagonal then the other ?
Options: a ) 3 : 8 , b ) 3 : 6 , c ) 3 : 7 , d ) 11 : 1 , e ) 3 : 3
Rationale: "d = 11 d d = d a √ 2 = 11 d a √ 2 = d a = 11 d / √ 2 a = d / √ 2 = > 11 : 1 answer : d"
Answer: d
Problem: a student has to obtain 40 % of the total marks to pass . he got 150 marks and failed by 50 marks . the maximum marks are ?
Options: a ) 500 , b ) 650 , c ) 400 , d ) 575 , e ) 610
Rationale: "let the maximum marks be x then , 40 % of x = 150 + 50 40 x / 100 = 200 x = 500 answer is a"
Answer: a
Problem: david has $ 1,800 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 500 , c ) $ 600 , d ) $ 800 , e ) $ 1,200
Rationale: suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1800 x = 1300 money not spend = 1300 - 800 = 500 answer : b
Answer: b
Problem: what number is 75 more than three - fourth of itself ?
Options: a ) 138 , b ) 225 , c ) 300 , d ) 324 , e ) 336
Rationale: "3 / 4 x + 75 = x that means 75 = 1 / 4 x x = 75 * 4 = 300 c is the answer"
Answer: c
Problem: kamal was 4 times as old as his son 8 years ago . after 8 years , kamal will be twice as old as his son . find out the present age of kamal .
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: let age of the son before 8 years = x then , age of kamal before 8 years ago = 4 x after 8 years , kamal will be twice as old as his son ⇒ 4 x + 16 = 2 ( x + 16 ) ⇒ x = 8 present age of kamal = 4 x + 8 = 4 × 8 + 8 = 40 answer is c .
Answer: c
Problem: 80 % of a number is added to 120 , the result is the same number . find the number ?
Options: a ) 600 , b ) 288 , c ) 1687 , d ) 997 , e ) 121
Rationale: "( 80 / 100 ) * x + 120 = x 2 x = 1200 x = 600 answer : a"
Answer: a
Problem: find the least number of complete years in which a sum of money put out at 13 % compound interest will be more than double of itself ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "6 years answer : b"
Answer: b
Problem: kiran has 85 currency notes in all , some of which were of rs . 100 denomination and the remaining of rs . 50 denomination . the total amount of all these currency notes was rs . 5000 . how much amount did she have in the denomination of rs . 50 ? a . b . c . none of these d . answer : option b explanation :
Options: a ) 1900 , b ) 3500 , c ) 4000 , d ) 2000 , e ) 2500
Rationale: let the number of 50 – rupee notes be x . then , the number of 100 - rupee notes = ( 85 – x ) 50 x + 100 ( 85 – x ) = 5000 x + 2 ( 85 – x ) = 100 = x = 70 so , required amount = rs . ( 50 x 70 ) = rs . 3500 answer : b
Answer: b
Problem: a man sells a car to his friend at 12 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 21136.36 , b ) rs . 31136.36 , c ) rs . 51136.36 , d ) rs . 61136.36 , e ) none of these
Rationale: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 12 % . now s . p = rs . 45000 and loss = 12 % c . p . rs . [ 100 / 88 ã — 45000 ] = rs . 51136.36 correct option : c"
Answer: c
Problem: the breath of a rectangle is three - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 2025 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the length is 10 units ?
Options: a ) 370 sq . units
b ) 270 sq . units
c ) 170 sq . units
d ) 470 sq . units
e ) 570 sq . units
Rationale: given that the area of the square = 2025 sq . units = > side of square = √ 2025 = 45 units the radius of the circle = side of the square = 45 units breath of the rectangle = 3 / 5 * 45 = 27 units given that length = 10 units area of the rectangle = lb = 27 * 10 = 270 sq . units answer : b
Answer: b
Problem: there are 3 workers in the factory a , b , c . the age of a is 4 more than the age of b and the age of b is 4 more than the age of c . if the sum of the square of the ages is 1202 . what is the sum of their ages ?
Options: a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 70
Rationale: let age of b = x ; age of a = x + 4 ; age of c = x - 4 ; sum of squares of ages = > 3 x ^ 2 + 32 = > x = 19.7 = > 20 sum of ages = 60 answer : c
Answer: c
Problem: if 12 men can reap 120 acres of land in 36 days , how many acres of land can 54 men reap in 54 days ?
Options: a ) 186 , b ) 188 , c ) 810 , d ) 167 , e ) 861
Rationale: "12 men 120 acres 36 days 54 men ? 54 days 120 * 54 / 12 * 54 / 36 10 * 54 * 3 / 2 54 * 15 = 810 answer : c"
Answer: c
Problem: how many cubes of 4 cm edge can be cut out of a cube of 28 cm edge
Options: a ) 343 , b ) 232 , c ) 216 , d ) 484 , e ) none of these
Rationale: "explanation : number of cubes = ( 28 x 28 x 28 ) / ( 4 x 4 x 4 ) = 343 answer : a"
Answer: a
Problem: the area of a square is equal to four times the area of a rectangle of dimensions 52 cm * 13 cm . what is the perimeter of the square ?
Options: a ) 200 , b ) 208 , c ) 210 , d ) 220 , e ) 228
Rationale: "area of the square = s * s = 4 ( 52 * 13 ) = > s = 52 cm perimeter of the square = 4 * 52 = 208 cm . answer : option b"
Answer: b
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 1100 more than d , what is b ' s share ?
Options: a ) rs . 500 , b ) rs . 1500 , c ) rs . 2200 , d ) rs . 2500 , e ) none of the above
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 1100 x = 1100 . b ' s share = rs . 2 x = rs . ( 2 x 1100 ) = rs . 2200 . answer = c"
Answer: c
Problem: find the sum lend at c . i . at 5 p . c per annum will amount to rs . 500 in 2 years ?
Options: a ) 221 , b ) 287 , c ) 453 , d ) 288 , e ) 171
Rationale: explanation : 500 = p ( 21 / 20 ) 2 p = 453.51 answer : c
Answer: c
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 20 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 277 , c ) 200 , d ) 257 , e ) 271
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 20 * 10 = 200 m . the length of the faster train = 200 m . answer : c"
Answer: c
Problem: x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 4 will be equal to :
Options: a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9 / 16
Rationale: "explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 4 ^ 2 = 9 / 16 answer : e"
Answer: e
Problem: the sum of all solutions for x in the equation x ^ 2 – 4 x + 14 = | x – 4 | + 8 is equal to :
Options: a ) – 7 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "x ^ 2 - 4 x + 6 = | x - 4 | rhs can be - ve or + ve x ^ 2 - 5 x + 10 = 0 x ^ 2 - 3 x + 2 = 0 x = 5 , 2,1 we test all 3 values in original equation , all ok . thus , sum = 5 + 2 + 1 = 8 ans ( b )"
Answer: b
Problem: r is the set of positive odd integers less than 50 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) two , c ) four , d ) five , e ) seven
Rationale: "squares < 50 { 1 , 4,9 , 16,25 , 36,49 } s = { 1,9 , 25,49 } r = { 1,3 , . . . . . 49 } hence c ."
Answer: c
Problem: in a sports club with 27 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 2 = 27 38 - 2 x + x = 27 38 - x = 27 x = 11 so 8 members play both badminton and tennis . e"
Answer: e
Problem: a & b can separately do a piece of work in 20 & 15 days . they worked together for 6 days , after which b was replaced by c . the work was finished in next 5 days . the no . of days in which c alone could do the work is
Options: a ) 10 days , b ) 20 days , c ) 30 days , d ) 40 days , e ) 50 days
Rationale: b worked for 6 days = > in 6 days b completed = 6 x 1 15 = 2 5 th work a worked for first 6 days and later 4 days = > in 10 days a completed = 10 x 1 20 = 1 2 of the work total work done by a and b = 2 5 + 1 2 = 4 + 5 10 = 9 10 balance work = 1 - 9 10 = 1 10 th of total work balance work was completed by c in 5 days c can do 1 / 10 of the work in 5 days . therefore c alone can do the work in 50 days . e
Answer: e
Problem: a string of 13 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.02 , what is the probability that the string of light bulbs will fail during the time period t ?
Options: a ) 0.02 , b ) ( 0.02 ) ^ 13 , c ) 1 - ( 0.02 ) ^ 13 , d ) ( 0.98 ) ^ 13 , e ) 1 - ( 0.98 ) ^ 13
Rationale: "the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 13 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.02 = 0.98 the the probability that none of the 13 light bulbs fails is 0.98 ^ 13 . hence , the probability that at least one light bulb fails is 1 - 0.98 ^ 13 . answer : e . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 13 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.02 = 2 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) ."
Answer: e
Problem: 145 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 32 liters , c ) 41 liters , d ) 50 liters , e ) 58 liters
Rationale: "milk = 3 / 5 * 145 = 87 liters water = 58 liters 87 : ( 58 + p ) = 3 : 4 174 + 3 p = 348 = > p = 58 58 liters of water are to be added for the ratio become 3 : 4 . answer : e"
Answer: e
Problem: edward ' s home have 3 taps , one tap , working alone at its maximum constant rate , can fill a certain sink in 270 seconds . a second tap working alone at its maximum constant rate , can fill a certain sink in 274 seconds . a third tap , working alone at its maximum constant rate , can fill the same sink in 276 seconds . if all taps work together at their respective maximum constant rates , the time it will take to fill the sink is closest to
Options: a ) 91 seconds , b ) 102 seconds , c ) 177 seconds , d ) 200 seconds , e ) 270 seconds
Rationale: tap 1 : 270 secs tap 2 : 274 secs tap 3 : 276 secs considering the average of these 3 taps : 273.33 secs . so 1 tap can fill the tank in 273.33 secs , so 3 taps can fill the tank in 273.33 / 3 = 91.11 secs . closest answer is a .
Answer: a
Problem: the overall age of x and y is 12 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 19
Rationale: "c 12 ( x + y ) – ( y + z ) = 12 x – z = 12"
Answer: c
Problem: the compound ratio of 1 : 3 , 1 : 2 and 1 : 5 ?
Options: a ) 1 : 30 , b ) 1 : 5 , c ) 1 : 7 , d ) 1 : 1 , e ) 1 : 6
Rationale: 1 / 3 * 1 / 2 * 1 / 5 = 1 / 30 1 : 30 answer : a
Answer: a
Problem: what is rate of interest if principal . amount be 400 , simple interest 140 and time 2 year .
Options: a ) 10 , b ) 17.5 , c ) 25 , d ) 12 , e ) 14.5
Rationale: "s . i = ( p * r * t ) / 100 140 = 800 r / 100 r = 140 / 8 = 17.5 % answer b"
Answer: b
Problem: the population of a village is 12000 . it increases annually at the rate of 24 % p . a . what will be its population after 2 years ?
Options: a ) 14567 , b ) 18451 , c ) 18789 , d ) 18786 , e ) 14400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 12000 × 124 / 100 × 124 / 100 = 18451 b"
Answer: b
Problem: a school has received 40 % of the amount it needs for a new building by receiving a donation of $ 400 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) $ 177.78 , c ) $ 100 , d ) $ 277.78 , e ) $ 77.78
Rationale: "let the amount school needs = x let total people school plans to solicit = t school has received 60 % of x = > ( 3 / 5 ) x people already solicited = 40 % of t = > ( 2 / 5 ) t now , as per the information given in the question : ( 3 / 5 ) x = $ 400 . ( 2 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 remaning amount is 40 % i . e ( 2 / 5 ) x - - - - - - because school has already received 60 % and the remaining people are 60 % i . e ( 3 / 5 ) . t - - - - - because 40 % of the people are already solicited so , average contribution required from the remaining targeted people is ( 2 / 5 ) x = ( amount required ) . ( 3 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 divide eqn 1 by eqn 2 amount required = $ 77.78 e"
Answer: e
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 40 meters . how many times did the ball bounce ?
Options: a ) 2 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "division of total distance travelled will be 16 + 16 + 8 ans : 2"
Answer: a
Problem: a trader sold an item at a loss of 35 % . if he had increased the price by $ 80 he would have made a gain of 5 % . what is the cost price of the item ?
Options: a ) $ 245 , b ) $ 150 , c ) $ 260 , d ) $ 220 , e ) $ 250
Rationale: "let c . p . be $ x then 105 % of x - 65 % of x = 100 40 % of x = 100 40 / 100 * x = 100 40 x = 10 000 x = 250 answer is e"
Answer: e
Problem: a and b can do a piece of work in 10 days , b and c in 15 days , c and a in 12 days . how long will c take to do it ?
Options: a ) 70 days , b ) 55 days , c ) 24 days , d ) 40 days , e ) 11 days
Rationale: "2 c = 1 / 15 + 1 / 12 – 1 / 10 = 1 / 20 c = 1 / 40 = > 40 days answer : d"
Answer: d
Problem: a certain telephone company company charges 3.10 cents for the first 1 / 5 of a minute plus 0.40 cents for each additional 1 / 5 of a minute . what would this company charge for a talk time of 8 minutes long ?
Options: a ) 15.60 , b ) 16.0 , c ) 17.8 , d ) 18.7 , e ) 19.1
Rationale: first 1 / 5 minute charge = 3.10 cents rest of the minute = 8 - ( 1 / 5 ) = 39 / 5 charge for the rest of the minute = 39 * 0.4 = 15.6 total charge = 3.10 + 15.6 = 18.7 cents answer is d .
Answer: d
Problem: a certain number of men complete a piece of work in 60 days . if there were 8 men more , the work could be finished in 10 days less . how many men were originally there ?
Options: a ) 30 , b ) 32 , c ) 36 , d ) 40 , e ) 45
Rationale: originally 1 et there be x men . more men , less days ( x + 8 ) : x ∷ 60 : 50 so , x + 8 / x = 60 / 50 or x = 40 . answer : d
Answer: d
Problem: how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 7.5 m x 6 m x 22.5 cm ?
Options: a ) 6000 , b ) 6410 , c ) 6440 , d ) 6500 , e ) 6800
Rationale: "number of bricks = volume of wall / volume of bricks = 750 x 600 x 22.5 / 25 x 11.25 x 6 = = 6000 answer : a"
Answer: a
Problem: if the function q is defined by the formula q = 5 w / ( 4 vf ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , f is doubled , and z is tripled ?
Options: a ) 1 / 9 , b ) 2 / 9 , c ) 4 / 9 , d ) 3 / 9 , e ) 2 / 27
Rationale: "we just need to find the factor thats all , w - > quadrupled - > 4 w f - > doubled - > 2 f z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and f * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b"
Answer: b
Problem: what is the remainder when 43 ^ 91 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 91 has the form 4 k + 3 so the units digit of 43 ^ 91 is 7 . the remainder when dividing by 5 is 2 . the answer is c ."
Answer: c
Problem: if a and b are integers and ( a * b ) ^ 5 = 64 y , y could be :
Options: a ) 16 , b ) 32 , c ) 64 , d ) 128 , e ) 256
Rationale: "distribute the exponent . a ^ 5 * b ^ 5 = 64 y find the prime factorization of 64 . this is 2 ^ 5 * 2 ^ 1 we need 2 ^ 4 ( or some other power of 2 that will give us a multiple of 2 ^ 5 as our second term ) . 2 ^ 4 = 16 the answer is a ."
Answer: a
Problem: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 90 only . men ’ s wages are ?
Options: a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 3 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 90 rs . 5 m + 5 m + 5 m - - - - - 90 rs . 15 m - - - - - - 90 rs . = > 1 m = 6 rs . answer : a"
Answer: a
Problem: each factor of 200 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 40 ?
Options: a ) 1 / 6 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "200 = the # of factors 200 has is = 12 ( see below ) ; so out of 12 factors only two are multiples of 40 : 40 and 200 , itself ; so , the probability is 2 / 12 = 1 / 6 . answer : a ."
Answer: a
Problem: a certain bag contains 100 balls — 50 white , 30 green , 10 yellow , 7 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 30 + 10 ) / 100 = 90 / 100 = 0.9 . answer is a"
Answer: a
Problem: if ( n + 2 ) ! = 2550 ( n ! ) ; find ’ n ’
Options: a ) 38 , b ) 35 , c ) 49 , d ) 43 , e ) 34
Rationale: "( n + 2 ) ! = 2550 ( n ! ) ( n + 2 ) ( n + 1 ) ( n ! ) = 2550 ( n ! ) ( n + 2 ) ( n + 1 ) = 2550 2 n + 3 n + 2 - 2550 = 0 2 n + 3 n - 2548 = 0 2 n + 52 n - 49 n - 2548 = 0 n ( n - 49 ) ( n + 52 ) = 0 n = 49 or n = - 52 answer : c"
Answer: c
Problem: find the remainder when 32 ^ 33 ^ 34 is divided by 11
Options: a ) 22 , b ) 10 , c ) 99 , d ) 76 , e ) 28
Rationale: "so 32103210 gives remainder 1 . now we have to write 32 ^ 33 ^ 34 in this format . so we have to find the remainder 33 ^ 34 when divided by 10 . the remainder is nothig but unit digit of the number . click here to learn this concept 33 ^ 34 gives unit digit of 9 . so 33 ^ 34 = 10 k + 9 323334 = 32 ( 10 k + 9 ) = ( 3210 ) k . 329323334 = 32 ( 10 k + 9 ) = ( 3210 ) k . 329 now this expression when divided by 11 leaves a remainder of 329329 which inturn is equal to ( − 1 ) 9 = − 1 = 10 answer : b"
Answer: b
Problem: a heap of coconuts is divided into groups of 2 , 3 and 11 and each time one coconut is left over . the least number of coconuts in the heap is ? a . 31 b . 41 c . 51 d . 61
Options: a ) a ) 31 , b ) b ) 41 , c ) c ) 51 , d ) d ) 67 , e ) e ) 71
Rationale: lcm = 66 = > 66 + 1 = 67 answer : d
Answer: d
Problem: along a yard 441 metres long , 22 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 12
Rationale: "explanation : 22 trees have 21 gaps between them , required distance ( 441 / 21 ) = 21 option d"
Answer: d
Problem: calculate the area of a triangle , if the sides are 30 cm , 21 cm and 10 cm , what is its area ?
Options: a ) 145 cm 2 , b ) 105 cm 2 , c ) 125 cm 2 , d ) 115 cm 2 , e ) 135 cm 2
Rationale: "the triangle with sides 30 cm , 21 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 21 * 10 = 105 cm 2 answer : b"
Answer: b
Problem: the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 32 ft long . what is the distance traveled by the cart , when the front wheel has done 5 more revolutions than the rear wheel ?
Options: a ) 20 ft , b ) 25 ft , c ) 750 ft , d ) 900 ft , e ) 2400 ft
Rationale: point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 32 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 75 . sub x = 75 either in ( x + 5 ) * 30 or in x * 32 to get the distance , which is 2400 . so the correct choice is e .
Answer: e
Problem: two pipes a and b can fill a cistern in 12 and 15 minutes respectively . both are opened together but after 4 minutes a is turned off . after how much more time will the cistern be filled ?
Options: a ) 6 , b ) 8 1 / 1 , c ) 8 1 / 4 , d ) 8 1 / 2 , e ) 8 3 / 7
Rationale: "4 / 12 + ( 4 + x ) / 15 = 1 x = 6 answer : a"
Answer: a
Problem: find the annual income derived by investing $ 6800 in 50 % stock at 136 .
Options: a ) 550 , b ) 2500 , c ) 250 , d ) 3000 , e ) 400
Rationale: "by investing $ 136 , income obtained = $ 50 . by investing $ 6800 , income obtained = $ [ ( 50 / 136 ) * 6800 ] = $ 2500 . answer b ."
Answer: b
Problem: a boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 15 minutes . then the speed of the current is :
Options: a ) 1 kmph , b ) 0.5 kmph , c ) 3 kmph , d ) 2.5 kmph , e ) 3.5 kmph
Rationale: "rate upstream = ( 1 / 20 * 60 ) = 3 kmph rate down stream = 1 / 15 * 60 = 4 kmph rate of the current = ½ ( 4 - 3 ) = 0.5 kmph answer : b"
Answer: b
Problem: a motorcyclist x drives along a circular fence at a rate of 2 rounds per hour and another motor cyclist y at a rate of 4 rounds per hour . after how long they will cross each other for the first time ?
Options: a ) 10 min , b ) 20 min , c ) 30 min , d ) 40 min , e ) none of these
Rationale: explanation : since x and y move in the same direction they cross each other when there is a difference of two round between the two . relative speed of x and y = 4 - 2 = 2 . time taken to complete one round at this speed = 1 / 2 hour = 30 minutes answer : c
Answer: c
Problem: a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 30 % lemonade syrup ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.14 , d ) 2.34 , e ) 2.64
Rationale: "let the total solution is 150 l with 80 l water 70 l syrup . to make 30 % syrup solution , the result solution must have 105 l syrup and 45 l syrup . therefore we are taking 25 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 25 l syrup in 53.6 l solution we started by multiplying 10 now to get to the result we need to divide by 25 = > amount of solution to be replaced with water = ( 53.6 / 25 ) = 2.14 . correct option : c"
Answer: c
Problem: a third of arun â € ™ s marks in mathematics exceed a half of his marks in english by 10 . if he got 230 marks in two subjects together how many marks did he got in english ?
Options: a ) 140,90 , b ) 180,60 , c ) 160,90 , d ) 150,80 , e ) none of them
Rationale: "let arun â € ™ s marks in mathematics and english be x and y then ( 1 / 3 ) x - ( 1 / 2 ) y = 10 2 x - 3 y = 60 â € ¦ â € ¦ > ( 1 ) x + y = 230 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 150 and y = 80 answer is d ."
Answer: d
Problem: how many times are the hands of a clock at right angle in 5 days ?
Options: a ) 202 , b ) 220 , c ) 210 , d ) 212 , e ) 222
Rationale: in 1 day , they are at right angles 44 times . in 5 days , they are at right angles 220 times . answer : option b
Answer: b
Problem: sebastian bought a meal at a restaurant and left a 15 % tip . with the tip , he paid exactly $ 36.57 . how much did the meal cost without the tip ?
Options: a ) $ 31.80 , b ) $ 29.91 , c ) $ 30.15 , d ) $ 30.60 , e ) $ 30.85
Rationale: the tip is a percent increase of 15 % , which is 115 % . let x equal the price before the tip . thus , 115 % of this price equals $ 36.57 : 1.15 x = 36.57 divide both sides by 1.15 : = > x = 36.57 / 1.15 = 31.80 correct answer a ) $ 31.80
Answer: a
Problem: what should be the least number to be added to the 4499 number to make it divisible by 9 ?
Options: a ) 1 , b ) 17 , c ) 18 , d ) 77 , e ) 26
Rationale: "answer : 1 option : a"
Answer: a
Problem: let c be defined as the sum of all prime numbers between 0 and 28 . what is c / 3
Options: a ) 155 , b ) 100 / 3 , c ) 61 , d ) 47 , e ) 43
Rationale: "prime numbers between 0 and 30 - 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 sum , c = 100 c / 3 = 11 / 3 answer b"
Answer: b
Problem: we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value e of the ratio a / b ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "e - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ."
Answer: a
Problem: how many books each of volume 100 meter cube can be packed into a crate of volume 4000 meter cube ?
Options: a ) 100
b ) 120
c ) can not be determined
d ) 180
e ) 200
Rationale: gud question with a simple concept . in geo if we want to insert one shape into another we need to know the dimensions of the two shapes . in above with volume given , we can come up with different shapes , so we cant know the answer for ex : 4000 m 3 can be 400 * 10 or 40 * 100 or just 4000 * 1 we do n ' t know , so we cant calculate answer : c
Answer: c
Problem: jane started baby - sitting when she was 20 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 32 years old , and she stopped baby - sitting 10 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: check two extreme cases : jane = 20 , child = 10 , years ago = 32 - 20 = 12 - - > child ' s age now = 10 + 12 = 22 ; jane = 22 , child = 11 , years ago = 32 - 22 = 10 - - > child ' s age now = 11 + 10 = 21 . answer : c .
Answer: c
Problem: if integer k is equal to the sum of all even multiples of 25 between 295 and 615 , what is the greatest prime factor of k ?
Options: a ) 5 , b ) 7 , c ) 11 , d ) 13 , e ) 17
Rationale: if we break down what the stem is asking what is the sum of all mult of 50 between 300 and 600 . using arithmetic progression to find n : 600 = 300 + ( n - 1 ) 50 300 + 50 = 50 n 350 = 50 n = > n = 7 the sum would be : 11 * mean mean = [ 600 + 300 ] / 2 = 450 7 * 450 = 4950 b
Answer: b
Problem: sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?
Options: a ) 9680 , b ) 4280 , c ) 2789 , d ) 7892 , e ) 2792
Rationale: "( 8000 * 3 * 2 ) / 100 = 480 9200 - - - - - - - - 9680 answer : a"
Answer: a
Problem: a certain city with a population of 60,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 10,900 , d ) d ) 11,000 , e ) e ) 5,000
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 60 k x = 5,000 answer : e"
Answer: e
Problem: the perimeter of a rectangular yard is completely surrounded by a fence that measures 10 meters . what is the length of the yard if the area of the yard is 6 meters squared ?
Options: a ) 8 , b ) 1 , c ) 5 , d ) 7 , e ) 3
Rationale: "perimeter of rectangular yard = 2 ( l + b ) = 10 - - > l + b = 5 area = l * b = 6 b = 5 - l l ( 5 - l ) = 6 5 l - l ^ 2 = 6 l ^ 2 - 5 l + 6 = 0 upon simplifying we get l = 2 or 3 . only 3 is there in the answer choice . answer : e"
Answer: e
Problem: how long does a train 150 m long traveling at 50 kmph takes to cross a bridge of 250 m in length ?
Options: a ) 28.8 sec , b ) 16.8 sec , c ) 15.2 sec , d ) 25.4 sec , e ) 16.2 sec
Rationale: "d = 150 + 250 = 400 m s = 50 * 5 / 18 = 125 / 9 t = 400 * 125 / 9 = 28.8 sec answer : a"
Answer: a
Problem: if 7 and 6 are factors of 60 n , what is the minimum value of n ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 14 , e ) 56
Rationale: "60 n / 7 * 6 should be integer = > 2 * 2 * 3 * 5 * n / 7 * 2 * 3 = 2 * 5 * n / 7 must be an integer for this to be true n must multiple of 7 , thus min of n = 7 hence c"
Answer: c
Problem: a train 50 m long passes a platform 100 m long in 10 seconds . the speed of the train in m / sec is ?
Options: a ) 150 , b ) 50 , c ) 10 , d ) 15 , e ) 12
Rationale: speed of train = distance covered / time . = ( 50 + 100 ) / 10 = 15 m / sec . answer : d
Answer: d
Problem: how many liters of water must be evaporated from 50 liters of a 4 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 30 , b ) 32 , c ) 34 , d ) 36 , e ) 38
Rationale: "4 % of a 50 liter solution is 2 l which is 10 % of the solution at the end . the solution at the end must be 20 l . we need to evaporate 30 liters . the answer is a ."
Answer: a
Problem: in a class of 70 students , 10 did not opt for math . 5 did not opt for science and 3 did not opt for either . how many students of the class opted for both math and science ?
Options: a ) 23 , b ) 25 , c ) 27 , d ) 37 , e ) 38
Rationale: "70 students total 10 did not opt for math 5 did not opt for science 3 did not opt for either total of 40 students in math and 2 did not opt for sci but did for math 40 - 2 = 38 38 students of the class opted for both math and science answer : e"
Answer: e
Problem: 562 ã — 99 = ?
Options: a ) 55684 , b ) 55432 , c ) 55638 , d ) 44530 , e ) 44538
Rationale: "562 ã — ( 100 - 1 ) 56200 - 562 = 55638 answer c"
Answer: c
Problem: the sale price sarees listed for rs . 550 after successive discount is 18 % and 12 % is ?
Options: a ) 298 , b ) 237 , c ) 342 , d ) 396 , e ) 291
Rationale: "550 * ( 88 / 100 ) * ( 82 / 100 ) = 396 answer : d"
Answer: d
Problem: an empty wooden vessel weighs 12 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled .
Options: a ) 3 / 5 , b ) 5 / 11 , c ) 1 / 24 , d ) 4 / 9 , e ) 2 / 5
Rationale: "an empty wooden vessel weighs 12 % of its total weight when filled with paint : vessel = 0.12 ( vessel + paint ) ; 12 v = v + p ( so the weight of completely filled vessel is 12 v ) p = 11 v ( so the weight of the paint when the vessels is completely filled is 11 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 12 v ; p ' = 5 v ( so the weight of the paint when the vessels is partially filled is 5 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 5 v / 11 v = 5 / 11 . answer : b ."
Answer: b
Problem: a side of beef lost 50 percent of its weight in processing . if the side of beef weighed 750 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 737 , d ) 840 , e ) 1,500
Rationale: "let weight of side of beef before processing = x ( 50 / 100 ) * x = 750 = > x = ( 750 * 100 ) / 50 = 1500 answer e"
Answer: e
Problem: 50 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 70 %
Rationale: "to maximize the percentage of companies offering both , let ' s assume that all 50 % of companies which offer wireless internet also offer snacks . the answer is d ."
Answer: d
Problem: a work which could be finished in 12 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?
Options: a ) 22 , b ) 20 , c ) 88 , d ) 71 , e ) 10
Rationale: x - - - - - - - 12 ( x + 10 ) - - - - 6 x * 12 = ( x + 10 ) 6 x = 10 \ answer : e
Answer: e
Problem: a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 23 per kg , then his gain percent is
Options: a ) 12 % , b ) 23 % , c ) 14 % , d ) 15 % , e ) 16 %
Rationale: explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 23 ) = rs . 184 . profit = 184 - 150 = 34 so , profit % = ( 34 / 150 ) * 100 = 23 % option b
Answer: b
Problem: a can run 4 times as fast as b and gives b a start of 69 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 70 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 92 m
Rationale: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 69 m he gains 69 * ( 4 / 3 ) i . e 92 m answer : e"
Answer: e
Problem: a car travels uphill at 30 km / hr and downhill at 40 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph
Rationale: "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 40 = 5 / 4 ; avg speed = 150 / ( 10 / 3 + 5 / 4 ) = 33 kmph answer : b"
Answer: b
Problem: the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 7.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 4.50 , b ) $ 5.10 , c ) $ 5.30 , d ) $ 7.50 , e ) $ 5.60
Rationale: "i tried using time / rate approach : - initial price difference = 7.80 - 3.20 = 4.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 4.6 = t ( 5.4 x ) - > t = ( 4.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 4.6 / 5.4 = 7.5 answer d ."
Answer: d
Problem: a person saved $ 10 in buying an item on sale . if he spent $ 400 for the item , approximately how much percent he saved in the transaction ?
Options: a ) 8 % , b ) 10 % , c ) 2 % , d ) 2.4 % , e ) 6 %
Rationale: "actual price = 400 + 10 = $ 410 saving = 10 / 410 * 100 = 100 / 41 = 2.4 % approximately answer is d"
Answer: d
Problem: the diagonals of the two squares are in the ratio of 7 : 9 find the ratio of their area
Options: a ) 78 : 89
b ) 5 : 48
c ) 49 : 81
d ) 74 : 36
e ) 25 : 49
Rationale: let the diagonals of the square be 7 x and 9 x respectively . ratio of their areas = 1 / 2 ( 7 x ) ^ 2 : 1 / 2 ( 9 x ) = 49 x ^ 2 : 81 x ^ 2 = 49 : 81 answer ( c )
Answer: c
Problem: in a certain parking lot , 10 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "let x be the number of cars and let y be the number of cars parked illegally . 10 % * x = 20 % * y y / x = 1 / 2 = 50 % the answer is c ."
Answer: c
Problem: for what value of â € œ k â €  will the equation ( 2 kx 2 + 7 kx + 2 ) = 0 have equal roots ?
Options: a ) 2 / 7 , b ) 16 / 49 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2
Rationale: "for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 7 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 49 answer : b"
Answer: b
Problem: in how many ways can 5 different rings be worn in 4 particular fingers ? ( some fingers may get more than one ring and some may get no rings . ) can somebody explain ?
Options: a ) 6720 , b ) 7720 , c ) 7820 , d ) 7950 , e ) 8120
Rationale: first ring can be worn in 4 ways ( on any of the four fingers ) ; second ring can be worn in 5 ways ( as it can go on any of four fingers - 4 ways ; plus it can go below the first one - 1 ) ; third ring can be worn in 6 ways ( the same logic as for the second ring ) ; fourth ring can be worn in 7 ways ; fifth ring can be worn in 8 ways ; total : 4 * 5 * 6 * 7 * 8 = 6720 . ans : a
Answer: a
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 50 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 5 , c ) 4 , d ) 6 , e ) 8
Rationale: 6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 50 = 6 k + 4 k = > k = 5 total red ' s in bag a will be 2 k = 10 b
Answer: b
Problem: a box contains 6 pairs of shoes ( 12 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 11 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9
Rationale: the problem with your solution is that we do n ' t choose 1 shoe from 12 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 11 as after taking one at random there are 11 shoes left and only one is the pair of the first one ) = 1 / 11 answer : a .
Answer: a
Problem: the number of stamps that kaye and alberto had were in the ration of 5 : 3 respectively . after kaye gave alberto 12 of her stamps , the ration of the number of kaye had to the number of alberto had was 8 : 6 . as a result of the gift , kaye had how many more stamps than alberto ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 32 , e ) 90
Rationale: c k 1 = 5 x a 1 = 3 x k 2 = 5 x - 12 a 2 = 3 x + 12 k 2 / a 2 = 8 / 6 ( 5 x - 12 ) / ( 3 x + 12 ) = 8 / 6 6 * ( 5 x - 12 ) = 8 * ( 3 x + 12 ) 30 x - 72 = 24 x + 96 6 x = 168 x = 28 k 2 = 5 * 28 - 12 = 128 a 2 = 3 * 28 + 12 = 96 k 2 - a 2 = 32 answer : d
Answer: d
Problem: you hold some gold in a vault as an investment . over the past year the price of gold increases by 30 % . in order to keep your gold in the vault , you must pay 2 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 27.5 % , b ) 27.4 % , c ) 27.6 % , d ) 27.7 % , e ) 28.4 %
Rationale: "( 100 % + 30 % ) * ( 100 % - 2 % ) = 130 * 0.98 = 127.4 % an increase of 27.4 % your gold holdings have increased in value by 27.4 % . the answer is b"
Answer: b
Problem: a number x is 11 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 90.9 , c ) 91.7 , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 11 . then y = 1 is less than x = 11 by ( 11 - 1 ) / 11 * 100 = 10 / 11 * 100 = 90.9 % . answer : b ."
Answer: b
Problem: ravi ' s 4 days average income is 1025.68 . but in a form he should write his average income as the greatest positive even integer less than or equal to his 4 days average income . what is the difference between his real average and form filling average ?
Options: a ) 2 , b ) 4.3 , c ) 1.68 , d ) 1.5 , e ) 3.2
Rationale: since ravi ' s 4 days average income for form filling is defined as the greatest positive even integer less than or equal to his avg income , then avg income for form filling = 1024 ( the greatest positive even integer less than or equal to 1025.68 is 1024 ) . hence the difference = 1025.68 - 1024 = 1.68 answer : c .
Answer: c
Problem: roy was suffering from severe headaches . he went to see his doctor and the doctor gave him 5 tablets asking him to take one tablet every 15 minutes . how much time will it take roy to consume all the 5 tablets ?
Options: a ) 60 min , b ) 50 min , c ) 70 min , d ) 65 min , e ) 80 min
Rationale: a 60 min roy will be able to consume all the five tablets in an hour . tablet 1 will be taken in 0 min . tablet 2 will be taken in 15 min . tablet 3 will be taken in 30 min . tablet 4 will be taken in 45 min . tablet 5 will be taken in 60 min .
Answer: a
Problem: if one root of the equation 2 x ^ 2 + 3 x – k = 0 is 7 , what is the value of k ?
Options: a ) 100 , b ) 110 , c ) 119 , d ) 120 , e ) 112
Rationale: we just enter this root into the equation in order to recieve an equation to find the answer ! 2 * 7 ^ 2 + 3 * 7 - k = 0 k = 98 + 21 = 119 the answer is c
Answer: c
Problem: what will be the compound interest on a sum of rs . 24,500 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 9920.736 , b ) s . 10823.20 , c ) s . 10123.20 , d ) s . 10123.29 , e ) s . 10123.28
Rationale: "explanation : amount = [ 24500 * ( 1 + 12 / 100 ) 3 ] = 24500 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 35123.20 c . i . = ( 34420.74 - 24500 ) = rs . 9920.736 answer : a"
Answer: a
Problem: at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 14 th highest price and the 21 st lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 33 , b ) 34 , c ) 35 , d ) 36 , e ) 37
Rationale: there were 13 items sold at a higher price than the radio and 20 items sold at a lower price than the radio . including the radio , there were 13 + 20 + 1 = 34 items sold . the answer is b .
Answer: b
Problem: what distance will be covered by a city bus moving at 72 kmph in 30 seconds ?
Options: a ) 200 m , b ) 300 m , c ) 600 m , d ) 500 m , e ) 400 m
Rationale: 72 kmph = 72 * 5 / 18 = 20 mps dist = speed * time = 20 * 30 = 600 m . answer c
Answer: c
Problem: the cost of 3 pens and 5 pencils is rs . 260 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?
Options: a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 780 , e ) none of these
Rationale: explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 260 15 x + 5 x = rs . 260 x = 260 / 20 = 13 : . cost of 1 pen = 5 x = 5 x 13 = 65 : . cost of 12 pens , i . e . ( one dozen ) = 65 x 12 = rs . 780 answer : option d
Answer: d
Problem: in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 107800 . how many times did he participate in the competition ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "107800 = 2 * 2 * 2 * 5 * 5 * 7 * 7 * 11 john participated 8 times . the answer is e ."
Answer: e
Problem: according to a recent student poll , 4 / 5 out of 25 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ?
Options: a ) 29 / 30 , b ) 4 / 49 , c ) 2 / 7 , d ) 45 / 49 , e ) 13 / 14
Rationale: "20 students are interested , 5 are not interested prob = 1 - 5 c 2 / 25 c 2 = 1 - ( 5 * 4 / ( 25 * 24 ) ) = 1 - 1 / 30 = 29 / 30 answer : a"
Answer: a
Problem: one side of a rectangular field is 16 m and one of its diagonal is 17 m . find the area of the field .
Options: a ) 100 , b ) 120 , c ) 91.2 , d ) 180 , e ) none
Rationale: "solution other side = √ ( 17 ) 2 - ( 16 ) 2 = √ 289 - 256 = √ 33 = 5.7 m . ∴ area = ( 16 x 5.7 ) m 2 = 91.2 m 2 . answer c"
Answer: c