regisss/math_qa huggingface dataset:
Problem: on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 320,000 ?
Options: a ) 30 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 320 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 160,000 = 6 years 160,000 - 320,000 = 6 years total 30 years ."
Answer: a
Problem: what is the total surface area in square meters of a rectangular solid whose length is 10 meters , width is 9 meters , and depth is 6 meters ?
Options: a ) 400 m 2 , b ) 404 m 2 , c ) 408 m 2 , d ) 401 m 2 , e ) 412 m 2
Rationale: "surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 10 * 9 + 9 * 6 + 10 * 6 ) = 2 ( 90 + 54 + 60 ) = 2 * 204 = 408 m 2 answer : c"
Answer: c
Problem: 39 persons can repair a road in 12 days , working 10 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 15 , e ) 26
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 39 : : 12 : x working hours / day 6 : 10 30 x 6 x x = 39 x 10 x 12 x = ( 39 x 10 x 12 ) / ( 30 x 6 ) x = 26 . answer : e"
Answer: e
Problem: find the lcm of 0.6 , 9.6 and 0.36 .
Options: a ) 26.3 , b ) 35.6 , c ) 32.9 , d ) 25.5 , e ) 28.8
Rationale: "the given numbers are equivalent to 0.60 , 9.60 and 0.36 . now , find the lcm of 60,960 and 36 . which is equal to 2880 . the required lcm = 28.80 . answer is e"
Answer: e
Problem: what is the rate percent when the simple interest on rs . 4000 amount to rs . 320 in 2 years ?
Options: a ) 4 % , b ) 4.1 % , c ) 4.2 % , d ) 4.3 % , e ) 4.5 %
Rationale: "interest for 1 year = 320 / 2 = 160 interest on rs 4000 p / a = 160 interest rate = 160 / 4000 * 100 = 4 % answer : a"
Answer: a
Problem: man can row upstream at 30 kmph and downstream at 40 kmph , and then find the speed of the man in still water ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 70 , e ) 45
Rationale: "us = 30 ds = 40 m = ( 30 + 40 ) / 2 = 35 answer : b"
Answer: b
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 4 hours and 10 hours respectively . the ratio of their speeds is
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 12 , d ) 4 : 8 , e ) 5 : 2
Rationale: let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 10 : 4 = 5 : 2 . answer : e
Answer: e
Problem: for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score q for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean q = 74 . answer : a .
Answer: a
Problem: the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 47 . what is a possible value for the mean of the distribution ?
Options: a ) 46 , b ) 54 , c ) 48 , d ) 49 , e ) 50
Rationale: the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 47 : { mean } - 3 * { sd } > 47 ; { mean } - 6 > 47 ; { mean } > 53 . answer : b .
Answer: b
Problem: a cycle is bought for rs . 900 and sold for rs . 1120 , find the gain percent ?
Options: a ) 11 , b ) 24 , c ) 99 , d ) 77 , e ) 18
Rationale: "900 - - - - 220 100 - - - - ? = > 24 % answer : b"
Answer: b
Problem: 6.006 / 3.003
Options: a ) 0.002 , b ) 0.02 , c ) 0.2 , d ) 20 , e ) 2
Rationale: "answer is 2 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 6006 / 3003 = 2 answer e"
Answer: e
Problem: the ratio between the sale price and the cost price of an article is 4 : 3 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 9 , b ) 2 : 5 , c ) 3 : 6 , d ) 2 : 0 , e ) 1 : 3
Rationale: "let c . p . = rs . 3 x and s . p . = rs . 4 x . then , gain = rs . x required ratio = x : 3 x = 1 : 3 answer : e"
Answer: e
Problem: two trains of equal length 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 27 seconds . what is the length of each train ( in meters ) ?
Options: a ) 50.5 , b ) 88.5 , c ) 37.5 , d ) 55.5 , e ) 23.5
Rationale: "the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 27 seconds , the relative difference in distance traveled is 27 * 25 / 9 = 75 meters this distance is twice the length of each train . the length of each train is 75 / 2 = 37.5 meters the answer is c ."
Answer: c
Problem: the average of 35 numbers is 25 . if each number is multiplied by 5 , find the new average ?
Options: a ) 125 , b ) 189 , c ) 297 , d ) 267 , e ) 298
Rationale: "sum of the 35 numbers = 35 * 25 = 875 if each number is multiplied by 5 , the sum also gets multiplied by 5 and the average also gets multiplied by 5 . thus , the new average = 25 * 5 = 125 . answer : a"
Answer: a
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 50 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 20 , b ) 27 , c ) 25 , d ) 99 , e ) 21
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 50 ) = 90 ( x - 5 ) 200 = 10 x = > x = 20 . answer : a"
Answer: a
Problem: if n = 5 ^ 11 – 5 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: always divide the power ( incase 11 ) by 4 and use the remainder as the new power . the question now becomes 5 ^ 3 - 5 . now 5 ^ 3 has last digit 5 . we subtract 5 from 5 = 0 is the answer . option a
Answer: a
Problem: p , q and r have rs . 4000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) rs . 3000 , b ) rs . 1600 , c ) rs . 2400 , d ) rs . 4000 , e ) none of these
Rationale: "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 4000 - r ) = > 3 r = 8000 - 2 r = > 5 r = 8000 = > r = 1600 . answer : b"
Answer: b
Problem: 8500 + ( 1600 ÷ ? ) of 1 / 5 = 8501
Options: a ) 310 , b ) 312 , c ) 320 , d ) 325 , e ) 345
Rationale: "explanation : = > 8500 + ( 1600 / ? ) × 1 / 5 = 8501 = > 1600 / ? × 1 / 5 = 8501 - 8500 = 1 = > ? = 1600 / 5 = 320 answer : option c"
Answer: c
Problem: 8.008 / 4.004
Options: a ) 2 , b ) 0.02 , c ) 0.2 , d ) 20 , e ) 2
Rationale: "answer is 2 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 8008 / 4004 = 2 answer a"
Answer: a
Problem: two friends a , b decided to share a lot of apples . each of them had half of the total plus half an apple in order . after each of them took their share 4 time , no apples were left . how many apples were there ?
Options: a ) 250 , b ) 255 , c ) 254 , d ) 253 , e ) 251
Rationale: whenever the rate of reduction is ' half of the total and half of it ' , the answer is always ( 2 ^ n ) - 1 , where ' n ' is the number of times the process is repeated . here , the process is repeated 8 times . so answer is ( 2 ^ 8 ) - 1 = 255 answer : e
Answer: e
Problem: find the simple interest on $ 10000 at 9 % per annum for 12 months ?
Options: a ) $ 410 , b ) $ 500 , c ) $ 650 , d ) $ 710 , e ) $ 900
Rationale: p = $ 10000 r = 9 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 9 * 1 / 100 = $ 900 answer is e
Answer: e
Problem: when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 5 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 15 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "n = 3 p + 1 = 5 q + 3 n + 2 = 3 p + 3 = 5 q + 5 n + 2 is a multiple of 3 and 5 , so it is a multiple of 15 . the answer is a ."
Answer: a
Problem: how many multiples of 4 are there between 64 and 256 ?
Options: a ) 47 , b ) 49 , c ) 42 , d ) 41 , e ) 40
Rationale: "it should be mentioned whether 64 and 256 are inclusive . if 64 and 256 are inclusive , then the answer is ( 256 - 64 ) / 4 + 1 = 49 . if 64 and 256 are not inclusive , then the answer is ( 252 - 68 ) / 4 + 1 = 47 . since oa is a , then we have not inclusive case ."
Answer: a
Problem: at the end of the month , a certain ocean desalination plant ’ s reservoir contained 14 million gallons of water . this amount is twice the normal level . if this amount represents 70 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?
Options: a ) 2 , b ) 5 , c ) 10 , d ) 12 , e ) 15
Rationale: the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 14 mg = 70 % of total . . total = 14 / . 7 = 20 mg . . normal level = 1 / 2 of 20 = 10 mg . . shortage of normal level = 20 - 10 = 10 mg . . c
Answer: c
Problem: of the 14,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
Options: a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
Rationale: "the number of employees is not reqd . . . 1 / 2 of 2 / 7 are shunted out so 1 / 7 left . . . there are another 5 equal parts ( 5 / 7 ) . . so total remaining parts = 6 , in which 1 part is journeyman . . . . therefore % = 1 / 6 * 100 = 16.67 % answer : b"
Answer: b
Problem: what is the value of x ^ 2 yz − xyz ^ 2 , if x = 1 , y = 1 , and z = 3 ?
Options: a ) 20 , b ) - 6 , c ) 30 , d ) 32 , e ) 48
Rationale: "1 * 1 * 3 - ( 1 * 1 * 9 ) = 3 - 9 = - 6 ans : b"
Answer: b
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 24 % 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 ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 54 ° , e ) 52 °
Rationale: "14 % microphotonics ; 24 % home electronics ; 10 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 24 + 10 + 29 + 8 ) = 15 % basic astrophysics . 15 % of 360 ° is 54 ° . answer : d ."
Answer: d
Problem: the difference between a 7 digit number and the number formed by reversing its digit is not a multiple of
Options: a ) 121 , b ) 11 , c ) 9 , d ) 10 , e ) 3
Rationale: "another approach is to test a number . let ' s say the original number is 1231231 so , the reversed number is 1321321 the difference = 1321321 - 1231231 = 90090 no check the answer choices 90090 is a multiple of 3,9 , 10,11 121 is not a multiple of 90090 answer : a"
Answer: a
Problem: f and e are midpoints of ab and ad respectively . if the side of square abcd is 8 , what is the area of triangle cef ?
Options: a ) 8 √ 2
b ) 9 √ 3
c ) 18
d ) 16 √ 2
e ) 24
Rationale: area of shaded figure = area of square - ( area of triangle aef + area of triangle fbc + area of triangle edc ) = 8 * 8 - ( 1 / 2 * 4 * 4 + 1 / 2 * 4 * 8 + 1 / 2 * 4 * 8 ) = 24 . answer e .
Answer: e
Problem: two trains of length 120 meter and 150 meter crosses a stationary man in 10 and 15 seconds respectively . in what time they will cross each other when they are moving in same direction .
Options: a ) 120 sec , b ) 125 sec , c ) 135 sec , d ) 140 sec , e ) none of these
Rationale: explanation : 120 = a * 10 , a = 12 m / sec ( speed of first train ) 150 = b * 15 , b = 10 m / sec ( speed of second train ) 270 = ( 2 ) * t , t = 135 seconds answer – c
Answer: c
Problem: a , b two inlet pipes takes 15,18 minutes to fill the tank and c an oulet pipe takes 45 minutes to empty the tank respectively . in what time the tank be filled if all of them are operated together ?
Options: a ) 11 minutes , b ) 10 minutes , c ) 12 minutes , d ) 13 minutes , e ) 14 minutes
Rationale: lcm = 90 no of days = [ 90 / ( 90 / 15 + 90 / 18 - 90 / 45 ) = [ 90 / ( 6 + 5 - 2 ) ] = [ 90 / 9 ] = 10 minutes answer : b
Answer: b
Problem: a car traveled from san diego to san francisco at an average speed of 63 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 63 x total distance traveled = 2 * 63 x = 126 x total time taken = x + 2 x = 3 x average speed = 126 x / 3 x = 42 answer : d"
Answer: d
Problem: at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 6 . if the price per share of stock k was $ 8 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?
Options: a ) 1.4 % , b ) 5.9 % , c ) 11.1 % , d ) 12.5 % , e ) 33.33 %
Rationale: "opening = 6 closing = 8 rise in price = 2 so , percent increase = 2 / 6 * 100 = 33.33 % answer : e"
Answer: e
Problem: a man engaged a servant on the condition that he would pay him rs . 900 and a uniform after one year service . he served only for 9 months and received uniform and rs . 650 , find the price of the uniform ?
Options: a ) 377 , b ) 197 , c ) 187 , d ) 100 , e ) 822
Rationale: "explanation : 9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 answer : d"
Answer: d
Problem: how many pieces of 85 cm length can be cut from a rod of 29.75 meters long ?
Options: a ) 55 , b ) 45 , c ) 35 , d ) 25 , e ) 15
Rationale: "number of pieces = 2975 / 85 = 35 the answer is c ."
Answer: c
Problem: for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 30 ) ?
Options: a ) 2 , b ) 5 , c ) 11 , d ) 13 , e ) 19
Rationale: "f ( 30 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 * 28 * 30 the greatest prime factor in this list is 13 . the answer is d ."
Answer: d
Problem: in a office work is distribute between p persons . if 1 / 3 members are absent then work increased for each person is ?
Options: a ) 13.28 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 50 %
Rationale: "let total % of work is 100 % total person = p 1 / 3 person are absent of total person . so absent person is 1 / 3 p ie p / 3 . left person is , p - p / 3 = 2 p / 3 . p person do the work 100 % 1 person do the work 100 * p % 2 p / 3 person do the work ( 100 * p * 3 ) / 2 p % = 150 % work increased for each person is = ( 150 - 100 ) % = 50 % answer : e"
Answer: e
Problem: find the area of a parallelogram with base 60 cm and height 16 cm ?
Options: a ) 960 cm 2 , b ) 240 cm 2 , c ) 480 cm 2 , d ) 45 cm 2 , e ) 250 cm 2
Rationale: "area of a parallelogram = base * height = 60 * 16 = 960 cm 2 answer : a"
Answer: a
Problem: in front of you lies a figure made up with 20 x 10 square blocks . will you be able to find out the number of unique squares and rectangles that are being formed inside this figure by combining two or more distinct squares ?
Options: a ) 11647
b ) 11550
c ) 12654
d ) 26537
e ) 32651
Rationale: b 11550 there is just one way to find it out and that is the generic computing method . the number of squares and rectangles formed = ( summation of column numbers ) = ( 1 + 2 + 3 + . . . . . . + 19 + 20 ) * ( 1 + 2 + 3 + . . . . . . + 9 + 10 ) = 210 * 55 = 11550
Answer: b
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8400 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 4580 , b ) s . 4570 , c ) s . 4500 , d ) s . 4550 , e ) s . 4900
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8400 = 33600 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 1600 salary of may is rs . 6500 salary of january = rs . 4900 answer : e"
Answer: e
Problem: if a light flashes every 6 seconds , how many times will it flash in 2 / 5 of an hour ?
Options: a ) 181 , b ) 211 , c ) 241 , d ) 271 , e ) 301
Rationale: "in 2 / 5 of an hour there are 24 * 60 = 1440 seconds the number of 6 - second intervals = 1440 / 6 = 240 after the first flash , there will be 240 more flashes for a total of 241 . the answer is c ."
Answer: c
Problem: the sides of the triangle are in the ratio 1 / 2 : 1 / 3 : 1 / 4 and its perimeter is 104 cm . the length of the longest side is ?
Options: a ) 32 cm
b ) 48 cm
c ) 50 cm
d ) 28 cm
e ) 30 cm
Rationale: ratio of sides = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 largest side = 104 * 6 / 13 = 48 cm answer is b
Answer: b
Problem: what percent of 11 is 11 percent of 1 ?
Options: a ) 1 , b ) 0.01 , c ) 0.1 , d ) 13 , e ) 101 .
Rationale: "11 % of 1 = ( 11 / 100 ) * 1 = 11 / 100 to determine what percentage of 11 this is : [ 11 ] [ / 100 * 11 ] * 100 = 1 % ans : a"
Answer: a
Problem: the area of a square is equal to five times the area of a rectangle of dimensions 20 cm * 16 cm . what is the perimeter of the square ?
Options: a ) 289 cm , b ) 160 cm , c ) 829 cm , d ) 288 cm , e ) 289 cm
Rationale: "area of the square = s * s = 5 ( 20 * 16 ) = > s = 40 = 40 cm perimeter of the square = 4 * 40 = 160 cm . answer : b"
Answer: b
Problem: on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number w of races we need to conduct to get the top 3 fastest horses ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "w = 7 is the correct answer . good solution buneul . b"
Answer: b
Problem: what is 66.67 % of 804 of 0.1666 ?
Options: a ) 19.33 , b ) 54.55 , c ) 89.33 , d ) 97.21 , e ) 68.77
Rationale: "66.67 % = 2 / 3 2 / 3 of 804 = 2 / 3 * 804 = 536 536 of 0.166 = 536 * ( 1 / 6 ) = 89.33 . . . . ans - c"
Answer: c
Problem: find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 870 ?
Options: a ) rs . 700 , b ) rs . 780 , c ) rs . 750 , d ) rs . 1000 , e ) none of these
Rationale: "explanation : 870 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 750 answer : option c"
Answer: c
Problem: how many multiples of 2 are there between 1 and 60 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 29 , d ) 26 , e ) 28
Rationale: "29 multiples of 2 between 1 and 60 exclusive . from 2 * 1 upto 2 * 29 , ( 1,2 , 3,4 , . . . , 29 ) . hence , 29 multiples ! correct option is c"
Answer: c
Problem: the bankers discount of a certain sum of money is rs . 576 and the true discount on the same sum for the same time is rs . 480 . the sum due is :
Options: a ) 2880 , b ) 2870 , c ) 2860 , d ) 2850 , e ) 2840
Rationale: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 576 * 480 ) / 576 - 480 ; 2880 answer : a"
Answer: a
Problem: a pair of articles was bought for $ 50 at a discount of 30 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 17.50 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 70 % of x = 25 x = 25 * . 7 = $ 17.50 answer is b"
Answer: b
Problem: in an intercollegiate competition that lasted for 3 days , 185 students took part on day 1 , 150 on day 2 and 200 on day 3 . if 100 took part on day 1 and day 2 and 110 took part on day 2 and day 3 and 50 took part on all three days , how many students took part only on day 3 ?
Options: a ) 45 , b ) 35 , c ) 55 , d ) 30 , e ) 40
Rationale: "day 1 & 2 = 100 ; only day 1 & 2 ( 100 - 50 ) = 50 , day 2 & 3 = 110 ; only day 2 & 3 ( 110 - 50 ) = 60 , only day 3 = 200 - ( 50 + 60 + 50 ) = 40 answer : e"
Answer: e
Problem: express a speed of 46 kmph in meters per second ?
Options: a ) 10.78 mps , b ) 12.78 mps , c ) 97.78 mps , d ) 17.78 mps , e ) 18.78 mps
Rationale: "46 * 5 / 18 = 12.78 mps answer : b"
Answer: b
Problem: simplify 80 â ˆ ’ [ 5 â ˆ ’ ( 6 + 2 ( 7 â ˆ ’ 8 â ˆ ’ 5 â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ ) ) ]
Options: a ) 23 , b ) 25 , c ) 89 , d ) 30 , e ) 32
Rationale: explanation : = 80 â ˆ ’ [ 5 â ˆ ’ ( 6 + 2 ( 7 â ˆ ’ 8 + 5 ) ) ] ( please check due to overline , sign has been changed ) = 80 â ˆ ’ [ 5 â ˆ ’ ( 6 + 2 ã — 4 ) ) ] = 80 â ˆ ’ [ â ˆ ’ 9 ] = 80 + 9 = 89 option c
Answer: c
Problem: solve the equation for x : 19 ( x + y ) + 17 = 19 ( - x + y ) - 21 ?
Options: a ) - 1 , b ) 77 , c ) 8 , d ) 3 , e ) 2
Rationale: "19 x + 19 y + 17 = - 19 x + 19 y - 21 38 x = - 38 = > x = - 1 answer : a"
Answer: a
Problem: if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 5 years the amount to be paid is ?
Options: a ) 3377 , b ) 2688 , c ) 2688 , d ) 9125 , e ) 1268
Rationale: "a = 7500 ( 26 / 25 ) ^ 5 = 9125 answer : d"
Answer: d
Problem: a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 204 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 22 , b ) 36 , c ) 55 , d ) 77 , e ) 88
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 204 = > . 1 x + 3 / 4 x = 204 = > x = 240 240 - 204 = pure gala = 36 . answer b"
Answer: b
Problem: ( 32323 + 7344 + 41330 ) - ( 317 x 91 ) = ?
Options: a ) 54210 , b ) 54250 , c ) 52150 , d ) none of these , e ) 521500
Rationale: "its speed and accuracy which decides the winner . you can use various methods including vedic mathematics to do complex calculations quickly . ( 32323 + 7344 + 41330 ) - ( 317 x 91 ) = 80997 - 28847 = 52150 answer is c"
Answer: c
Problem: an amount of rs . 1560 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ?
Options: a ) rs . 390 , b ) rs . 368 , c ) rs . 380 , d ) rs . 360 , e ) rs . 311
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of c = 3 / 13 * 1560 = rs . 360 . answer : d"
Answer: d
Problem: 42 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 28 , b ) 77 , c ) 36 , d ) 25 , e ) 13
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 42 : : 18 : x [ please pay attention , we have written 27 : 42 rather than 42 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 42 \ times 18 } { 27 } } x = 28 so 28 days will be required to get work done by 27 men . answer : a"
Answer: a
Problem: how many three - digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6 ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "the possible number n can be written as follow : n = multiple of lcm ( 6,10 ) + 1 st such number n = 30 x + 1 possible values = 1 , 31 , 61 , 91 , 121,151 , 181,211 , 241,271 . . . . . 991 answer : none : a"
Answer: a
Problem: find the area of a parallelogram with base 32 cm and height 18 cm ?
Options: a ) 576 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 267 cm 2 , e ) 286 cm 2
Rationale: "area of a parallelogram = base * height = 32 * 18 = 576 cm 2 answer : a"
Answer: a
Problem: the number 91 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 8 , b ) 12 , c ) 21 , d ) 27 , e ) 39
Rationale: "3 ^ 3 + 4 ^ 3 = 91 therefore number is 3 * 4 = 12 b"
Answer: b
Problem: a student multiplied a number by 3 / 5 instead of 5 / 3 . what is the percentage error in the calculation ?
Options: a ) 54 , b ) 48 , c ) 65 , d ) 25 , e ) 64
Rationale: let the number be x . then , error = 5 / 3 x - 3 / 5 x = 16 / 15 x . error % = ( 16 x / 15 * 3 / 5 x * 100 ) % = 64 % answer e ) 64 %
Answer: e
Problem: angelina walked 250 meters from her home to the grocery at a constant speed . she then walked 360 meters to the gym at double the speed . she spent 70 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 250 / x . . the speed to gym = 2 x . . so time taken = 360 / 2 x = 180 / x . . its given 250 / x - 180 / x = 70 . . 70 / x = 70 . . x = 1 m / secs . . so grocery to gym = 2 * 1 = 2 m / s . . . answer : a"
Answer: a
Problem: 2 + 2 + 2 ^ 2 + 2 ^ 3 + 2 ^ 4 + 2 ^ 5 + 2 ^ 6 + 2 ^ 7 + 2 ^ 8 =
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 12 , d ) 2 ^ 16 , e ) 2 ^ 20
Rationale: let ' s see that : 2 + 2 is 2 ^ 2 , then : 2 ^ 2 + 2 ^ 2 becomes 2 x 2 ^ 2 that is 2 ^ 3 . you follow with the next : 2 ^ 3 + 2 ^ 3 is equal to 2 x 2 ^ 3 that is 2 ^ 4 . then is assumed right before 2 ^ 8 : 2 ^ 8 x 2 ^ 8 becomes 2 x 2 ^ 8 that is 2 ^ 9 . option a , 2 ^ 9 .
Answer: a
Problem: a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 400 before any discount ?
Options: a ) $ 230.00 , b ) $ 224.00 , c ) $ 263.80 , d ) $ 282.00 , e ) $ 210.00
Rationale: "since the question is essentially just about multiplication , you can do the various mathstepsin a variety of ways ( depending on whichever method you find easiest ) . we ' re told that the first discount is 10 % to 30 % , inclusive . we ' re told that the next discount is 20 % off of the discounted price . . . . we ' re told to maximize the discount ( thus , 30 % off the original price and then 20 % off of the discounted price ) . thatmathcan be written in a number of different ways ( fractions , decimals , etc . ) : 30 % off = ( 1 - . 3 ) = ( 1 - 30 / 100 ) = ( . 7 ) and the same can be done with the 20 % additional discount . . . the final price of an item that originally cost $ 400 would be . . . . . ( $ 400 ) ( . 7 ) ( . 8 ) = ( $ 400 ) ( . 56 ) = 224 final answer : b"
Answer: b
Problem: logx 16 = 0.8 then what is the value of x ?
Options: a ) 32 , b ) 34 , c ) 35 , d ) 36 , e ) 37
Rationale: x ^ 0.8 = 16 x = ( 2 ^ 4 ) ^ ( 10 / 8 ) x = 2 ^ 5 x = 32 answer : a
Answer: a
Problem: a 16 % stock yielding 8 % is quoted at ?
Options: a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 200
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 16 , money invested = 100 × 16 / 8 = rs . 175 ie , market value of the stock = rs . 200 answer is e ."
Answer: e
Problem: at an elementary school , 70 % of the faculty members are women and 40 % of the faculty members are married . if 1 ⁄ 3 of the men are single , what fraction of the men are married ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 5 , e ) 2 / 7
Rationale: "- - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - - 20 - - - - - 20 - - - - - - - - - 40 not married - - - - - 10 - - - - - 50 - - - - - - - - - 60 total - - - - - - - - - - - - - 30 - - - - - 70 - - - - - - - - 100 need married man / total man , so 20 / 30 = 2 / 3 c"
Answer: c
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 12 of money ?
Options: a ) 1200 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2789
Rationale: "p = 12 ( 100 / 10 ) 2 = > p = 1200 answer : a"
Answer: a
Problem: a man whose bowling average is 12.4 , takes 3 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "12.4 * x + 26 = ( 3 + x ) 12 solve equation x = 25 answer : c"
Answer: c
Problem: a 40 - liter solution of alcohol and water is 5 percent alcohol . if 3.5 liters of alcohol and 6.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 8 % , b ) 11 % , c ) 14 % , d ) 17 % , e ) 20 %
Rationale: "the percent of alcohol in the solution is ( 0.05 ( 40 ) + 3.5 ) / 50 = 5.5 / 50 = 11 % the answer is b ."
Answer: b
Problem: how long does a train 110 m long traveling at 90 kmph takes to cross a bridge of 170 m in length ?
Options: a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
Rationale: "d = 110 + 170 = 280 m s = 90 * 5 / 18 = 50 / 2 t = 280 * 2 / 50 = 11.2 sec answer : d"
Answer: d
Problem: if 12 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
Options: a ) 127 , b ) 237 , c ) 300 , d ) 450 , e ) 281
Rationale: "explanation : let the required no of hectares be x . then men - - - hectares - - - days 12 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 12 * 30 / 24 * 80 x = 300 answer : c"
Answer: c
Problem: a martian bat flies at 60 yards per second from its nest to a dry lake . when it arrives there , it immediately continues at 45 yards per second to a nearby cave . if the distance between the lake and the cave is half the distance between the nest and the lake , what is the average speed , in yards per second , of the bat during the whole flight ?
Options: a ) 36 , b ) 40 , c ) 42 , d ) 54 , e ) 65
Rationale: distance from nest to lake = d , speed = 60 , time = d / 60 distance from lake to cave = d / 2 , speed = 45 , time = d / 90 average speed = ( d + d / 2 ) / ( d / 60 + d / 90 ) = ( 3 / 2 ) / ( 1 / 36 ) = 54 answer : d
Answer: d
Problem: the sum of all the integers k such that – 20 < k < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 37
Rationale: "- 19 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 19 - 18 sum of which is - 37 . hence option d . e"
Answer: e
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 2,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 6.25 % , d ) 6.67 % , e ) 11.7 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 8000 = 1 / 16 = 6.25 % the answer is c ."
Answer: c
Problem: a tank is filled in 10 hours by 3 pipes a , b and c . pipe a is twice as fast as pipe b , and b is twice as fast as c . how much time will pipe b alone take to fill the tank ?
Options: a ) 56 hours , b ) 28 hours , c ) 35 hours , d ) 66 hours , e ) 47 hours
Rationale: 1 / a + 1 / b + 1 / c = 1 / 10 ( given ) also given that a = 2 b and b = 2 c = > 1 / 2 b + 1 / b + 2 / b = 1 / 10 = > ( 1 + 2 + 4 ) / 2 b = 1 / 10 = > 2 b / 7 = 10 = > b = 35 hours . answer : c
Answer: c
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum e of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : e = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Problem: a , b and c rents a pasture for rs . 928 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 289 , c ) 288 , d ) 255 , e ) 552
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 928 = 288 answer : c"
Answer: c
Problem: in a class of 28 students in an examination in maths 4 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) a ) 47.3 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48 , e ) e ) 49
Rationale: "explanation : total marks obtained by a class of 25 students = 4 * 95 + 3 * 0 + 21 * 45 = 1325 average marks of whole class = 1325 / 28 = 47.3 answer : option a"
Answer: a
Problem: gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 65 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 10 , e ) 11
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 65 . thus , 3434 ( 90 + x ) = 65 + x or 270 + 3 x = 260 + 4 x or x = 10 answer : d"
Answer: d
Problem: the temperature of a certain cup of coffee 30 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 120 , c ) 80 , d ) 85 , e ) 90
Rationale: "first , we have to find a . we know that after t = 30 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 30 a ) + 60 60 = 120 * ( 2 ^ - 30 a ) 60 / 120 = 2 ^ - 30 a 1 / 2 = 2 ^ - 30 a 2 ^ - 1 = 2 ^ - 30 a - 1 = - 30 a 1 / 30 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 30 * 30 ) + 60 f = 120 * ( 2 ^ - 1 ) + 60 f = 120 * ( 1 / 2 ^ 1 ) + 60 f = 120 * 1 / 2 + 60 f = 60 + 60 = 120 answer b !"
Answer: b
Problem: the sum of three consecutive even numbers is 246 . what are the numbers ?
Options: a ) 80 , 82,84 , b ) 65 , 68,71 , c ) 45 , 47,42 , d ) 100 , 102,49 , e ) 87 , 88,89
Rationale: "first x make the first x second x + 2 even numbers , sowe add 2 to get the next third x + 4 add 2 more ( 4 total ) to get the third f + s + t = 246 summeansaddfirst ( f ) plussecond ( s ) plusthird ( t ) ( x ) + ( x + 2 ) + ( x + 4 ) = 246 replace each f , s , and t withwhatwe labeled them x + x + 2 + x + 4 = 246 here the parenthesis are not needed 3 x + 6 = 246 combine like terms x + x + x and 2 + 4 − 6 − 6 subtract 6 fromboth sides 3 x = 240 the variable ismultiplied by 3 3 3 divide both sides by 3 x = 80 our solution for x first 80 replace x in the origional listwith 80 . second ( 80 ) + 2 = 82 the numbers are 80 , 82 , and 84 . third ( 80 ) + 4 = 84 correct answer a"
Answer: a
Problem: two pipes a and b can separately fill a cistern in 60 minutes and 120 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 60 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 100 min , c ) 110 min , d ) 120 min , e ) 130 min
Rationale: "1 / 60 - ( 1 / 60 + 1 / 120 ) = - 1 / 120 third pipe can empty in 120 minutes answer : d"
Answer: d
Problem: if the average of 10 consecutive integers is 23.5 then the 10 th integer is : -
Options: a ) 15 , b ) 20 , c ) 23 , d ) 28 , e ) 25
Rationale: "the average falls between the 5 th and 6 th integers , integer 5 = 23 , integer 6 = 24 . counting up to the tenth integer we get 28 . answer : d"
Answer: d
Problem: a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 2.9 hrs , b ) 8.9 hrs , c ) 2.9 hrs , d ) 7.2 hrs , e ) 8.6 hrs
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 9 ) = 5 / 36 the cistern will be filled in 36 / 5 hrs i . e . , 7.2 hrs . answer : d"
Answer: d
Problem: the distance between west - town to east - town is 16 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 5 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ?
Options: a ) 3 . , b ) 7 . , c ) 10 . , d ) 12 . , e ) 16 .
Rationale: "time taken by the birds to meet = 16 / ( 5 + 1 ) = 4 mins distance traveled by the bird traveling from west - town = 4 * 4 = 16 answer : e"
Answer: e
Problem: which 2 digit number has its digits reversed when you double it and take 1 ?
Options: a ) 33 , b ) 34 , c ) 35 , d ) 36 , e ) 37
Rationale: reverse it and you get 73 which is 2 * 37 - 1 . answer : e
Answer: e
Problem: by selling 8 pencils for a rupee a man loses 10 % . how many for a rupee should he sell in order to gain 10 % ?
Options: a ) 6.54 , b ) 9.45 , c ) 7.34 , d ) 6.67 , e ) 5.09
Rationale: "90 % - - - 8 110 % - - - ? 90 / 110 * 8 = 6.54 answer : a"
Answer: a
Problem: if the sum of a number and its square is 132 , what is the number ?
Options: a ) 15 , b ) 11 , c ) 28 , d ) 91 , e ) none of these
Rationale: let the number be x . then , x + x 2 = 132 ( x + 12 ) ( x - 11 ) = 0 x = 11 answer : b
Answer: b
Problem: during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 180 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
Options: a ) 280 , b ) 320 , c ) 360 , d ) 420 , e ) 480
Rationale: "easy 480 is the answer . 3 / 4 ( x / 2 ) = 180 x = 180 * 8 / 3 = 480 . answer e"
Answer: e
Problem: a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 25 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 260 before any discount ?
Options: a ) $ 136.50 , b ) $ 145.60 , c ) $ 163.80 , d ) $ 182.00 , e ) $ 210.00
Rationale: since the question is essentially just about multiplication , you can do the various mathstepsin a variety of ways ( depending on whichever method you find easiest ) . we ' re told that the first discount is 10 % to 30 % , inclusive . we ' re told that the next discount is 25 % off of the discounted price . . . . we ' re told to maximize the discount ( thus , 30 % off the original price and then 20 % off of the discounted price ) . thatmathcan be written in a number of different ways ( fractions , decimals , etc . ) : 30 % off = ( 1 - . 3 ) = ( 1 - 30 / 100 ) = ( . 7 ) and the same can be done with the 20 % additional discount . . . the final price of an item that originally cost $ 260 would be . . . . . ( $ 260 ) ( . 7 ) ( . 75 ) = ( $ 260 ) ( . 525 ) = 136.5 final answer : a
Answer: a
Problem: if 2464 / 1.12 = 2200 , then 246.4 / 11.2 is equal to ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 25
Rationale: "answer given expression 246.4 / 11.2 = 2464 / 112 = 2464 / ( 1.12 x 100 ) = 2200 / 100 = 22 correct option : c"
Answer: c
Problem: if 4 men can paint 60 m long wall in 3 days , then 5 men can paint 50 m long wall in
Options: a ) 3 days , b ) 2 days , c ) 5 days , d ) 6 days , e ) 1 day
Rationale: the length of wall painted by one man in one day = 60 / 4 ã — 3 = 5 m no . of days required to paint 50 m wall by 5 men = 50 / 5 ã — 5 = 2 day . b
Answer: b
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 10 % while buying and by 10 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 22.22 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 110 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 110 - 90 ) / 90 * 100 = ~ 22.22 % answer : d ."
Answer: d
Problem: a cricketer scored 152 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 46.2 % , b ) 54.54 % , c ) 60.52 % , d ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 152 - ( 12 x 4 + 2 x 6 ) = 152 - ( 60 ) = 92 now , we need to calculate 92 is what percent of 152 . = > 92 / 152 * 100 = 60.52 % answer : c"
Answer: c
Problem: what is the square root of 96,721 ?
Options: a ) 476 , b ) 489 , c ) 289 , d ) 511 , e ) 311
Rationale: "1 ) checking the last digits in the answer options a , c , e are out since last digit of the square is known to be 1 . 2 ) c = 489 ^ 2 and e = 511 ^ 2 c = ( 300 - 11 ) ^ 2 and e = ( 300 + 11 ) ^ 2 since we need the answer less than 90000 = > c is out . thus we have e as the ans ."
Answer: e
Problem: a profit of rs . 20000 is to be distributed among a , b , c in the proportion 2 : 3 : 5 . what will be the difference between b ’ s and c ’ s shares
Options: a ) 4000 , b ) 3000 , c ) 5500 , d ) 4500 , e ) none of these
Rationale: explanation : b ' s share = rs 20000 * ( 3 / 10 ) = rs 6000 c ' s share = rs 20000 * ( 5 / 10 ) = rs 10000 difference in b ' s and c ' s shares = rs 4000 answer : a
Answer: a
Problem: find the first term and the common ratio of a g . p whose fourth term is 250 and seventh term is 31,250
Options: a ) 2 / 5,25 , b ) 4,5 / 2 , c ) 1,16 , d ) 2,5 , e ) 1,5
Rationale: a * r ^ 3 = 250 , a * r ^ 6 = 31,250 , r ^ 3 = 31,250 / 250 = 125 r = 5 , a * 125 = 250 , a = 2 answer : d
Answer: d
Problem: a sum of money deposited at c . i . amounts to rs . 6000 in 6 years and to rs . 7500 in 7 years . find the rate percent ?
Options: a ) 25 % , b ) 20 % , c ) 15 % , d ) 10 % , e ) 5 %
Rationale: "6000 - - - 1500 100 - - - ? = > 25 % answer : a"
Answer: a
Problem: a dog breeder would like to make the largest profit off of his latest litter of puppies . puppies with more than 4 spots sell for more money . the last litter had 10 puppies ; 6 had 5 spots , 3 had 4 spots , and 1 had 2 spots . what % of puppies can the dog breeder expect to sell for a greater profit ?
Options: a ) 90 % , b ) 65 % , c ) 50 % , d ) 85 % , e ) 80 %
Rationale: number of dogs with profitable spots = ( 6 + 3 ) = 6 + 3 = 9 now , we need to calculate 9 is what percent of 10 . = > 9 / 10 * 100 = 90 % a
Answer: a
Problem: paulson spends 75 % of his income . his income is increased by 20 % and he increased his expenditure by 10 % . find the percentage increase in his savings .
Options: a ) 25 , b ) 35 , c ) 50 , d ) 20 , e ) 15
Rationale: let the original income = $ 100 . then , expenditure = $ 75 and savings = $ 25 new income = $ 120 , new expenditure = $ ( ( 110 / 100 ) * 75 ) = rs . 165 / 2 new savings = $ ( 120 - ( 165 / 2 ) ) = $ 75 / 2 increase in savings = $ ( ( 75 / 2 ) - 25 ) = $ 25 / 2 increase % = ( ( 25 / 2 ) * ( 1 / 25 ) * 100 ) % = 50 % . answer c ) 50 .
Answer: c
Problem: on the average mr . jackson has 2 hours to plan for an long hour meeting he talk to his assistant 7 hours to prepare the paper work needed . how much hours should jackson and assistant has t plan for 30 min meeting ?
Options: a ) 4.5 hr , b ) 4.8 hr , c ) 4.9 hr , d ) 5.5 hr , e ) 6.5 hr
Rationale: for a 1 hour talk he took total of 9 hr time 1 hr = 9 hr ( 2 + 7 ) 30 min = 1 / 2 hr = ? so 9 * 1 / 2 div by 1 4.5 hr answer : a
Answer: a
Problem: there are 4 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 24 , d ) d ) 50 , e ) e ) 100
Rationale: using anagram method : 6 _ 5 _ 4 _ 3 _ 2 _ 1 r _ r _ r _ r _ b _ b so . . 6 ! / number of repeated letters ( 4 ! ) ( 2 ! ) = 5 ans : d
Answer: d
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum t of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : t = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Problem: what should be added to 4440 so that it may become a perfect square ?
Options: a ) 44
b ) 45
c ) 46
d ) 47
e ) 49
Rationale: 67 x 67 = 4489 4489 - 4440 = 49 if added to 49 get perfect square answer = e
Answer: e
Problem: a chemist mixes one liter of pure water with x liters of a 50 % salt solution , and the resulting mixture is a 10 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: concentration of salt in pure solution = 0 concentration of salt in salt solution = 50 % concentration of salt in the mixed solution = 10 % the pure solution and the salt solution is mixed in the ratio of - - > ( 50 - 10 ) / ( 10 - 0 ) = 4 / 1 1 / x = 4 / 1 x = 1 / 4 answer : a
Answer: a
Problem: how many positive even integers less than 100 contain digits 3 or 9 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 10
Rationale: "two digit numbers : 3 at tens place : 30 , 32,34 , 36,38 9 at tens place : 90 , 92,94 , 96,98 if 3 and 7 is at units place , the number cant be even total : 5 + 5 = 10 answer e"
Answer: e
Problem: a can contains a mixture of two liquids a and b in the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many litres of liquid a was contained by the can initially ?
Options: a ) 25 , b ) 21 , c ) 20 , d ) 10 , e ) 15
Rationale: suppose the can initially contains 7 x and 5 x litres mixtures a and b respectively quantity of a in mix . left = [ 7 x – 7 / 12 * 9 ] = [ 7 x – 21 / 4 ] quantity of b in mix . left = [ 5 x – 5 / 12 * 9 ] = [ 5 x - 15 / 4 ] therefore [ 7 x - 21 / 4 ] = 7 / 9 or 28 x - 21 = 7 / 9 [ 5 x - 15 / 4 ] + 9 20 x + 21 252 x - 189 = 140 x + 147 or 112 x = 336 , x = 3 . quantity of a in the can initially = 7 * 3 = 21 answer : b
Answer: b
Problem: in a company of 12 employees , 5 employees earn $ 36,000 , 4 employees earn $ 45,000 , and the 3 highest - paid employees earn the same amount . if the average annual salary for the 12 employees is $ 47,500 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 60,000 , b ) $ 65,000 , c ) $ 70,000 , d ) $ 75,000 , e ) $ 80,000
Rationale: 5 * 36,000 + 4 * 45,000 + 3 x = 12 * 47,500 3 x = 570,000 - 180,000 - 180,000 3 x = 210,000 x = 70,000 the answer is c .
Answer: c
Problem: if y is 75 % greater than x , than x is what % less than y ?
Options: a ) 30.6 % , b ) 34.4 % , c ) 38.7 % , d ) 42.9 % , e ) 46.5 %
Rationale: "y = 1.75 x x = y / 1.75 = 100 y / 175 = 4 y / 7 x is 3 / 7 less which is about 42.9 % less than y . the answer is d ."
Answer: d