regisss/math_qa huggingface dataset:
Problem: a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1986 on her 30 nd birthday first be eligible to retire under this provision ?
Options: a ) 2003 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: "she must gain at least 70 points , now she has 30 and every year gives her two more points : one for age and one for additional year of employment , so 30 + 2 * ( # of years ) = 70 - - > ( # of years ) = 20 - - > 1986 + 20 = 2006 . answer : d ."
Answer: d
Problem: i had rs . 10000 with me . out of this , money i lent some money to a for 2 years at 15 % simple interest . i lent the remaining money to b for an equal number of years at 18 % simple interest . after 2 years , i found that a had given me rs . 360 more as interest as compared to ( b ) the amount of money which i had lent to b must have been
Options: a ) 2000 , b ) 3000 , c ) 4000 , d ) 5000 , e ) 6000
Rationale: explanation : total amount = rs . 10000 let money lent a = rs . x and money lent to b = rs . ( 10000 x ) x = rs . 6000 . so the amount of money lent to b = rs . 4000 answer : c
Answer: c
Problem: what percent is 320 gm of 1 kg ?
Options: a ) 25 % , b ) 40 % , c ) 10 % , d ) 8 % , e ) 32 %
Rationale: "1 kg = 1000 gm 320 / 1000 ã — 100 = 32000 / 1000 = 32 % answer is e"
Answer: e
Problem: to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 785 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 197 , c ) 193 , d ) 212 , e ) 213
Rationale: "total movies submitted are 785 . as per question we need to take 1 / 4 of 785 to be considered for top 10 movies = 196.25 approximate the value we 197 . imo option b is the correct answer . . ."
Answer: b
Problem: the number 0.5 is how much greater than 1 / 3 ?
Options: a ) 1 / 6 , b ) 2 / 10 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500
Rationale: "let x be the difference then . 5 - 1 / 3 = x 5 / 10 - 1 / 3 = x x = 1 / 6 ans a"
Answer: a
Problem: the concentration of spirit in 3 different vessels a , b and c are 45 % , 30 % and 10 % respectively . if 4 litres from vessel a , 5 litres from vessel b and 6 litres from vessel c are mixed , find the concentration of spirit in the resultant solution .
Options: a ) 26 % , b ) 33 % , c ) 34 % , d ) 35 % , e ) 24 %
Rationale: quantity of spirit in new solution = ( 4 * 45 / 100 ) + ( 5 * 30 / 100 ) + ( 6 * 10 / 100 ) = 1.8 + 1.5 + 0.6 = 3.9 liters so % concentration of spirit = 100 * 3.9 / ( 4 + 5 + 6 ) = 26 % answer : a
Answer: a
Problem: there are 2 sections a and b in a class , consisting of 50 and 70 students respectively . if the average weight of section a is 50 kg and that of section b is 70 kg , find the average of the whole class ?
Options: a ) 50.78 kg , b ) 49.32 kg , c ) 61.67 kg , d ) 69.15 kg , e ) 70.89 kg
Rationale: "total weight of 50 + 70 students = 50 * 50 + 70 * 70 = 7400 average weight of the class is = 7400 / 120 = 61.67 kg answer is c"
Answer: c
Problem: a number is increased by 20 % and then decreased by 20 % . find the net increase or decrease per cent .
Options: a ) 9 % , b ) 8 % , c ) 7 % , d ) 3 % , e ) 4 %
Rationale: "let the number be 100 . increase in the number = 20 % = 20 % of 100 = ( 20 / 100 ã — 100 ) = 20 therefore , increased number = 100 + 20 = 120 this number is decreased by 20 % therefore , decrease in number = 20 % of 120 = ( 20 / 100 ã — 120 ) = 2400 / 100 = 24 therefore , new number = 120 - 24 = 96 thus , net decreases = 100 - 96 = 4 hence , net percentage decrease = ( 4 / 100 ã — 100 ) % = ( 400 / 100 ) % = 4 % answer : e"
Answer: e
Problem: if x ^ 2 – 3 x = 18 , then one possible value of x – 4 =
Options: a ) - 9 , b ) - 5 , c ) - 3 , d ) - 1 , e ) 2
Rationale: x ^ 2 – 3 x = 18 i . e . x ^ 2 – 3 x - 18 = 0 i . e . x ^ 2 – 6 x + 3 x - 18 = 0 i . e . ( x - 6 ) ( x + 3 ) = 0 i . e . x = 6 or - 3 i . e . x - 4 = 6 - 4 or - 3 - 4 i . e . x - 4 = 2 or - 7 answer : option e
Answer: e
Problem: if 4 x + y = 8 and 3 x - 4 y = 5 , then what is the value of 7 x - 3 y ?
Options: a ) 23 , b ) 3 , c ) 15 , d ) 52 / 7 , e ) 60 / 7
Rationale: 4 x + y = 8 . . . equation 1 3 x - 4 y = 5 . . . equation 2 adding both the equations 7 x - 3 y = 23 correct answer option a
Answer: a
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 11 cm .
Options: a ) 335 cm 2 , b ) 209 cm 2 , c ) 285 cm 2 , d ) 825 cm 2 , e ) 725 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 11 ) = 209 cm 2 answer : b"
Answer: b
Problem: working alone , a can complete a certain kind of job in 3 hours . a and d , working together at their respective rates , can complete one of these jobs in 2 hours . in how many hours can d , working alone , complete one of these jobs ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: let total time taken by d to complete the job = d total time taken by a to complete the job = 3 work done by a in an hour 1 / a = 1 / 3 working together a and d can complete the job in 2 hours 1 / a + 1 / d = 1 / 2 = > 1 / d = 1 / 2 - 1 / a = 1 / 2 - 1 / 3 = 1 / 6 = > d = 6 hours answer c
Answer: c
Problem: a class of boys stands in a single line , one boy is 19 th in order from both the ends , how many boys are there in the class ?
Options: a ) 37 , b ) 38 , c ) 27 , d ) 29 , e ) 11
Rationale: explanation : number of boys in the class = ( 18 + 1 + 18 ) = 37 answer : a ) 37
Answer: a
Problem: what number must be added to 6 , 16 and 8 to get an average of 13 ?
Options: a ) 23 , b ) 22 , c ) 44 , d ) 33 , e ) 55
Rationale: b 22
Answer: b
Problem: the average age of 30 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .
Options: a ) 46 , b ) 55 , c ) 43 , d ) 39 , e ) 54
Rationale: "explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 30 ) = 46 years answer : a"
Answer: a
Problem: if x = the product of 7 distinct prime numbers , how many factors does x have besides 1 and itself ?
Options: a ) 108 , b ) 114 , c ) 120 , d ) 126 , e ) 132
Rationale: since x has 7 distinct prime factors , x has a total of 2 ^ 7 = 128 factors . besides 1 and itself , x has 126 factors . the answer is d .
Answer: d
Problem: how many integers n are prime numbers in the range 200 < n < 220 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: to test a number n on whether it is a prime number , take square root ( n ) . consider as it is if it is a natural number . otherwise , increase the sq . root to the next natural no . then divide given no . by all prime numbers below the sq . root obtained . if the no . is divisible by any of the prime numbers , then it is not a prime number ; else it is . square root of 200 or 220 is less than 15 so , lets check if any number between 200 and 220 is not divisible by prime numbers 2 , 35 , 711 ( < 15 ) . that ' s it . out : 201 , 202 , 203 , 204 , 205 , 206 , 207 , 208 , 209 , 210 , 212 , 213 , 214 , 215 , 216 , 217 , 218 , 219 only 211 is a prime number in the given range correct option : a
Answer: a
Problem: a sum of $ 800 amounts to $ 920 in 3 years at simple interest . if the interest rate is increased by 3 % it would amount to how much ?
Options: a ) $ 506 , b ) $ 774 , c ) $ 992 , d ) $ 854 , e ) $ 1021
Rationale: s . i = 920 - 800 = 120 p = $ 800 t = 3 years r = 100 * 120 / 800 * 3 = 5 % new rate = 5 + 3 = 8 % new s . i . = 800 * 8 * 3 / 100 = $ 192 new amount = 800 + 192 = $ 992 answer is c
Answer: c
Problem: a copy machine , working at a constant rate , makes 35 copies per minute . a second copy machine , working at a constant rate , makes 65 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?
Options: a ) 3,000 , b ) 2,700 , c ) 4,500 , d ) 5,400 , e ) 324,000
Rationale: "together the two machines make 35 + 65 = 100 copies per minute . so , in half an hour they will make 100 * 30 = 3,000 copies . answer : a ."
Answer: a
Problem: what will be the compound interest on a sum of rs . 28,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 10123.77 , b ) s . 10123.21 , c ) s . 10123.20 , d ) s . 10123.28 , e ) s . 11337.98
Rationale: "amount = [ 28000 * ( 1 + 12 / 100 ) 3 ] = 28000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 39337.984 c . i . = ( 39337.984 - 28000 ) = rs . 11337.98 answer : e"
Answer: e
Problem: what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 5 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 5 ? 9 ^ 5 = ( 3 ^ 2 ) ^ 5 = 3 ^ 10 c . 10"
Answer: c
Problem: 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 4554 , how much was it in the beginning ?
Options: a ) 7349 , b ) 6300 , c ) 6325 , d ) 6939 , e ) 2989
Rationale: "x * ( 90 / 100 ) * ( 80 / 100 ) = 4554 x = 6325 answer : c"
Answer: c
Problem: cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost w is what percent of the original cost ?
Options: a ) w = 200 , b ) w = 600 , c ) w = 800 , d ) w = 1600 , e ) w = 50
Rationale: "original cost w , c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"
Answer: d
Problem: if a car went the first third of the distance at 80 kmh , the second third at 30 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 36 kmh , b ) 40 kmh , c ) 42 kmh , d ) 45 kmh , e ) 50 kmh
Rationale: assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 30 and 48 ) so : 240 = 80 * t 1 = 3 hrs 240 = 30 * t 2 = 8 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 16 hrs d = rt ( 240 * 3 ) = r * 16 r = 45 answer : d
Answer: d
Problem: a cement mixture is composed of 3 elements . by weight , 1 / 2 of the mixture is sand , 1 / 5 of the mixture is water , and the remaining 15 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 80
Rationale: "let the total weight be x . sand content = ( 1 / 2 ) x water content = ( 1 / 5 ) x gravel = x - ( 1 / 2 ) x - ( 1 / 5 ) x = ( 3 / 10 ) x = 15 x = 50 then answer will be c = 50"
Answer: c
Problem: the compound ratio of 2 / 3 , 6 / 7 , 4 / 3 and 1 / 8 is given by ?
Options: a ) 2 / 21 , b ) 1 / 48 , c ) 1 / 98 , d ) 1 / 96 , e ) 1 / 68
Rationale: "2 / 3 * 6 / 7 * 4 / 3 * 1 / 8 = 48 / 504 = 2 / 21 answer : a"
Answer: a
Problem: the center of a circle lies on the origin of the coordinate plane . if a point ( x , y ) is randomly selected inside of the circle , what is the probability that y > x or x > 0 ?
Options: a ) 7 / 8 , b ) 5 / 6 , c ) 3 / 8 , d ) 1 / 2 , e ) 3 / 4
Rationale: "the line y = x divides the circle into two equal areas . all the points above the line y = x satisfy the condition that y > x . all the points to the right of the y - axis satisfy the condition that x > 0 . the union of these two areas is 7 / 8 of the circle . the answer is a ."
Answer: a
Problem: reema took a loan of rs 900 with simple interest for as many years as the rate of interest . if she paid rs . 729 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : let rate = r % then time = r years . = > 900 ∗ r ∗ r / 100 = 729 = > r 2 = 81 = > r = 9 % option e"
Answer: e
Problem: of the 20 members of a kitchen crew , 17 can use the meat - cutting machine , 18 can use the bread - slicing machine , and 15 can use both machines . if one member is chosen at random , what is the probability that the member chosen will be someone who can not use either machine ?
Options: a ) 0 , b ) 1 / 10 , c ) 1 / 7 , d ) 1 / 4 , e ) 1 / 3
Rationale: you know how to solve for total number of people who can use at least one machine : total = n ( a ) + n ( b ) - n ( a and b ) total people who can use at least one machine = 17 + 18 - 15 = 20 so all 20 people know how to use at least one machine . hence , if you pick anyone , the probability is 0 that he would n ' t know how to use any machine . answer a
Answer: a
Problem: the average of first 9 natural numbers is ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5
Rationale: "sum of 10 natural no . = 90 / 2 = 45 average = 45 / 10 = 4.5 answer : d"
Answer: d
Problem: buses a and b start from a common bus stop x . bus a begins to travel in a straight line away from bus b at a constant rate of 20 miles per hour . one hour later , bus b begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour . if both buses travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes bus b to cover the exact distance that bus a has covered and the amount of time it takes bus b to cover twice the distance that bus a has covered ?
Options: a ) 36 , b ) 72 , c ) 132 , d ) 144 , e ) 180
Rationale: 1 st part : - in 1 hr , bus a covers 30 miles . relative speed of bus abus b is ( 80 - 30 ) = 50 mph . so time required for bus b to cover the exact distance as a is 50 * t = 30 t = 3 / 5 = 36 min 2 nd part 80 * t = 2 d - b has to cover twice the distance 30 * ( t + 1 ) = d - a traveled 1 hr more and has to travel only only d so d / 30 - 2 d / 80 = 1 d = 120 t = 3 hrs = 180 min question asks for + ve difference between part 1 and part 2 in minutes = 180 - 36 = 132 min c
Answer: c
Problem: a student committee on academic integrity has 132 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "xc 1 * ( x - 1 ) c 1 = 132 x ^ 2 - x - 132 = 0 ( x - 12 ) ( x + 11 ) = 0 x = 12 , - 11 - 11 ca n ' t possible . hence 12 should be the answer e"
Answer: e
Problem: a grocery store bought some mangoes at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?
Options: a ) 1 : 4 , b ) 16 : 9 , c ) 2 : 3 , d ) 1 : 2 , e ) 2 : 5
Rationale: the cost price of a mango = 1 / 5 dollars . the selling price of a mango from the first stack = 1 / 3 dollars - - > the profit from one mango = 1 / 3 - 1 / 5 = 2 / 15 = 4 / 30 dollars . the selling price of a mango from the second stack = 1 / 8 dollars - - > the loss from one mango = 1 / 5 - 1 / 8 = 3 / 40 dollars . the profit from one mango from the first stack is 4 times the loss from one mango from the second stack . the ratio is 4 / 30 * 40 / 3 = 16 / 9 b
Answer: b
Problem: if an investor puts $ 800 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?
Options: a ) $ 878 , b ) $ 880 , c ) $ 882 , d ) $ 884 , e ) $ 886
Rationale: "1.05 * 1.05 * 800 = $ 882 the answer is c ."
Answer: c
Problem: in an election between two candidates , one got 55 % of the total valid votes . 20 % of the votes were invalid . if the total number of votes was 7500 , what was the number of valid votes that the other candidate got ?
Options: a ) 2800 , b ) 2700 , c ) 2100 , d ) 2500 , e ) 3000
Rationale: "total no of votes = 7500 20 % invalid = > 80 % valid tot valid votes = 7500 * 80 / 100 = > valid for 2 nd candidate got 7500 * 80 / 100 * 45 / 100 = 2700 answer b"
Answer: b
Problem: the average of first five multiples of 6 is ?
Options: a ) 6 , b ) 18 , c ) 9 , d ) 5 , e ) 7
Rationale: "average = 6 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 90 / 5 = 18 . answer : b"
Answer: b
Problem: indu gave bindu rs . 625 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 1 , b ) 2 , c ) 7 , d ) 4 , e ) 9
Rationale: "625 = d ( 100 / 4 ) 2 d = 1 answer : a"
Answer: a
Problem: a bag contains 3 red , 5 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Rationale: "total number of balls = 3 + 5 + 4 = 12 n ( s ) = 12 c 3 = 12 * 11 * 10 / 3 * 2 = 220 n ( e ) = 3 c 1 * 5 c 1 * 4 c 1 = 3 * 5 * 4 = 60 probability = 60 / 220 = 3 / 11 answer is c"
Answer: c
Problem: the market value of a certain machine decreased by 10 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 6,400 , e ) $ 800
Rationale: d market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 10 / 100 ) = 8000 - 800 = $ 7200 market value in 1984 = market value in 1983 - ( 10 % of $ 8000 ) = 7200 - 800 = $ 6400
Answer: d
Problem: two numbers are less than third number by 60 % and 74 % respectively . how much percent is the second number less than by the first ?
Options: a ) 18 % , b ) 29 % , c ) 35 % , d ) 41 % , e ) none of these
Rationale: "explanation : let the third number is x . then first number = ( 100 - 60 ) % of x = 40 % of x = 4 x / 10 second number is ( 26 x / 100 ) difference = 4 x / 10 - 26 x / 100 = 14 x / 10 so required percentage is , difference is what percent of first number = > ( 14 x / 100 * 10 / 4 x * 100 ) % = 35 % answer : c"
Answer: c
Problem: a 1400 m long train crosses a tree in 100 sec , how much time will it take to pass a platform 700 m long ?
Options: a ) 288 , b ) 190 , c ) 150 , d ) 188 , e ) 12
Rationale: "l = s * t s = 1400 / 100 s = 14 m / sec . total length ( d ) = 2100 m t = d / s t = 2100 / 14 t = 150 sec answer : c"
Answer: c
Problem: the product of two positive integers is 675 and their difference is 2 . what is the bigger number ?
Options: a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 29
Rationale: "let ' s use trial and error to find the two numbers . 25 * 23 = 575 ( too low ) 27 * 25 = 675 the answer is d ."
Answer: d
Problem: during the last 4 years , a large truck company purchased diesel at rates of $ 1.2 , $ 1.3 , $ 1.8 and $ 2.1 per gallon . what was the mean cost of diesel over the 4 - year period if the company spends the same amount of dollars on diesel each year ?
Options: a ) $ 2.5 , b ) $ 2.55 , c ) $ 1.52 , d ) $ 3.25 , e ) $ 3.0
Rationale: finding the harmonic mean here . hm = 4 / ( 1 / 12 + 1 / 13 + 1 / 18 + 1 / 21 ) = 15.18 c
Answer: c
Problem: after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 5200 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these
Rationale: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 5200 = 20700 exp in % = 100 - 10 = 90 % , 20700 = 90 % saving = 10 % = 20700 x 10 / 90 = rs . 2300 answer : d"
Answer: d
Problem: shekar scored 76 , 65 , 82 , 47 and 85 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 71 , b ) 69 , c ) 75 , d ) 85 , e ) 90
Rationale: "explanation : average = ( 76 + 65 + 82 + 47 + 85 ) / 5 = 355 / 5 = 71 hence average = 71 answer : a"
Answer: a
Problem: at an elementary school , 70 % of the faculty members are women and 60 % of the faculty members are married . if 2 ⁄ 3 of the men are single , what fraction of the women are married ?
Options: a ) 5 ⁄ 7 , b ) 7 ⁄ 10 , c ) 1 ⁄ 3 , d ) 7 ⁄ 30 , e ) 5 ⁄ 70
Rationale: "plugging in numbers for this . assume 100 faculty members . 70 faculty members are women 30 faculty members are men 60 total faculty members are married 1 / 3 of men are married ( 10 ) , which means 20 men are single 10 of the 60 married faculty members are men , which means that 50 women are married . 50 / 70 women are married , reduced to 5 / 7 ans a"
Answer: a
Problem: how many multiples of 4 are there between 12 and 104 , inclusive ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the multiples of 4 are from 4 * 3 up to 4 * 26 . 26 - 3 + 1 = 24 . the answer is d ."
Answer: d
Problem: a high school has 400 students 1 / 2 attend the airthmetic club , 5 / 8 attend the physics club and 3 / 4 attend the chemistry club . 3 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .
Options: a ) 80 , b ) 70 , c ) 60 , d ) 50 , e ) 30
Rationale: "a - club has 200 members ( 1 / 2 of 400 ) b - club has 250 members ( 5 / 8 of 400 ) c - club has 300 members ( 3 / 4 of 400 ) we can create an equation to solve this : 200 + 250 + 300 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 150 ) . 750 = 400 + x + 300 x = 50 d"
Answer: d
Problem: how many kg of rice at rs . 6.60 per kg . be mixed with 56 kg of rice at rs . 9.60 per kg to get a mixture worth rs . 8.20 per kg
Options: a ) 56 kg , b ) 52 kg , c ) 44 kg , d ) 49 kg , e ) none of these
Rationale: explanation : by the rule of alligation , we have cost of 1 kg of 1 st kind rice cost of 1 kg of 2 nd kind rice 6.6 9.6 price of 1 kg of the mixture 8.2 9.6 - 8.2 = 1.4 8.2 - 6.6 = 1.6 quantity of 1 st kind rice : quantity of 2 nd kind rice = 1.4 : 1.6 = 7 : 8 quantity of 1 st kind rice : 56 = 7 : 8 = > quantity of 1 st kind rice = 56 × 78 = 49 answer : option d
Answer: d
Problem: a box measuring 36 inches long by 45 inches wide by 18 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 32 , b ) 34 , c ) 38 , d ) 40 , e ) 42
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 9 is the biggest number that could divide all three , 36 , 45 and 18 . thus side of cube must be 9 , and total number of cubes = 36 / 9 * 45 / 9 * 18 / 9 = 40 ans d ."
Answer: d
Problem: the dimensions of a rectangular solid are 4 inches , 5 inches , and 12 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a ) 10 : 17 , b ) 2 : 5 , c ) 5 : 16 , d ) 25 : 7 , e ) 10 : 21
Rationale: answer : e .
Answer: e
Problem: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 90 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "circumference of a = 2 ( pie ) r = 8 so r = 4 / pie volume = pie ( 4 / pie ) ^ 2 * 10 = 160 / pie circumference of b = 2 ( pie ) r = 10 so r = 5 / pie volume = pie ( 5 / pie ) ^ 2 * 8 = 200 / pie so ratio of capacities = 160 / 200 = 0.8 so capacity of a will be 80 % of the capacity of b answer : e"
Answer: e
Problem: a person ' s present age is two - fifth of the age of his mother . after 8 years , he will be one - half of the age of his mother . how old is the mother at present
Options: a ) 38 , b ) 40 , c ) 42 , d ) 44 , e ) 45
Rationale: "explanation : let the mother ' s present age be x years . then , the person ' s present age = ( 2 / 5 x ) years . = > ( 2 / 5 x + 8 / 2 ) = 1 ( x + 8 ) = > 2 ( 2 x + 40 ) = 5 ( x + 8 ) = > x = 40 answer : option b"
Answer: b
Problem: in town x , 64 percent of the population are employed , and 47 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 46 % , c ) 32 % , d ) 24 % , e ) 52 %
Rationale: "answer b male - employed - 64 % female - employed - 17 % total employed 64 % means total unemployed = 36 % therefore d and e are not correct because female unemployed has to be less than 36 % female - unemployed = 32 % male unemployed = 4 % 48 % + 4 % = 52 % 16 % + 32 % = 48 % plug in a and b in place of 32 % and the sum is not 100 % 17 / 64 = 26 d"
Answer: d
Problem: when positive integer n is divided by positive integer j , the remainder is 18 . if n / j = 134.03 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 600
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.03 , the decimal part of the decimal quotient , must equal the remainder , 18 , divided by the divisor j . 0.03 = 18 / j 0.03 * j = 18 j = 18 / 0.03 = 1800 / 3 = 600 so j = 600 , answer = e ."
Answer: e
Problem: the present population of a town is 3744 . population increase rate is 20 % p . a . find the population of town before 2 years ?
Options: a ) 2500 , b ) 2600 , c ) 3500 , d ) 3600 , e ) 2050
Rationale: "p = 3744 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 3744 / ( 1 + 20 / 100 ) ^ 2 = 3744 / ( 6 / 5 ) ^ 2 = 2600 ( approximately ) answer is b"
Answer: b
Problem: at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 6.50 per hour , how much less than a manager does a chef earn each hour ?
Options: a ) $ 2.6 , b ) $ 2.40 , c ) $ 3.40 , d ) $ 4.40 , e ) $ 5.40
Rationale: manager wages per hour = $ 6.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 6.50 ) = = > $ 3.25 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 3.25 = ( 20 * ( $ 3.25 ) ) / 100 - - > ( $ 65 ) / 100 - - > $ 0.65 therefore , chef wages per hour = $ 3.25 + $ 0.65 = = > $ 3.9 difference of wages between manager and chef = $ 6.50 - $ 3.9 = = > $ 2.6 answer : a
Answer: a
Problem: the cost of paint is 60 per kilograme . a kilogram paint covers 20 square feet . how much will it cost to paint the outside of a cube having each side 10 feet ?
Options: a ) 3000
b ) 900
c ) 1800
d ) 360
e ) none of these
Rationale: area of cube = 6 × ( side ) 2 = 6 × 10 × 10 = 600 square feet . cost to paint outside of the cube = 600 ⁄ 20 × 60 = 1800 answer c
Answer: c
Problem: a man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 0.5 kmph , find his average speed for the total journey ?
Options: a ) 4 , b ) 3.5 , c ) 3 , d ) 3.1 , e ) 2.8
Rationale: "m = 4.5 s = 2.5 ds = 7 us = 2 as = ( 2 * 7 * 2 ) / 9 = 3.1 answer : d"
Answer: d
Problem: the original price of a suit is $ 160 . the price increased 25 % , and after this increase , the store published a 25 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 25 % off the increased price , how much did these consumers pay for the suit ?
Options: a ) $ 140 , b ) $ 145 , c ) $ 150 , d ) $ 155 , e ) $ 160
Rationale: 0.75 * ( 1.25 * 160 ) = $ 150 the answer is c .
Answer: c
Problem: the least perfect square , which is divisible by each of 21 , 36 and 66 is
Options: a ) 213414 , b ) 213424 , c ) 213434 , d ) 213444 , e ) none of these
Rationale: "explanation : l . c . m . of 21 , 36 , 66 = 2772 now , 2772 = 2 x 2 x 3 x 3 x 7 x 11 to make it a perfect square , it must be multiplied by 7 x 11 . so , required number = 2 x 2 x 3 x 3 x 7 x 7 x 11 x 11 = 213444 option d"
Answer: d
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 40 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.4 c ( 40 % profit ) x = 1.4 / . 8 * c x = 7 / 4 c original selling price is 1.75 c which is 75 % profit answer e"
Answer: e
Problem: in a throw of dice what is the probability of getting number greater than 5
Options: a ) 1 / 7 , b ) 1 / 6 , c ) 1 / 11 , d ) 1 / 13 , e ) 2 / 9
Rationale: "number greater than 5 is 6 , so only 1 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 1 / 6 b )"
Answer: b
Problem: in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 4 % . what is population of after 2 year .
Options: a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 147
Rationale: "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 4 % so total man = 150 * . 96 = 144 women will be = 175 - 144 = 31 so population after two years = [ 135 ^ 2 + 31 ^ 2 ] ^ . 5 = 147.30 = 147 so population after two year = 147 answer : e"
Answer: e
Problem: if | x + 132 | = 32 what is the sum of all the values of x .
Options: a ) - 264 , b ) 200 , c ) - 64 , d ) 0 , e ) - 328
Rationale: there will be two cases x + 132 = 32 and x + 132 = - 32 solve for x = > x = 32 - 132 = > x = - 100 or x = - 32 - 132 = > x = - 164 the sum of both values will be - 164 + - 100 = - 264 answer is a
Answer: a
Problem: of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 19 boys and 41 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
Options: a ) 2 , b ) 7 , c ) 6 , d ) 8 , e ) 10
Rationale: "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 19 boys . so 19 - 6 - 6 = 7 boys must be neither happy nor sad . answer ( b )"
Answer: b
Problem: a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 64 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )
Options: a ) 48 , b ) 52 , c ) 54 , d ) 58 , e ) 56
Rationale: "let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 64 or 1 / 7 t + 1 t = 64 therefore t = 64 * 7 / 8 = 56 e"
Answer: e
Problem: if the radius of a circle that centers at the origin is 5 , how many points q on the circle have integer coordinates ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20
Rationale: "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : q = c"
Answer: c
Problem: the ratio of the radius of two circles is 1 : 5 , and then the ratio of their areas is ?
Options: a ) 1 : 7 , b ) 2 : 9 , c ) 1 : 25 , d ) 3 : 7 , e ) 3 : 4
Rationale: "r 1 : r 2 = 1 : 5 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 1 : 25 answer : c"
Answer: c
Problem: the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 98 , and last 6 numbers is 65 then find 6 th number ?
Options: a ) a ) 318 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48
Rationale: 6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 98 + 6 * 65 - 11 * 60 = 318 answer is a
Answer: a
Problem: a man bought 40 shares of rs . 60 at 8 discount , the rate of dividend being 1212 % the rate of interest obtained is
Options: a ) 13.64 % , b ) 15.5 % , c ) 14 % , d ) 14.42 % , e ) 14.95 %
Rationale: "explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 8 = rs . 52 number of shares = 40 dividend = 12 1 / 2 % = 25 / 2 % dividend per share = 60 × 25 / 2 × 100 = rs . 7.5 total dividend = ( 40 × 7.5 ) ie , he got a dividend of ( 40 × 7.5 ) for an investment of rs . ( 40 × 52 ) interest obtained = 40 × 7.5 × 100 / 40 × 52 = 14.42 % answer : option d"
Answer: d
Problem: the area of a triangle is 615 m 2 . if one of its sides is 123 metre , find the length of the perpendicular dropped on that side from opposite vertex .
Options: a ) 15 metres
b ) 12 metres
c ) 10 metres
d ) 9 metres
e ) none of these
Rationale: in a triangle , area = 1 ⁄ 2 × length of perpendicular × base or 615 = 1 ⁄ 2 × length of perpendicular × 123 ∴ length of perpendicular = 615 × 2 / 123 = 10 m answer c
Answer: c
Problem: in an election between the two candidates , the candidates who gets 60 % of votes polled is wined by 280 votes majority . what is the total number of votes polled ?
Options: a ) 1400 , b ) 1500 , c ) 1600 , d ) 1700 , e ) 1800
Rationale: note : majority ( 20 % ) = difference in votes polled to win ( 60 % ) & defeated candidates ( 40 % ) 20 % = 60 % - 40 % 20 % - - - - - > 280 ( 20 × 14 = 280 ) 100 % - - - - - > 1400 ( 100 × 14 = 1400 ) a
Answer: a
Problem: solve the equation for x : 6 x - 47 + 3 x = 4 + 9 - x
Options: a ) 4 , b ) 5 , c ) 7 , d ) 9 , e ) 6
Rationale: "e 6 9 x + x = 13 + 47 10 x = 60 = > x = 6"
Answer: e
Problem: what is the remainder if 7 ^ 12 is divided by 100 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 7 ^ 16 can be written as ( 7 ^ 4 ) ^ 3 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 3 by 100 , the reminder is 1 ^ 3 = 1 answer : a
Answer: a
Problem: calculate the average of all the numbers between 10 and 86 which are divisible by 9 .
Options: a ) 49.5 , b ) 41.5 , c ) 45.5 , d ) 40.5 , e ) 47.5
Rationale: "explanation : numbers divisible by 9 are 18,27 , 36,45 , 54,63 , 72,81 , average = ( 18 + 27 + 36 + 45 + 54 + 63 + 72 + 81 , ) / 8 = 396 / 8 = 49.5 answer : a"
Answer: a
Problem: what is the length of a bridge ( in meters ) , which a train 156 meters long and travelling at 45 km / h can cross in 30 seconds ?
Options: a ) 203 , b ) 211 , c ) 219 , d ) 227 , e ) 235
Rationale: speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 30 seconds , the train can travel 25 / 2 * 30 = 375 meters 375 = length of train + length of bridge length of bridge = 375 - 156 = 219 meters the answer is c .
Answer: c
Problem: zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 6 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 6 questions did zachary answer correctly ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "i got two equations : 3 x - 2 y = 25 x + y = 6 3 x - 2 ( 6 - x ) = 25 3 x - 12 + 2 x = 25 5 x = 37 x = 7.4 or between 7 and 8 . ( ans b )"
Answer: b
Problem: the average of first 17 even numbers is ?
Options: a ) 10 , b ) 11 , c ) 18 , d ) 20 , e ) 24
Rationale: "sum of 17 even numbers = 17 * 18 = 306 average = 306 / 17 = 18 answer : c"
Answer: c
Problem: the average of all odd numbers up to 200 is
Options: a ) 50 , b ) 100 , c ) 120 , d ) 75 , e ) 80
Rationale: "the numbers are 1,3 , 5,7 , - - - - - - - - , 197,199 average = ( 199 - 1 ) / 2 + 1 = 100 answer is b"
Answer: b
Problem: a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 11 multiples of 14 , how many multiples of 7 are there in q ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: "halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 11 + 10 = 21 . the answer is c ."
Answer: c
Problem: the ratio between the presents of the a and b is 2 : 3 . if b is 5 years older than a , what will be the ratio of the ages of a and b after 5 years ?
Options: a ) 3 : 4 , b ) 1 : 2 , c ) 2 : 3 , d ) 5 : 6 , e ) 1 : 3
Rationale: "let a and b ages will be 2 x and 3 x 3 x - 2 x = 5 x = 5 required ratio = 2 x + 5 : 3 x + 5 = 15 : 20 = 3 : 4 answer is a"
Answer: a
Problem: a man gains 40 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 180 % , c ) 150 % , d ) 160 % , e ) 170 %
Rationale: "explanation : let the c . p . = x , then s . p . = ( 140 / 100 ) x = 7 x / 5 new s . p . = 2 ( 7 x / 5 ) = 14 x / 5 profit = 14 x / 5 - x = 9 x / 5 profit % = ( profit / c . p . ) * 100 = > ( 9 x / 5 ) * ( 1 / x ) * 100 = 180 % option b"
Answer: b
Problem: if x * y = xy – 2 ( x + y ) for all integers x and y , then 1 * ( – 3 ) =
Options: a ) – 16 , b ) – 11 , c ) – 4 , d ) 4 , e ) 1
Rationale: "1 * ( - 3 ) = 1 * ( - 3 ) - 2 ( 1 + ( - 3 ) ) = - 3 + 4 = 1 option ( e )"
Answer: e
Problem: on increasing the price of t . v . sets by 40 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 4 , b ) 5 , c ) 56 , d ) 12 , e ) 7
Rationale: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 140 × 80 ) = rs . 11200 increase % = 1200 / 10000 × 100 = 12 % answer : d"
Answer: d
Problem: 0.002 x 0.5 = ?
Options: a ) 0.0001 , b ) 0.001 , c ) 0.01 , d ) 0.1 , e ) none of these
Rationale: "explanation : 2 x 5 = 10 . sum of decimal places = 4 0.002 x 0.5 = 0.001 answer - b"
Answer: b
Problem: a 10 % stock yields 8 % . the market value of the stock is :
Options: a ) rs . 72 , b ) rs . 125 , c ) rs . 112.50 , d ) rs . 116.50 , e ) none of these
Rationale: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 10 , investment = rs . ( 100 / 8 x 10 ) = rs . 125 ∴ market value of rs . 100 stock = rs . 125 answer b"
Answer: b
Problem: a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 300 . find the sum ?
Options: a ) 7000 , b ) 2500 , c ) 2778 , d ) 2800 , e ) 2791
Rationale: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 300 = > 36 x / 100 - 24 x / 100 = 300 = > 12 x / 100 = 300 = > x = 2500 . answer : b"
Answer: b
Problem: at a monthly meeting , 3 / 5 of the attendees were males and 7 / 8 of the male attendees arrived on time . if 4 / 5 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?
Options: a ) 47 / 200 , b ) 31 / 200 , c ) 17 / 100 , d ) 11 / 100 , e ) 7 / 50
Rationale: "males who did not arrive on time are 1 / 8 * 3 / 5 = 3 / 40 of the attendees . females who did not arrive on time are 1 / 5 * 2 / 5 = 2 / 25 of the attendees . the fraction of all attendees who did not arrive on time is 3 / 40 + 2 / 25 = 31 / 200 the answer is b ."
Answer: b
Problem: how many quarters are equal to 4 dollars ?
Options: a ) 16 , b ) 8 , c ) 12 , d ) 9 , e ) 7
Rationale: "4 * 4 = 16 quarters answer : a"
Answer: a
Problem: 1391 x 1391 = ?
Options: a ) a ) 1951609 , b ) b ) 1951601 , c ) c ) 1951602 , d ) d ) 1951603 , e ) e ) 1934881
Rationale: "1391 x 1391 = ( 1391 ) 2 = ( 1400 - 9 ) 2 = ( 1400 ) 2 + ( 9 ) 2 - ( 2 x 1400 x 9 ) = 1960000 + 81 - 25200 = 1960081 - 25200 = 1934881 . answer : e"
Answer: e
Problem: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 33 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 16.5 minutes , b ) 33 minutes , c ) 49.5 minutes , d ) 66 minutes , e ) 99 minutes
Rationale: "danny ' s time is 33 minutes . the time to reach halfway is 16.5 minutes . steve ' s time is 66 minutes . the time to reach halfway is 33 minutes . the time difference is 33 - 16.5 = 16.5 minutes the answer is a ."
Answer: a
Problem: the compound interest on $ 30,000 at 7 % p . a is $ . 4347 . find out the period ( in years ) ?
Options: a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3
Rationale: "amount = 30,000 + 4347 = 34347 . . . . . . . . . now by using compound interest formula we get , 30,000 * ( 107 / 100 ) ^ n = 34347 = = = = > n = 2 years ans - c"
Answer: c
Problem: a fair 2 sided coin is flipped 4 times . what is the probability that tails will be the result at least twice , but not more than 4 times ?
Options: a ) 1 / 8 , b ) 2 / 3 , c ) 5 / 8 , d ) 4 / 7 , e ) 3 / 7
Rationale: "at least twice , but not more than 4 timesmeans exactly 2 times , 3 times , 4 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 4 c 2 / 2 ^ 4 + 4 c 3 / 2 ^ 4 = 10 / 16 = 5 / 8 option : c"
Answer: c
Problem: i have only 1 $ and 2 $ note . i want to give 95 $ to john . how many maximum number of 1 $ note i need ?
Options: a ) 53 , b ) 35 , c ) 47 , d ) 95 , e ) 62
Rationale: "to give 95 $ we need of 95 1 $ notes so ans is d"
Answer: d
Problem: how many multiples of 6 are less than 5000 , and also multiples of 8 ?
Options: a ) 104 , b ) 208 , c ) 625 , d ) 832 , e ) 833
Rationale: "lcm of 6 & 8 = 24 tried dividing 5000 by 24 got quotient 208.33 ' so b is answer"
Answer: b
Problem: audrey 4 hours to complete a certain job . ferris can do the same job in 3 hours . audrey and ferris decided to collaborate on the job , working at their respective rates . while audrey worked continuously , ferris took 5 breaks of equal length . if the two completed the job together in 2 hours , how many minutes long was each of ferris ’ breaks ?
Options: a ) 5 , b ) 6 , c ) 15 , d ) 20 , e ) 25
Rationale: "audery and ferris collective work rate : 1 / 4 + 1 / 3 = 7 / 12 collective work time = 12 / 7 = 1.7 hrs job was actually done in = 2 ( includes breaks ) breaks = actual time taken - collective work time = 2 - 1.7 = . 3 hrs = 1 / 2 so ferrais took 5 breaks = . 3 / 5 = . 06 hrs = 6 m so answer is b ) 10 mins"
Answer: b
Problem: find the sum of divisors of 544 which are perfect squares .
Options: a ) 32 , b ) 64 , c ) 42 , d ) 21 , e ) none of these
Rationale: "544 = 25 + 171 = ( 2 ) 0 + ( 2 ) 1 + ( 2 ) 2 + ( 2 ) 3 + ( 2 ) 4 + ( 2 ) 5 x ( 17 ) 0 + ( 17 ) 1 . here 20 = 1 = 11 a perfect square , 22 and 24 = 16 = 44 are perfect squares , hence , 1 + 4 + 16 = 21 . correct answer is : d"
Answer: d
Problem: a glass was filled with 10 ounces of water , and 0.03 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.006 % , b ) 0.06 % , c ) 0.6 % , d ) 6 % , e ) 60 %
Rationale: "we are given that 0.03 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.01 by 20 . this gives us : 0.03 x 20 = 0.6 ounces finally , we are asked for “ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 0.6 / 10 ) x 100 % ( 6 / 100 ) x 100 % = 6 % answer d"
Answer: d
Problem: a cistern is normally filled in 6 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?
Options: a ) 33 , b ) 88 , c ) 24 , d ) 99 , e ) 11
Rationale: 1 / 6 - 1 / x = 1 / 8 x = 24 answer : c
Answer: c
Problem: a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 50 percent .
Options: a ) 145 , b ) 150 , c ) 175 , d ) 160 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 50 percent 150 min . answer : b
Answer: b
Problem: the diagonals of a rhombus are 10 cm and 12 cm . find its area ?
Options: a ) 158 , b ) 60 , c ) 150 , d ) 123 , e ) 117
Rationale: "1 / 2 * 10 * 12 = 60 answer : b"
Answer: b
Problem: a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 8 g / cm 3 , then the weight of the pipe is :
Options: a ) 3.6 kg , b ) 3.696 kg , c ) 36 kg , d ) 36.9 kg , e ) none
Rationale: "solution external radius = 4 cm , internal radius = 3 cm . volume of iron = ( 22 / 7 × ( 42 ) - ( 32 ) × 21 ) cm 3 = ( 22 / 7 × 7 × 1 × 21 ) cm 3 = 462 cm 3 . weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg . answer b"
Answer: b
Problem: in the forestside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 50 . , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .
Rationale: given there are 50 students in the forestside summer camp , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . imo option a is correct .
Answer: a
Problem: on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 b )"
Answer: b
Problem: kathleen can paint a room in 4 hours , and anthony can paint an identical room in 5 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?
Options: a ) 8 / 15 , b ) 40 / 9 , c ) 15 / 8 , d ) 9 / 4 , e ) 15 / 4
Rationale: "( 1 / 4 + 1 / 5 ) t = 2 t = 40 / 9 answer : b"
Answer: b
Problem: if 0.75 : x : : 10 : 8 , then x is equal to :
Options: a ) a ) 0.6 , b ) b ) 0.8 , c ) c ) 0.85 , d ) d ) 0.5 , e ) e ) none
Rationale: "( x * 10 ) = ( 0.75 * 8 ) x = 6 / 10 x = 0.6 answer = a"
Answer: a
Problem: there are 2 sections a and b in a class , consisting of 36 and 44 students respectively . if the average weight of section a is 40 kg and that of section b is 35 kg , find the average of the whole class ?
Options: a ) 35.29 kg , b ) 37.25 kg , c ) 42.45 kg , d ) 55.12 kg , e ) 29.78 kg
Rationale: total weight of 36 + 44 students = 36 * 44 + 44 * 35 = 2980 average weight of the class is = 2980 / 80 = 37.25 kg answer is b
Answer: b
Problem: a box contains 100 pairs of shoes ( 200 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 199 , d ) 1 / 10 , e ) 1 / 9
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 200 , 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 / 199 ( as after taking one at random there are 199 shoes left and only one is the pair of the first one ) = 1 / 199 answer : c ."
Answer: c
Problem: the nasdaq index has decreased by 70 % since year 2000 . how much should the index increase in order to gain the same value as in year 2000 ?
Options: a ) 400 % , b ) 80 % , c ) 233 % , d ) 60 % , e ) none of the above
Rationale: let x be the index in the year 2000 . after the decrease it becomes 0.3 x now for 0.3 x to reach 1 x it has to raise by 0.7 x . the increase needs to be 0.7 x / 0.3 x * 100 = 233.3 % answer c
Answer: c