regisss/math_qa huggingface dataset:
Problem: john and jacob set out together on bicycle traveling at 15 and 9 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john one hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 15 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible )
Options: a ) 3 , b ) 3 1 / 3 , c ) 3 1 / 2 , d ) 4 , e ) 1 1 / 4
Rationale: john ' s speed - 15 miles / hr jacob ' s speed - 9 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 15 x 2 / 3 = 10 miles . jacob continues to ride for a total of 1 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 1 hour 40 min ( i . e 5 / 3 hr ) = 9 x 5 / 3 = 15 miles . now , when john starts riding back , the distance between them is 7.5 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 15 - 9 = 6 miles / hr . thus , to cover 7.5 miles at 6 miles / hr , john will take 7.5 / 6 = 1.25 hours answer e
Answer: e
Problem: 23 × 19 × ? ÷ 19 ÷ 17 = 115
Options: a ) 65 , b ) 75 , c ) 85 , d ) 95 , e ) 45
Rationale: "explanation : 23 × 19 × ? ÷ 19 ÷ 17 = 115 = > ( 23 × 19 × ? ) / ( 19 × 17 ) = 115 = > ? = ( 115 × 19 × 17 ) / ( 23 × 19 ) = 85 answer : option c"
Answer: c
Problem: a city with a population of 97500 is to be divided into 6 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ?
Options: a ) 15,000 , b ) 15,500 , c ) 16,000 , d ) 16,500 , e ) 17,000
Rationale: the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 97,500 = p + 5 ( 1.1 ) p 6.5 p = 97,5000 p = 15,000 the answer is a .
Answer: a
Problem: pipe a can fill a tank in 10 hr , pipe b in 20 hr and pipe c in 40 hr . if all the pipes are open in how many hours will tank be filled ?
Options: a ) 1 hr , b ) 30 min , c ) 15 min , d ) 17 min , e ) 10 min
Rationale: part filled by ( a + b + c ) in 1 hour = 1 / 10 + 1 / 20 + 1 / 40 = 7 / 40 all the 3 pipes together will fill the tank in 17 min approximately answer is d
Answer: d
Problem: a 40 kg metal bar made of alloy of tin and silver lost 4 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 4 kg when 40 kg alloy is immersed . this is a loss of ( 4 / 40 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e
Answer: e
Problem: in a sports club with 28 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 19 - x ) + x + 2 = 28 38 - 2 x + x = 28 38 - x = 28 x = 10 so 8 members play both badminton and tennis . d"
Answer: d
Problem: village x has a population of 74000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 15 , b ) 16 , c ) 11 , d ) 18 , e ) 13
Rationale: "let the population of two villages be equal after p years then , 74000 - 1200 p = 42000 + 800 p 2000 p = 32000 p = 16 answer is b ."
Answer: b
Problem: the radius of a semi circle is 6.5 cm then its perimeter is ?
Options: a ) 32.7 , b ) 32.4 , c ) 33.4 , d ) 32.8 , e ) 32.1
Rationale: "36 / 7 r = 6.5 = 33.4 answer : c"
Answer: c
Problem: a number x is 3 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 66.6 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 3 . then y = 1 is less than x = 3 by ( 3 - 1 ) / 3 * 100 = 2 / 3 * 100 = 66.6 % . answer : b ."
Answer: b
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 36 kmph . in how much time will the trains cross each other ?
Options: a ) 12 sec , b ) 13 sec , c ) 15 sec , d ) 16 sec , e ) 17 sec
Rationale: "d relative speed = ( 54 + 36 ) * 5 / 18 = 5 * 5 = 25 mps . the time required = d / s = ( 100 + 100 + 200 ) / 25 = 400 / 25 = 16 sec ."
Answer: d
Problem: if a car had traveled 20 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 60 km , at what speed did it travel ?
Options: a ) 35 kmh , b ) 40 kmh , c ) 50 kmh , d ) 60 kmh , e ) 65 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 60 / x - 60 / ( x + 20 ) = 1 / 2 substitute the value of x from the options . - - > x = 40 - - > 60 / 40 - 60 / 60 = 3 / 2 - 1 = 1 / 2 answer : b"
Answer: b
Problem: a student has to obtain 33 % of the total marks to pass . he got 59 marks and failed by 40 marks . the maximum marks are ?
Options: a ) 450 , b ) 300 , c ) 500 , d ) 610 , e ) 175
Rationale: "let the maximum marks be x then , 33 % of x = 59 + 40 33 x / 100 = 99 x = 300 answer is b"
Answer: b
Problem: the ratio of the volumes of two cubes is 1728 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 144 : 121 , b ) 141 : 127 , c ) 144 : 191 , d ) 181 : 161 , e ) 81 : 182
Rationale: "explanation : ratio of the sides = ³ √ 1728 : ³ √ 1331 = 12 : 11 ratio of surface areas = 12 ^ 2 : 11 ^ 2 = 144 : 121 answer : option a"
Answer: a
Problem: the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 4 years is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 9724 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 4 = rs 9724 answer : c"
Answer: c
Problem: there are 6 working days in a regular week and for each day , the working hours are 10 . a man earns rs . 2.10 per hour for regular work and rs . 4.20 per hour for overtime . if he earns rs . 525 in 4 weeks , how many hours did he work ?
Options: a ) 225 , b ) 235 , c ) 215 , d ) 255 , e ) 245
Rationale: egular working hours in 4 weeks = ( 4 × 6 × 10 ) = 240 hours amount earned by working in these regular working hours = 240 × 2.10 = rs . 504 additional amount he earned = 525 - 504 = rs . 21 hours he worked overtime = 21 / 4.2 = 210 / 42 = 5 hours total hours he worked = 240 + 5 = 245 hours answer is e .
Answer: e
Problem: due to construction , the speed limit along an 7 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "7 / 35 - 7 / 55 = 7 / 5 * ( 11 - 7 ) / 77 = 7 / 5 * 4 / 77 * 60 min = 7 * 12 * 4 / 77 = 336 / 77 ~ 4.3 answer - c"
Answer: c
Problem: if the price of gasoline increases by 25 % and a driver intends to spend only 5 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
Options: a ) 20 % , b ) 16 % , c ) 15 % , d ) 12 % , e ) 10 %
Rationale: "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.05 ( p * x ) y = ( 1.05 / 1.25 ) x = 0.84 x which is a reduction of 16 % . the answer is b ."
Answer: b
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) 4000 , b ) 345 , c ) 5673 , d ) 6530 , e ) 8154
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 9 = rs . 8154 answer : option e"
Answer: e
Problem: d and e are two points respectively on sides ab and ac of triangle abc such that de is parallel to bc . if the ratio of area of triangle ade to that of the trapezium decb is 25 : 144 and bc = 13 cm , then find the length of de .
Options: a ) 12 , b ) 5 , c ) 14 , d ) 11 , e ) 15
Rationale: "abc and ade are similar triangles . so ( side of abc / side of ade ) ^ 2 = 169 / 25 side of abc / side of ade = 13 / 5 so the length of de = 5 answer - b"
Answer: b
Problem: there are 24 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?
Options: a ) 800 , b ) 820 , c ) 650 , d ) 870 , e ) 900
Rationale: "the total number of stations = 26 from 26 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 26 p 2 ways . 26 p 2 = 26 * 25 = 650 answer : c"
Answer: c
Problem: jaclyn buys $ 50 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 1187.5 , b ) 1234 , c ) 1289 , d ) 1345 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 answer : a"
Answer: a
Problem: x does a work in 30 days . y does the same work in 45 days . in how many days they together will do the same work ?
Options: a ) 18 , b ) 12 , c ) 20 , d ) 30 , e ) 15
Rationale: "x ' s 1 day ' s work = 1 / 30 y ' s 1 day ' s work = 1 / 45 ( x + y ) ' s 1 day ' s work = ( 1 / 30 + 1 / 45 ) = 1 / 18 both together will finish the work in 18 days . correct option is a"
Answer: a
Problem: how many positive integer solutions does the equation 2 x + 3 y = 100 have ?
Options: a ) 50 , b ) 33 , c ) 16 , d ) 35 , e ) 14
Rationale: "formula : ( constant ) / ( lcm of two nos ) = 100 / ( 2 * 3 ) = 15.5 answer : c"
Answer: c
Problem: if 3 : 7 : : x : 21 , then find the value of x
Options: a ) 7 , b ) 8 , c ) 11 , d ) 6 , e ) 9
Rationale: explanation : treat 3 : 7 as 3 / 7 and x : 21 as x / 21 , treat : : as = so we get 3 / 7 = x / 21 = > 7 x = 63 = > x = 9 option e
Answer: e
Problem: how many pieces of 0.42 meteres can be cut from a rod 36.5 meteres long
Options: a ) 30 , b ) 40 , c ) 86 , d ) 89 , e ) 95
Rationale: "explanation : we need so simple divide 36.5 / 0.42 , = ( 3650 / 42 ) = 86 option c"
Answer: c
Problem: if the cost price is 94 % of sp then what is the profit %
Options: a ) 5.07 % , b ) 6 % , c ) 5.7 % , d ) 6.50 % , e ) 6.25 %
Rationale: "sol . sp = rs 100 : then cp = rs 94 : profit = rs 6 . profit = { ( 6 / 94 ) * 100 } % = 6.25 % answer is e ."
Answer: e
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 1 and the units digit of ( a + 1 ) ^ 2 is 0 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 . , b ) 3 . , c ) 5 . , d ) 7 . , e ) 9 .
Rationale: "if the units digit of a ^ 2 is 1 , then the units digit of a is either 1 or 9 . if the units digit of ( a + 1 ) ^ 2 is 0 , then the units digit of a + 1 is 0 . to satisfy both conditions , the units digit of a must be 9 . then a + 2 has the units digit of 1 , thus the units digit of ( a + 2 ) ^ 2 will be 1 . the answer is a ."
Answer: a
Problem: a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 5 feet and a height of 10 feet , how far did the oil level drop in the stationary tank ?
Options: a ) 2.5 ft
b ) 1 ft
c ) 0.5 ft
d ) 0.25 ft
e ) 0.025 ft
Rationale: in order to fill up the tank , same volume is shifted from one tank to the other . pi r 1 ^ 2 h 1 = pi r 2 ^ 2 h 2 5 * 5 * 10 = 100 * 100 * h 2 h 2 = . 025 ft e is the answer
Answer: e
Problem: a person saved $ 10 in buying an item on sale . if he spent $ 100 for the item , approximately how much percent he saved in the transaction ?
Options: a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 6 %
Rationale: actual price = 100 + 10 = $ 110 saving = 10 / 110 * 100 = 100 / 11 = 10 % approximately answer is b
Answer: b
Problem: two family reunions are happening at the same hotel , the oates reunion and the yellow reunion . all 100 guests at the hotel attend at least one of the reunions . if 42 people attend the oates reunion and 65 people attend the yellow reunion , how many people attend both reunions ?
Options: a ) 2 , b ) 7 , c ) 10 , d ) 16 , e ) 22
Rationale: no of people in oates reunion = 42 no of people in yellow reunion = 65 attending both = x all guests attend at least one . therefore , 100 = 42 + 65 - ( both ) both = 7 answer b
Answer: b
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 140 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Rationale: "number of newborns that can die in first month = 1 / 10 * 200 = 20 survived = 180 number of newborns that can die in second month = 1 / 10 * 180 = 18 survived = 162 number of newborns that can die in third month = 1 / 10 * 162 = 16 survived = 146 answer : b"
Answer: b
Problem: the surface of a cube is 150 sq cm . find its volume ?
Options: a ) 8 cc , b ) 9 cc , c ) 125 cc , d ) 4 cc , e ) 6 cc
Rationale: "6 a 2 = 150 = 6 * 25 a = 5 = > a 3 = 125 cc answer : c"
Answer: c
Problem: two numbers are in the ratio of 5 : 7 . if 7 is subtracted from each number , they are in the ratio of 2 : 3 . what are the two numbers ?
Options: a ) 35 , 49 , b ) 40 , 56 , c ) 45 , 63 , d ) 50 , 70 , e ) 55 , 77
Rationale: "( 5 x - 7 ) : ( 7 x - 7 ) = 2 y : 3 y 5 x - 7 = 2 y 7 x - 7 = 3 y 49 - 35 = 15 y - 14 y 14 = y 5 x - 7 = 28 x = 7 the two numbers are 5 x and 7 x which are 35 and 49 . the answer is a ."
Answer: a
Problem: a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 40 - sided polygon have ?
Options: a ) 875 , b ) 740 , c ) 1425 , d ) 2025 , e ) 2500
Rationale: "there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 40 . plugging it in , we get 740 diagonals ! answer ( b ) ."
Answer: b
Problem: in covering a distance of 24 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 4 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7.5 kmph , e ) 7.8 kmph
Rationale: "let abhay ' s speed be x km / hr . then , 24 / x - 24 / 2 x = 3 6 x = 24 x = 4 km / hr . answer : option a"
Answer: a
Problem: 20 workers can finish a work in 30 days . after how many days should 5 workers leave the job so the work is completed in 35 days ?
Options: a ) 7 , b ) 6 , c ) 15 , d ) 4 , e ) 3
Rationale: work done by 15 workers in 35 days = 15 * 35 = 525 men days . now , work remaining = 600 – 525 = 75 men days and we have 5 workers . so 5 workers will work for 75 / 5 = 15 days . answer : c
Answer: c
Problem: a glass was filled with 10 ounces of water , and 0.02 ounce of the water evaporated each day during a 30 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.006 % , b ) 0.06 % , c ) 6 % , d ) 2 % , e ) 60 %
Rationale: "in 30 days 30 * 0.02 = 0.6 ounces of water evaporated , which is 0.6 / 10 â ˆ — 100 = 6 of the original amount of water . answer : c ."
Answer: c
Problem: a train 284 m in length crosses a telegraph post in 18 seconds . the speed of the train is ?
Options: a ) 77 kmph , b ) 55 kmph , c ) 57 kmph , d ) 58 kmph , e ) 76 kmph
Rationale: "s = 284 / 18 * 18 / 5 = 57 kmph answer : c"
Answer: c
Problem: roy is now 8 years older than julia and half of that amount older than kelly . if in 2 years , roy will be 3 times as old as julia , then in 2 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 72 , b ) 84 , c ) 88 , d ) 96 , e ) 108
Rationale: r = j + 8 = k + 4 r + 2 = 3 ( j + 2 ) ( j + 8 ) + 2 = 3 j + 6 j = 2 r = 10 k = 6 in 2 years ( r + 2 ) ( k + 2 ) = 12 * 8 = 96 the answer is d .
Answer: d
Problem: a mixture of 120 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 2 liters , b ) 3 liters , c ) 8 liters , d ) 5 liters , e ) 7 liters
Rationale: number of liters of water in 120 liters of the mixture = 20 % of 120 = 20 / 100 * 120 = 24 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 24 + p ) and total volume of mixture is ( 120 + p ) . ( 24 + p ) = 25 / 100 * ( 120 + p ) 96 + 4 p = 120 + p p = 8 liters . answer : c
Answer: c
Problem: 5 friends visited a fruit stall , and everyone decided to contribute equally to the total bill of $ 100 . if one of the friends had a coupon for 6 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ?
Options: a ) 18 , b ) 18.8 , c ) 19 , d ) 17.8 , e ) 17.9
Rationale: at the non - discounted price , each friend would pay $ 20 , as $ 100 divided by 5 friends is $ 20 per friend . but if the bill is 6 % off , then each friend would pay 6 % less . 6 % of $ 20 is $ 1.2 , so each friend saves $ 1.2 and pays the remaining 18.8 correct option : option b
Answer: b
Problem: a certain country is divided into 5 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 15 the total number of progressives in the entire country , what fraction of the country is traditionalist ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 15 the total number of traditionalists is 5 p / 15 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e ."
Answer: e
Problem: an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 22050 / - in 3 years at the same rate of interest . find the rate percentage ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 25 %
Rationale: "explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 22050 / - - 17640 / - = rs . 4410 / - rate of interest = ( 4410 / 17640 ) × ( 100 / 1 ) = > 25 % answer : option e"
Answer: e
Problem: which number can we add to 859722 to get a number exactly divisible by 456 ?
Options: a ) 294 , b ) 306 , c ) 318 , d ) 338 , e ) 362
Rationale: "859722 / 456 = 1885 with a remainder of 162 . we need to add 456 - 162 = 294 the answer is a ."
Answer: a
Problem: find the l . c . m of 12 , 25 , 24 and 20 .
Options: a ) 240 , b ) 600 , c ) 320 , d ) 150 , e ) 250
Rationale: "explanation : 6 x 2 x 2 x 5 x 5 = 600 answer : option b"
Answer: b
Problem: walking with 4 / 5 of my usual speed , i miss the bus by 3 minutes . what is my usual time ?
Options: a ) 16 min , b ) 26 min , c ) 34 min , d ) 20 min , e ) 12 min
Rationale: speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 3 4 - - - - - - - - - ? è 12 answer : e
Answer: e
Problem: what is the probability of getting a sum 9 from two throws of a dice ?
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 12 , e ) none of these
Rationale: "in two throws of a dice , n ( s ) = ( 6 x 6 ) = 36 . let e = event of getting a sum = { ( 3 , 6 ) , ( 4 , 5 ) , ( 5 , 4 ) , ( 6 , 3 ) } . p ( e ) = n ( e ) / n ( s ) = 4 / 36 = 1 / 9 . answer : c"
Answer: c
Problem: in the hillside summer camp there are 100 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 ) 150 . , b ) 145 . , c ) 100 . , d ) 30 . , e ) 25 .
Rationale: "given there are 100 students , 90 % of 50 = 90 boys and remaining 10 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 1000 to existing 90 then the count will be 190 and the girls number will be 10 as it . now boys are 95 % and girls are 5 % . ( out of 200 students = 190 boys + 10 girls ) . imo option c is correct ."
Answer: c
Problem: what is the sum of the integers from - 185 to 195 inclusive ?
Options: a ) 0 , b ) 5 , c ) 375 , d ) 1905 , e ) 965
Rationale: "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = - 185 + 195 / 2 = 5 number of items ( n ) = b - a + 1 = 195 - ( - 185 ) + 1 = 195 + 186 = 381 . sum = average * n = 5 * 381 = 1905 . answer is d"
Answer: d
Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 5 yellow , and 4 orange marbles , and 2 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 6 / 22
Rationale: "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 6 possible orderings the probabbility is the same . so , it should be ( 1 / 22 ) * ( 6 ) , which indeed is 6 / 22 . e"
Answer: e
Problem: 10 years ago , the average age of a family of 4 members was 24 years . two children having been born ( with age diference of 2 years ) , the present average age of the family is the same . the present age of the youngest child is ?
Options: a ) 1 , b ) 7 , c ) 3 , d ) 9 , e ) 2
Rationale: total age of 4 members , 10 years ago = ( 24 x 4 ) years = 96 years . total age of 4 members now = [ 96 + ( 10 x 4 ) ] years = 136 years . total age of 6 members now = ( 24 x 6 ) years = 144 years . sum of the ages of 2 children = ( 144 - 136 ) years = 8 years . let the age of the younger child be years . then , age of the elder child = years . so , age of younger child = 3 years . answer : c
Answer: c
Problem: a certain quantity of 70 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 7 / 9
Rationale: let ' s say that the total original mixture a is 100 ml the original mixture a thus has 70 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 70 ml and 25 ml is 45 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 45 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 35 % . therefore , 35 out of 45 is 7 / 9 and e is the answer .
Answer: e
Problem: f 1 ( x ) f 1 ( x ) = 2 x - 1 and fn ( x ) = f 1 ( fn − 1 ( x ) ) fn ( x ) = f 1 ( fn − 1 ( x ) ) for n ≥ ≥ 2 . find f 5 ( 2 )
Options: a ) 7 , b ) 6 , c ) 78 , d ) 9 , e ) 1
Rationale: answer : a
Answer: a
Problem: of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 22 boys and 38 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
Options: a ) 2 , b ) 4 , 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 22 boys . so 22 - 6 - 6 = 10 boys must be neither happy nor sad . answer ( e )"
Answer: e
Problem: real - estate salesman z is selling a house at a 10 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 10 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 10 percent discount . salesman y ' s final price is what fraction of salesman x ' s final price ?
Options: a ) 38 / 6 , b ) 38 / 5 , c ) 77 / 81 , d ) 38 / 7 , e ) 38 / 10
Rationale: "let the retail price be = x selling price of z = 0.90 x selling price of x = 0.90 * 0.90 x = 0.81 x selling price of y = ( ( 0.90 x + 0.81 x ) / 2 ) * 0.90 = 0.86 x * 0.90 = 0.77 x 0.77 x = k * 0.81 x k = 0.77 / 0.81 = 77 / 81 answer : c"
Answer: c
Problem: find the distance covered by a man walking for 42 min at a speed of 10 km / hr ?
Options: a ) 7 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "distance = 10 * 42 / 60 = 7 km answer is a"
Answer: a
Problem: the output of a factory was increased by 15 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 20 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 27 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: the original output increases by 15 % and then 20 % . total % change = a + b + ab / 100 total % change = 15 + 20 + 15 * 20 / 100 = 38 % now , you want to change it to 0 , so , 0 = 38 + x + 38 x / 100 x = - 38 ( 100 ) / 138 = 27 % approximately answer is b
Answer: b
Problem: in a sample of associates at a law firm , 30 percent are second - year associates , and 60 percent are not first - year associates . what percentage of the associates at the law firm have been there for more than two years ?
Options: a ) 10 , b ) 20 , c ) 30 % , d ) 40 , e ) 50
Rationale: let the sample be 100 . given 60 % are not first year i . e . there could be second year ( x ) and more than 2 years ( y ) possibility . 60 % = ( x ) + y given 30 % = second year ( x ) club both , we get y = 30 % . answer : option c is correct answer .
Answer: c
Problem: in a company of 160 employees , 90 are females . a total of 80 employees have advanced degrees and the rest have a college degree only . if 40 employees are males with college degree only , how many employees are females with advanced degrees ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "the number of males is 160 - 90 = 70 . the number of males with advanced degrees is 70 - 40 = 30 . the number of females with advanced degrees is 80 - 30 = 50 . the answer is c ."
Answer: c
Problem: in business , a and c invested amounts in the ratio 3 : 2 , whereas the ratio between amounts invested by a and b was 3 : 1 , if rs 60000 was their profit , how much amount did c receive .
Options: a ) 10000 , b ) 20000 , c ) 15000 , d ) 61000 , e ) 26000
Rationale: "explanation : a : b = 3 : 1 = 3 : 1 = > a : c = 3 : 2 = 3 : 2 = > a : b : c = 3 : 1 : 2 c share = ( 2 / 6 ) * 60000 = 20000 option b"
Answer: b
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 50 , and what number ?
Options: a ) 40 , b ) 45 , c ) 55 , d ) 45 , e ) 50
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 60 = 45 d"
Answer: d
Problem: an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 49 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 49 , e ) 40
Rationale: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 49 ( x - y ) - - > x + y = 49 . answer : d ."
Answer: d
Problem: how many times will the digit 4 be written when listing the integers from 1 to 1000 ?
Options: a ) 512 , b ) 300 , c ) 294 , d ) 264 , e ) 385
Rationale: "many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 4 ) 3000 / 10 = 300 times . answer : b ."
Answer: b
Problem: jonathan can type a 20 page document in 50 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?
Options: a ) 5 minutes , b ) 11 minutes , c ) 15 minutes , d ) 18 minutes , e ) 20 minutes
Rationale: you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 20 / 50 + 20 / 30 + 20 / 24 = 20 / x if you solve this equation , you get the same answer b ( 11 )
Answer: b
Problem: in a certain village , 150 litres of water are required per household per month . at this rate , if there are 10 households in the village , how long ( in months ) will 6000 litres of water last ?
Options: a ) 8 , b ) 10 , c ) 6 , d ) 2 , e ) 4
Rationale: "i find it much easier to understand with real numbers , so choose ( almost ) any numbers to replace m , n and p : in a certain village , m 150 litres of water are required per household per month . at this rate , if there aren 10 households in the village , how long ( in months ) willp 2000 litres of water last ? water required is 150 * 10 = 1500 ( m * n ) water available is 6000 ( p ) it will last 4 months ( p / m * n ) ans : e"
Answer: e
Problem: one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 20 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3 , b ) 7 and 10 , c ) 11 and 8 , d ) 3 and 10 , e ) 10 and 10
Rationale: "let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 20 cm 2 more than the first area . therefore a 1 + 20 = a 2 x ( x − 3 ) + 20 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 20 = x 2 + x − 2 x − 2 2 x = 22 x = 11 . so , the sides of the rectangle are 11 cm and ( 11 − 3 ) = 8 cm long . so answer is c ."
Answer: c
Problem: a rope of which a calf is tied is increased from 12 m to 18 m , how much additional grassy ground shall it graze ?
Options: a ) 1217 , b ) 1219 , c ) 1210 , d ) 565.7 , e ) 1312
Rationale: "π ( 182 – 122 ) = 565.7 answer : d"
Answer: d
Problem: find a two digit number , given that the sum of the digits is 12 and the difference of the digits is 2 . ?
Options: a ) 66 , b ) 87 , c ) 75 , d ) 88 , e ) 90
Rationale: "using elimination method find which of the options fit the description of the number . . . from the option only 75 meets this description sum of digits - - - 7 + 5 = 12 difference of digits - - - 7 - 5 = 2 answer c ."
Answer: c
Problem: lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 24 more photos than claire . how many photos has claire taken ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: l = r l = 3 c r = c + 24 3 c = c + 24 c = 12 the answer is d .
Answer: d
Problem: what is 25 % of 4 / 12 of 520 ?
Options: a ) 49 , b ) 56 , c ) 60 , d ) 43 , e ) 70
Rationale: 25 % = 25 / 100 = 1 / 4 of 4 / 12 = 1 / 4 * 4 / 12 = 1 / 12 of 520 = 1 / 12 * 520 = 43.33 = = 43 ans - d
Answer: d
Problem: 42 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 16 , c ) 13 , d ) 14 , e ) 19
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 : 42 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 42 x 5 x 12 x = ( 42 x 5 x 12 ) / ( 30 x 6 ) x = 14 answer d"
Answer: d
Problem: calculate the circumference of a circular field whose radius is 6 centimeters .
Options: a ) 2 π cm , b ) 1 π cm , c ) 15 π cm , d ) 12 π cm , e ) 19 π cm
Rationale: "circumference c is given by c = 2 π r = 2 π * 6 = 12 π cm answer : d"
Answer: d
Problem: for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 30 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 27 % , b ) 26 % , c ) 29 % , d ) 30 % , e ) 60 %
Rationale: "in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 30 % of 200 seeds germinated , so 0.30 x 200 = 60 seeds germinated . since 75 + 60 = 135 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 135 / 500 ) x 100 % , or 27 % . answer : a ."
Answer: a
Problem: if x : y = 1 : 4 , then find the value of ( 7 x + 3 y ) : ( 2 x + y )
Options: a ) 14 : 5 , b ) 15 : 5 , c ) 16 : 5 , d ) 19 : 6 , e ) none of these
Rationale: explanation : let x = 1 k and y = 4 k , so = 7 ( k ) + 3 ( 4 k ) / 2 ( k ) + 1 ( 4 k ) = 19 k / 6 k = 19 : 6 option d
Answer: d
Problem: ages of two persons differ by 24 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 14,30 , c ) 16,32 , d ) 18,42 , e ) 19,34
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 24 ) = > 3 ( x - 6 ) = ( x + 24 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 18 = > x = 18 . so other person age is x + 24 = 42 answer : option d"
Answer: d
Problem: john want to buy a $ 100 trouser at the store , but he think it â € ™ s too expensive . finally , it goes on sale for $ 55 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 45 %
Rationale: "the is always the difference between our starting and ending points . in this case , it â € ™ s 100 â € “ 55 = 45 . the â € œ original â €  is our starting point ; in this case , it â € ™ s 100 . ( 45 / 100 ) * 100 = ( 0.45 ) * 100 = 45 % . e"
Answer: e
Problem: in a garden , 26 trees are planted at equal distances along a yard 800 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 10 , b ) 8 , c ) 32 , d ) 14 , e ) 16
Rationale: "26 trees have 25 gaps between them . length of each gap = 800 / 25 = 32 i . e . , distance between two consecutive trees = 32 answer is c ."
Answer: c
Problem: the average age of a , b and c is 28 years . if the average age of a and c is 29 years , what is the age of b in years ?
Options: a ) 19 , b ) 26 , c ) 20 , d ) 32 , e ) 21
Rationale: "age of b = age of ( a + b + c ) â € “ age of ( a + c ) = 28 ã — 3 â € “ 29 ã — 2 = 84 â € “ 58 = 26 years b"
Answer: b
Problem: evaluate : 986 x 237 + 986 x 863
Options: a ) 986000 , b ) 968000 , c ) 978000 , d ) 987000 , e ) none of them
Rationale: "986 x 137 + 986 x 863 = 986 x ( 137 + 863 ) = 986 x 1000 = 986000 . answer is a ."
Answer: a
Problem: a reduction of 30 % in the price of oil enables a house wife to obtain 3 kgs more for rs . 700 , what is the reduced price for kg ?
Options: a ) 70 , b ) 50 , c ) 60 , d ) 80 , e ) 65
Rationale: "700 * ( 30 / 100 ) = 210 - - - - 3 ? - - - - 1 = > rs . 70 answer : a"
Answer: a
Problem: a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many f ways can the test be completed if every question is unanswered ?
Options: a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024
Rationale: "5 choices for each of the 4 questions , thus total f of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c ."
Answer: c
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 8 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 17 : 7 , b ) 18 : 8 , c ) 19 : 9 , d ) 19 : 5 , e ) 19 : 4
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 8 = 5 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 + 7 / 2 = 17 / 2 = 8.5 litres as 12 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 8.5 : 3.5 = 17 : 7 . answer : a"
Answer: a
Problem: mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 10 candidates . she plans to have one working interview with 3 of the 10 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 120 , c ) 300 , d ) 30 , e ) 333
Rationale: "there are c 310 = 120 different groups of three possible out of 10 candidates and since each of these groups is interviewed every day then total of 120 days are needed . answer : b"
Answer: b
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 34 years . what is deepak present age ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 21 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 34 = > x = 7 so deepak age is = 3 ( 7 ) = 21 answer : d"
Answer: d
Problem: a retailer bought a machine at a wholesale price of $ 99 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 132 , e ) 160
Rationale: "my solution : wholesale price = 99 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 99 + 1 / 5 ( 99 ) x = 132 ; answer : d"
Answer: d
Problem: a store reported total sales of $ 480 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 50 % , d ) 65 % , e ) 83 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 480 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 480 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 480 – 320 ) / 320 ] x 100 = 50 % . the answer is c ."
Answer: c
Problem: a cricket bat is sold for $ 850 , making a profit of $ 215 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 34 % , d ) 36 % , e ) 40 %
Rationale: "215 / ( 850 - 215 ) = 215 / 635 = 43 / 127 = 34 % . answer : c ."
Answer: c
Problem: arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 35 % profit ?
Options: a ) 16.39 , b ) 16.33 , c ) 16.35 , d ) 17.01 , e ) 16.32
Rationale: c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 135 % of rs . 630 = 135 / 100 * 630 = rs . 850.50 . s . p . per kg = 850.50 / 50 = rs . 16.38 = 16.30 . answer : d
Answer: d
Problem: how many times are the hands of a clock at right angle in 2 days ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: "in 1 day , they are at right angles 44 times . in 2 days , they are at right angles 88 times . answer : option e"
Answer: e
Problem: a cyclist rides a bicycle 8 km at an average speed of 10 km / hr and again travels 10 km at an average speed of 8 km / hr . what is the average speed for the entire trip ?
Options: a ) 9.28 , b ) 8.48 , c ) 8.78 , d ) 8.98 , e ) 9.18
Rationale: "distance = 18 km time = 8 / 10 + 10 / 8 = ( 64 + 100 ) / 80 = 164 / 80 = 41 / 20 hours average speed = ( 18 * 20 ) / 41 = 8.78 km / h the answer is c ."
Answer: c
Problem: find the value of 72516 x 9999 = m ?
Options: a ) 456578972 , b ) 436567874 , c ) 725087484 , d ) 725117481 , e ) 357889964
Rationale: "72516 x 9999 = 72516 x ( 10000 - 1 ) = 72516 x 10000 - 72516 x 1 = 725160000 - 72516 = 725087484 c"
Answer: c
Problem: what is the tens digit of 7 ^ 1001 ?
Options: a ) 0 , b ) 0 , c ) 2 , d ) 3 , e ) 4
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 1001 = 4 * 250 + 1 the ten ' s digit will be 1 . answer b"
Answer: b
Problem: suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3872 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) s . 345 , b ) s . 350 , c ) s . 352 , d ) s . 362 , e ) s . 368
Rationale: "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3872 × 1 / 11 = rs . 352 . c"
Answer: c
Problem: john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 5,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
Options: a ) 10000 , b ) 10100.5 , c ) 20000 , d ) 15000 , e ) 19000
Rationale: "a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 5,000 ( 1 + 0.04 / 4 ) ^ 4 - 5,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 5,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 5,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 5,000 ( 1.0201 + 1 ) = 10 , 100.5 hence answer is b ."
Answer: b
Problem: what number is obtained by adding the units digits of 734 ^ 98 and 347 ^ 82 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "the units digit of 734 ^ 98 is 6 because 4 raised to the power of an even integer ends in 6 . the units digit of 347 ^ 82 is 9 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 82 is in the form 4 n + 2 , the units digit is 9 . then 6 + 9 = 15 . the answer is e ."
Answer: e
Problem: in a certain alphabet , 20 letters contain a dot and a straight line . 36 letters contain a straight line but do not contain a dot . if that alphabet has 60 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 4 , b ) 3 , c ) 14 , d ) 20 , e ) 28
Rationale: "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 20 + 36 = 56 ; next , we find the total # of letters without line : 60 - 56 = 4 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 4 - 0 = 4 ."
Answer: a
Problem: an auction house charges a commission of 25 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 165,000 , c ) $ 215,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: "say the price of the house was $ x , then 0.25 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 165,000 ( 25 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : b ."
Answer: b
Problem: a meal cost $ 35.50 adn there was no tax . if the tip was more than 15 pc but less than 25 pc of the price , then the total amount paid should be :
Options: a ) 41 - 44 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: "15 % ( 35.5 ) = 5.325 25 % ( 35.5 ) = 8.875 total amount could have been 35.5 + 5.325 and 35.5 + 8.875 = > could have been between 40.825 and 44.375 = > approximately between 41 and 44 answer is a ."
Answer: a
Problem: the sum of the even numbers between 1 and n is 95 * 96 , where n is an odd number , then n = ?
Options: a ) 167 , b ) 175 , c ) 183 , d ) 191 , e ) 199
Rationale: "let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 95 * 96 then a = 95 and n = 191 . the answer is d ."
Answer: d
Problem: the present ratio of students to teachers at a certain school is 50 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
Options: a ) 3 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: we are given that the ratio of students to teacher is 50 to 1 . we can rewrite this using variable multipliers . students : teachers = 50 x : x we are next given that student enrollment increases by 50 and the number of teachers increases by 5 . with this change the new ratio becomes 25 to 1 . we can put all this into an equation : students / teachers  25 / 1 = ( 30 x + 50 ) / ( x + 5 ) if we cross multiply we have : 25 ( x + 5 ) = 50 x + 50 25 x + 125 = 50 x + 50 3 = x since x is the present number of teachers , currently there are 3 teachers . answer a .
Answer: a