regisss/math_qa huggingface dataset:
Problem: a grocer has a sale of rs . 6345 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) rs . 3000 , b ) rs . 4991 , c ) rs . 5991 , d ) rs . 6001 , e ) none
Rationale: "sol . total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . ∴ required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 34009 ) = rs . 4991 . answer b"
Answer: b
Problem: at deluxe paint store , fuchsia paint is made by mixing 4 parts of red paint with 2 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 6 parts blue paint . how many liters of blue paint must be added to 24 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 24
Rationale: "in 24 liters , red = 4 / 6 * 24 = 16 and blue = 8 so , 16 / ( 8 + x ) = 3 / 6 or , x = 24 ( answer e )"
Answer: e
Problem: h . c . f of 136 , 144 and a third number is 8 and their l . c . m is 2 ^ 4 * 3 ^ 2 * 17 * 7 . the third number is :
Options: a ) 154 , b ) 248 , c ) 360 , d ) 424 , e ) 168
Rationale: 136 = 2 ^ 3 * 17 ; 144 = 2 ^ 4 * 3 ^ 2 h . c . f = 2 ^ 3 = 8 since h . c . f is the product of lowest powers of common factors , so the third number must have ( 2 ^ 3 ) as its factor . since l . c . m is the product of highest powers of common prime factors , so the third number must have 3 and 7 as its factors . third number = 2 ^ 3 * 3 * 7 = 168 answer : e
Answer: e
Problem: from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 25 percent . what percent of the stock â € ™ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 90 , c ) 95 , d ) 100 , e ) 112.5
Rationale: "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 25 % = 90 * 1.25 = 112.5 thus ratio = 112.5 / 100 = 1.125 ( in % terms = 12.5 % ) . thus e is the correct answer ."
Answer: e
Problem: express a speed of 70 kmph in meters per second ?
Options: a ) 10 mps , b ) 19.44 mps , c ) 97.44 mps , d ) 17.44 mps , e ) 18.44 mps
Rationale: "70 * 5 / 18 = 19.44 mps answer : b"
Answer: b
Problem: if n = ( 33 ) ^ 43 + ( 43 ) ^ 32 what is the units digit of n ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: first of all , the units digit of ( 33 ) ^ 43 is the same as that of 3 ^ 43 and the units digit of ( 43 ) ^ 32 is the same as that of 3 ^ 32 . so , we need to find the units digit of 3 ^ 43 + 3 ^ 33 . next , the units digit of 3 in positive integer power repeats in blocks of four { 3 , 9 , 7 , 1 } : 3 ^ 1 = 3 ( the units digit is 3 ) 3 ^ 2 = 9 ( the units digit is 9 ) 3 ^ 3 = 27 ( the units digit is 7 ) 3 ^ 4 = 81 ( the units digit is 1 ) 3 ^ 5 = 243 ( the units digit is 3 again ! ) . . . thus : the units digit of 3 ^ 43 is the same as the units digit of 3 ^ 3 , so 7 ( 43 divided by the cyclicity of 4 gives the remainder of 3 ) . the units digit of 3 ^ 33 is the same as the units digit of 3 ^ 1 , so 3 ( 33 divided by the cyclicity of 4 gives the remainder of 1 ) . therefore the units digit of ( 33 ) ^ 43 + ( 43 ) ^ 32 is 7 + 5 = 2 . answer : b .
Answer: b
Problem: on a certain transatlantic crossing , 20 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 20 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "let t be the total number of passengers . let x be the number of people with round trip tickets . 0.2 t had round trip tickets and took their cars . 0.8 x had round trip tickets and took their cars . 0.8 x = 0.2 t x = 0.25 t the answer is b ."
Answer: b
Problem: a train running at the speed of 126 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 150 meter , b ) 286 meter , c ) 186 meter , d ) 315 meter , e ) 265 meter
Rationale: "speed = 126 * ( 5 / 18 ) m / sec = 35 m / sec length of train ( distance ) = speed * time ( 35 ) * 9 = 315 meter answer : d"
Answer: d
Problem: what is the smallest number which when diminished by 20 , is divisible 15 , 30 , 45 and 60 ?
Options: a ) 200 , b ) 220 , c ) 240 , d ) 322 , e ) 342
Rationale: "required number = ( lcm of 15 , 30 , 45 and 60 ) + 20 = 180 + 20 = 200 option a"
Answer: a
Problem: mrs . evans gave a test to her freshmen economics class , which has 25 students enrolled and 22 of them answered question 1 correctly . if 20 answered question 2 correctly and 3 did not take the test then how many answered both questions correctly ?
Options: a ) 30 , b ) 20 , c ) 23 , d ) 17 , e ) 19
Rationale: "total number of enrolled students = 25 number of students who did not take test = 3 hence , number of students who took test = 25 - 3 = 22 number of students who answered q 2 correctly = 20 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 20 . number of students who answered both q 1 & q 2 correctly = 20 . answer : b"
Answer: b
Problem: in two alloys , copper and tin are related in the ratios of 4 : 1 and 1 : 3 . 10 kg of ist alloy , 16 kg of 2 nd alloy and some pure copper melted together . an alloy obtained in which the ratio of copper and tin was 3 : 2 . find the weight of the new alloy .
Options: a ) 34 kg , b ) 35 kg , c ) 36 kg , d ) 30 kg , e ) 32 kg
Rationale: suppose x kg of pure copper is melted with 10 kg of ist alloy and 16 kg of 2 nd alloy , then pure cooper in new alloy = 10 * 4 / 5 + 16 * 1 / 4 + x = 12 + x kg pure tin in new alloy = 10 * 1 / 5 + 16 * 3 / 4 = 14 kg as per given condition ( 12 + x ) / 14 = 3 / 2 24 + 2 x = 42 x = 9 kg total weight of new alloy = 10 + 16 + 9 = 35 kg answer : b
Answer: b
Problem: a farmer planned to plough a field by doing 120 hectares a day . after two days of work he increased his daily productivity by 25 % and he finished the job two days ahead of schedule . a ) what is the area of the field ? b ) in how many days did the farmer get the job done ? c ) in how many days did the farmer plan to get the job done ?
Options: a ) 2337 , b ) 2667 , c ) 1440 , d ) 2887 , e ) 2661
Rationale: first of all we will find the new daily productivity of the farmer in hectares per day : 25 % of 120 hectares is 25100 ⋅ 120 = 3025100 ⋅ 120 = 30 hectares , therefore 120 + 30 = 150120 + 30 = 150 hectares is the new daily productivity . lets x be the planned number of days allotted for the job . then the farm is 120 ⋅ x 120 ⋅ x hectares . on the other hand , we get the same area if we add 120 ⋅ 2120 ⋅ 2 hectares to 150 ( x − 4 ) 150 ( x − 4 ) hectares . then we get the equation 120 x = 120 ⋅ 2 + 150 ( x − 4 ) 120 x = 120 ⋅ 2 + 150 ( x − 4 ) x = 12 x = 12 so , the job was initially supposed to take 12 days , but actually the field was ploughed in 12 - 2 = 10 days . the field ' s area is 120 ⋅ 12 = 1440120 ⋅ 12 = 1440 hectares . answer : c
Answer: c
Problem: 12 men complete a work in 9 days . after they have worked for 6 days , 6 more men join them . how many days will they take to complete the remaining work ?
Options: a ) 2 days , b ) 7 days , c ) 8 days , d ) 9 days , e ) 45 days
Rationale: 1 man ' s 1 day work = 1 / 108 12 men ' s 6 day ' s work = 1 / 9 * 6 = 2 / 3 remaining work = 1 - 2 / 3 = 1 / 3 18 men ' s 1 day work = 1 / 108 * 18 = 1 / 6 1 / 6 work is done by them in 1 day . 1 / 3 work is done by them in 6 * 1 / 3 = 2 days . answer : a
Answer: a
Problem: joe has a total of $ 200 in his two pockets . he takes one fourth of the money in his left pocket and puts it in his right pocket . he then takes $ 20 from his left pocket and puts it in his right pocket . if he now has an equal amount of money in each pocket , then how much money did he originally have in his left pocket ?
Options: a ) $ 120 , b ) $ 130 , c ) $ 140 , d ) $ 150 , e ) $ 160
Rationale: joe had $ 100 in his left and $ 100 in his right pocket at the end . so , he had $ 120 in his left pocket ( and $ 80 in his right pocket ) before moving $ 20 from his left to his right pocket . thus , he had $ 160 in his left pocket originally ( solve x − x / 4 = 120 ) . correct answer e
Answer: e
Problem: if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 200 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 25 hours , d ) 12 hours , e ) 8 hours
Rationale: here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 200 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 200 units is ' 10 times ' 20 , we need ' 10 times ' more time . ( 2.5 hours ) ( 10 times ) = 25 hours final answer : [ reveal ] spoiler : c
Answer: c
Problem: the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 60 per cent . the two reductions together are equal to a single reduction of
Options: a ) 45 % , b ) 70 % , c ) 35 % , d ) 32.5 % , e ) 30 %
Rationale: "price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 60 percent is reduced which means the new price is merely 40 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 2 / 5 ) p = 6 / 20 p is the new price after both deduction which is 30 percent of the original value p . this implies this entire series of deduction is worth having discounted 70 % of p . so answer is b = 70 %"
Answer: b
Problem: given a number , there is an algorithm described here to find it ' s sum and number of factors . for example , let us take the number 1225 ?
Options: a ) 1767 , b ) 1800 , c ) 1812 , d ) 1890 , e ) none
Rationale: solving for 1225 = 52 × 72 sum of divisors = ( ap + 1 – 1 ) / ( a – 1 ) × ( bq + 1 – 1 ) / ( b – 1 ) here a = 5 , b = 7 prime factors p = 2 and q = 2 sum of divisors = ( 53 – 1 ) / ( 5 – 1 ) × ( 73 – 1 ) / ( 7 – 1 ) = ( 124 / 4 ) × ( 342 / 6 ) = ( 31 × 57 ) = 1767 option a
Answer: a
Problem: total 60 cows 20 cow gives each 2 liter milk 20 cow gives each 3 / 4 liter milk 20 cow gives each 1 / 4 liter milk this is split into 3 son per each 20 cows & 20 liter milk how ?
Options: a ) 20 , b ) 10 , c ) 15 , d ) 16 , e ) 18
Rationale: 20 cow 2 liter each = 40 liter 20 cow 3 / 4 liter each = 3 / 4 = 0.75 * 20 = 15 20 cow 1 / 4 liter each = 1 / 4 = 0.25 * 20 = 5 add 40 + 15 + 5 = 60 milk split into 3 son each 20 liter then 60 / 3 = 20 answer : a
Answer: a
Problem: x starts a business with rs . 45000 . y joins in the business after 5 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 1 : 3 , d ) 3 : 1 , e ) 18 : 7
Rationale: explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 ã — 12 : 30000 ã — 7 = 45 ã — 12 : 30 ã — 7 = 3 ã — 12 : 2 ã — 7 = 18 : 7 answer : option e
Answer: e
Problem: ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 2000 then loss of pyarelal ?
Options: a ) 1600 , b ) 1700 , c ) 1800 , d ) 1900 , e ) 1000
Rationale: "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 2000 , loss of pyarelal = 2000 * 9 x / 10 x = 1800 answer : c"
Answer: c
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 1200 more than d , what is b ' s share ?
Options: a ) rs . 500 , b ) rs . 1500 , c ) rs . 2000 , d ) rs . 2400 , e ) none of the above
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 1200 x = 1200 . b ' s share = rs . 2 x = rs . ( 2 x 1200 ) = rs . 2400 . answer = d"
Answer: d
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 $ 60 , 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 ) 105 / 2 , b ) 45 , c ) 44 , d ) 52 , e ) 50
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 = 60 or 1 / 7 t + 1 t = 60 therefore t = 60 * 7 / 8 = 105 / 2 a"
Answer: a
Problem: you hold some gold in a vault as an investment . over the past year the price of gold increases by 60 % . in order to keep your gold in the vault , you must pay 10 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 45 % , b ) 46 % , c ) 50 % , d ) 55 % , e ) 44 %
Rationale: "( 100 % + 60 % ) * ( 100 % - 10 % ) = 160 * 0.90 = 144 % an increase of 44 % your gold holdings have increased in value by 44 % . the answer is e"
Answer: e
Problem: there is a square of side 6 cm . a circle is inscribed inside the square . find the ratio of the area of circle to square .
Options: a ) 11 / 14
b ) 1 / 14
c ) 13 / 14
d ) 12 / 14
e ) 5 / 14
Rationale: let the side of square = a unit so area of square = a ^ 2 diameter of inscribed circle = side of square = a radius of circle = a / 2 area of circle = ( 22 / 7 ) ( a / 2 ) ^ 2 ratio of area of circle to square = { ( 22 / 7 ) ( a / 2 ) ^ 2 } / a ^ 2 = 11 / 14 answer : a
Answer: a
Problem: if p and q are prime numbers , how many divisors does the product p ^ 4 * q ^ 9 have ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 50 , e ) 60
Rationale: "when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is d . 5 * 10 = 50"
Answer: d
Problem: 30 is subtracted from 40 % of a number , the result is 50 . find the number ?
Options: a ) 200 , b ) 997 , c ) 266 , d ) 288 , e ) 271
Rationale: "( 40 / 100 ) * x – 30 = 50 4 x = 800 x = 200 answer : a"
Answer: a
Problem: calculate how many days it will take for 5 boys to paint a 65 m long wall if 2 boys can paint a 40 m long wall in 4 days ,
Options: a ) 2.6 days , b ) 3.6 days , c ) 5.6 days , d ) 6 days , e ) 2 days
Rationale: "the length of wall painted by one boy in one day = 40 / 2 * 1 / 4 = 5 m no . of days required to paint 50 m cloth by 8 boys = 65 / 5 * 1 / 5 = 2.6 days . a"
Answer: a
Problem: if a - b = 3 and a 2 + b 2 = 29 , find the value of ab ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 17 , e ) 18
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 29 - 9 = 20 ab = 10 a )"
Answer: a
Problem: mary invested a certain sum of money in a bank that paid simple interest . the amount grew to $ 260 at the end of 2 years . she waited for another 4 years and got a final amount of $ 380 . what was the principal amount that she invested at the beginning ?
Options: a ) $ 200 , b ) $ 220 , c ) $ 230 , d ) $ 240 , e ) $ 250
Rationale: "what shall be the rate of interest . ? does that is not required for the calculation ? not really ! keep in mind that the interest earned each year will be the same in simple interest . at the end of 2 years , amount = $ 260 at the end of 6 years , amount = $ 380 this means she earned an interest of $ 120 in 4 years . or $ 30 in each year . we know that the interest earned each year will be the same . therefore she must have earned $ 60 in 2 years . hence principal amount = $ 260 - $ 60 = $ 200 option a"
Answer: a
Problem: pipe a can fill a tank in 32 minutes . pipe b can fill the same tank 5 times faster than pipe a . if both the pipes are connected to the tank so that they fill the tank simultaneously , how long will it take for the empty tank to overflow ?
Options: a ) 4 minutes , b ) 2 / 7 minutes , c ) 32 / 7 minutes , d ) 224 / 7 minutes , e ) 28 minutes
Rationale: "pipe a can fill a tank in 32 minutes - - > the rate of a = 1 / 32 tank / minute ; pipe b can fill the same tank 5 times fasterthan pipe a - - > the rate of b = 1 / 32 + 5 / 32 = 6 / 32 tank / minute . their combined rate = 1 / 32 + 6 / 32 = 7 / 32 tank / minute ; therefore , a and b can fill the tank in 32 / 7 minutes . answer : c"
Answer: c
Problem: one side of a rectangular field is 4 m and its length along diagonal is 5 m . what is the area of the field ?
Options: a ) 12 , b ) 27 , c ) 98 , d ) 27 , e ) 29
Rationale: "lb = 3 * 4 = 12 answer : a"
Answer: a
Problem: a taxi company charges $ 1.85 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 3 miles , e ) 6 1 / 4 miles
Rationale: "if we start out with $ 4.90 and have to spend $ 1.85 for the first quarter - mile , we will have $ 3.05 left to spend on quarter - mile intervals . since $ 3.05 / $ 0.15 = 20.33 , we can buy 20.33 more quarter - miles , and will travel 21.33 quarter miles in all : 21.33 × 1 / 4 = 5 1 / 3 miles . the correct answer is choice ( d ) ."
Answer: d
Problem: the speed of a train is 64 kmph . what is the distance covered by it in 9 minutes ?
Options: a ) 10 kmph , b ) 11 kmph , c ) 88 kmph , d ) 18 kmph , e ) 12 kmph
Rationale: "64 * 9 / 60 = 9.6 kmph answer : a"
Answer: a
Problem: if it is a 3 x 3 matrix , for which elements in first row are ( v , 50 , w ) , second row ( 196 , x , y ) and in third row are ( 269 , z , 123 ) . it is given that the sum of the numbers in each row , column , diagonal are same . then find the value of ( y + z ) .
Options: a ) 1012 , b ) 1011 , c ) 1212 , d ) 1122 , e ) 1021
Rationale: v 50 w 196 x y 269 z 123 in 1 st row and 1 st column v + 196 + 269 = v + 50 + w w = 415 again , in 2 nd column and 3 rd row 50 + x + z = 269 + z + 123 x = 342 as sum of each row column and diagonal are same . so , 269 + 342 + 415 = 1026 415 + y + 123 = 1026 y = 488 269 + z + 123 = 1026 z = 634 y + z = 488 + 634 = 1122 answer : d
Answer: d
Problem: in an examination 35 % of the students passed and 455 failed . how many students appeared for the examination ?
Options: a ) 540 , b ) 400 , c ) 700 , d ) 650 , e ) 840
Rationale: "let the number of students appeared be x then , 65 % of x = 455 65 x / 100 = 455 x = 455 * 100 / 65 = 700 answer is c"
Answer: c
Problem: a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 140 , how many coins of each type are there ?
Options: a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 80 coins , e ) none of these
Rationale: let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 140 ⇒ 1.75 x = 140 ⇒ x = 80 coins answer d
Answer: d
Problem: a 80 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?
Options: a ) 20 , b ) 12 , c ) 13 , d ) 14 , e ) 16
Rationale: "amount of salt = 8.0 assume x gallons of water are added . 8.0 / 80 + x = 8 / 100 800 = 8 x + 640 8 x = 160 x = 20 correct option : a"
Answer: a
Problem: what least value should be replaced by * in 223431 * so the number become divisible by 5
Options: a ) 0 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : trick : number is divisible by 5 , if last digit is 0 or 5 so that least number is 0 . answer : option a
Answer: a
Problem: the average height of 35 boys in a class was calculated as 184 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?
Options: a ) 187.89 cm , b ) 182.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm
Rationale: "calculated average height of 35 boys = 184 cm . wrong total height of 35 boys = 184 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm + 106 cm ) / 35 = 184 cm - 60 / 35 cm = 184 cm - 1.71 cm = 182.29 cm . answer : b"
Answer: b
Problem: a certain country had a total annual expenditure of $ 2.4 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1,000 , c ) $ 2,000 , d ) $ 3,000 , e ) $ 5,000
Rationale: "total expenditure / population = per capita expenditure hence , ( 2,4 x 10 ^ 11 ) / 240 000 000 = ( 2,4 x 10 ^ 11 ) / ( 2,4 x 10 ^ 8 ) = 1 x 10 ^ ( 11 - 8 ) = 1 x 10 ^ 3 = 1000 . answer is b ."
Answer: b
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 336 votes . find the number of votes casted to the winning candidate ?
Options: a ) 288 , b ) 744 , c ) 788 , d ) 868 , e ) 177
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 336 62 % - - - - - - - - ? = > 868 answer : d"
Answer: d
Problem: a train running at the speed of 60 km / hr crosses a pole in 3 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 180 metres , c ) 324 metres , d ) 50 metres , e ) 180 metres
Rationale: "speed = ( 60 x 5 / 18 ) / m / sec = 50 / 3 m / sec . length of the train = ( speed x time ) . length of the train = 50 x 3 / 3 m = 50 m . answer : option d"
Answer: d
Problem: two positive integers differ by 4 , and sum of their reciprocals is 5 then one of the numbers is
Options: a ) a ) 3 , b ) b ) 1 , c ) c ) 5 , d ) d ) 21 , e ) 4
Rationale: "algebraic approach : let n be the smaller integer = > 1 / n + 1 / ( n + 4 ) = 5 or ( ( n + 4 ) + n ) / n ( n + 4 ) = 6 or ( n ^ 2 + 4 n ) * 5 = 2 n + 4 or n = 2 as n can not be - negative solve for n = > n = 4 . hence , e"
Answer: e
Problem: jennifer had $ 90 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?
Options: a ) $ 12 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 0
Rationale: "1 / 5 x $ 90 = $ 15 for sandwich 1 / 6 x $ 90 = $ 45 for museum 1 / 2 x $ 90 = $ 78 for book $ 15 + $ 45 + $ 18 = $ 78 spent $ 90 - $ 78 = $ 12 left over correct answer a"
Answer: a
Problem: the surface of a cube is 24 sq cm . find its volume ?
Options: a ) 8 , b ) 6 , c ) 4 , d ) 3 , e ) 1
Rationale: "6 a 2 = 24 a = 2 = > a 3 = 8 cc answer : a"
Answer: a
Problem: in one hour , a boat goes 11 km along the stream and 5 km against it . find the speed of the boat in still water
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "explanation : we know we can calculate it by 1 / 2 ( a + b ) = > 1 / 2 ( 11 + 5 ) = 1 / 2 ( 16 ) = 8 km / hr answer is c"
Answer: c
Problem: how long does a train 145 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?
Options: a ) 52.66 , b ) 53.66 , c ) 54.66 , d ) 58.66 , e ) 59.66
Rationale: "t = ( 660 + 145 ) / 54 * 18 / 5 t = 53.66 answer : b"
Answer: b
Problem: in a group of ducks and cows , the total number of legs are 36 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 10 , b ) 12 , c ) 13 , d ) 15 , e ) 18
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 36 = > 2 x = 36 = > x = 18 e"
Answer: e
Problem: in town x , 60 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 20 % , c ) 31 % , d ) 40 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 60 % , out of which 48 are employed males , hence 12 % are employed females . ( employed females ) / ( total employed people ) = 12 / 60 = 1 / 5 = 20 % answer : b ."
Answer: b
Problem: what is the remainder when 1273 * 1275 * 1277 * 1285 is divided by 12 ?
Options: a ) 9 , b ) 1 , c ) 11 , d ) 0 , e ) 7
Rationale: "1271 * 1275 * 1277 * 1285 = ( 1272 + 1 ) ( 1272 + 3 ) ( 1284 - 7 ) ( 1284 + 1 ) = ( multiple of 12 - 1 ) ( multiple of 12 + 3 ) ( multiple of 12 - 7 ) ( multiple of 12 + 1 ) now , if we expand this expression all terms but the last one will have a multiple of 12 in them , thus will leave no remainder upon division by 12 , the last term will be ( 1 ) ( 3 ) ( - 7 ) ( 1 ) = 21 . thus the question becomes : what is the remainder upon division of 21 by 12 ? the answer to this question is 9 . answer : a"
Answer: a
Problem: find large number from below question the difference of two numbers is 1335 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1254 , b ) 1376 , c ) 1456 , d ) 1599 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1335 ) . x + 1335 = 6 x + 15 5 x = 1320 x = 264 large number = 264 + 1335 = 1599 d"
Answer: d
Problem: in a sample of college students , 20 percent are third year students and 80 percent are not second - year students . what fraction of those students who are not third - year students are second - year students ?
Options: a ) 1 / 4 , b ) 2 / 3 , c ) 4 / 7 , d ) 1 / 2 , e ) 3 / 7
Rationale: "= 20 / 80 . = 1 / 4 my answer is a too"
Answer: a
Problem: what is the product of all the possible values of x if x ^ 2 - 9 x + 20 ?
Options: a ) – 29 , b ) – 12 , c ) 12 , d ) 20 , e ) 168
Rationale: "explanation : = > y = x ^ 2 - 9 x + 20 = > y = ( x - 4 ) ( x - 5 ) = > x = 4 , y = 5 product y = ( 4 ) ( 5 ) = 20 answer option 20 answer : d"
Answer: d
Problem: in a group of ducks and cows , the total number of legs are 28 more than twice the number of heads . find the total number of cows .
Options: a ) 14 , b ) 12 , c ) 16 , d ) 8 , e ) 6
Rationale: "explanation : let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 28 more than twice the number of heads = > 2 ( d + 2 c ) = 28 + 2 ( c + d ) = > d + 2 c = 14 + c + d = > 2 c = 14 + c = > c = 14 i . e . , total number of cows = 14 answer : a"
Answer: a
Problem: a dog takes 3 leaps for every 8 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 9 : 8 , b ) 9 : 9 , c ) 9 : 6 , d ) 9 : 1 , e ) 9 : 2
Rationale: "explanation : dog : hare = ( 3 * 3 ) leaps of hare : 8 leaps of hare = 9 : 5 . answer : a ) 9 : 8"
Answer: a
Problem: a certain no . when divided by 50 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 9
Rationale: "explanation : 50 + 25 = 75 / 15 = 5 ( remainder ) c"
Answer: c
Problem: a retailer bought a coat at wholesale and marked it up 90 % to its initial price of $ 76 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: let x be the wholesale price . then 1.9 x = 76 and x = 76 / 1.9 = 40 . to achieve a 100 % markup , the price needs to be $ 80 . the retailer needs to increase the price by $ 4 more . the answer is b .
Answer: b
Problem: if bat = 58 hat = 52 cat = 57 then whats rat = ?
Options: a ) 42 , b ) 45 , c ) 34 , d ) 76 , e ) 25
Rationale: a 42
Answer: a
Problem: ( 700 + 200 ) ã — 4 ã — ( 4 + 2 ) = ?
Options: a ) 24500 , b ) 21600 , c ) 36600 , d ) 22400 , e ) 12500
Rationale: "( 700 + 200 ) ã — 4 ã — ( 4 + 2 ) = ? or , ? = 900 ã — 4 ã — 6 = 21600 answer b"
Answer: b
Problem: there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 16 other amateurs , what is the total number of chess games possible to be played in the tournament ?
Options: a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 120
Rationale: "each person is one participant of 4 games . so there are in all 16 * 5 = 80 instances of one participant games . but each game has 2 participants so total number of games = 80 / 2 = 40 c"
Answer: c
Problem: find the highest common factor of 36 and 84 .
Options: a ) 12 , b ) 10 , c ) 16 , d ) 19 , e ) 18
Rationale: "36 = 2 ^ 2 x 3 ^ 2 84 = 2 ^ 2 x 3 x 7 h . c . f . = 2 ^ 2 x 3 = 12 . answer : option a"
Answer: a
Problem: a basket contains 7 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ?
Options: a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 9 , d ) 3 / 5 , e ) 4 / 11
Rationale: "the total number of ways to choose 2 apples is 7 c 2 = 21 the number of ways that include the spoiled apple is 6 c 1 = 6 p ( the spoiled apple is included ) = 6 / 21 = 2 / 7 the answer is b ."
Answer: b
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1275 , find the loss % ?
Options: a ) 15 % , b ) 16 % , c ) 17 % , d ) 78 % , e ) 28 %
Rationale: "1500 - - - - 225 100 - - - - ? = > 15 % answer : a"
Answer: a
Problem: a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 54 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) none of these
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 54 km time taken = distance / speed = 54 / 27 = 2 hours . answer : option d"
Answer: d
Problem: the sum of the ages of 5 children born at the intervals of 3 year each is 60 year . what is the age of the eldest child ?
Options: a ) 4 year , b ) 18 year , c ) 10 year , d ) none of these , e ) 9 year
Rationale: "solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 60 â ‡ ” 5 x = 30 â ‡ ” x = 6 . â ˆ ´ age of the eldest child = x + 12 = 6 + 12 = 18 years . answer b"
Answer: b
Problem: the average age of 15 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 37 , c ) 99 , d ) 38 , e ) 27
Rationale: "total age increased = ( 15 * 2 ) years = 30 years . sum of ages of two new men = ( 21 + 23 + 30 ) years = 74 years average age of two new men = ( 74 / 2 ) years = 37 years . answer : b"
Answer: b
Problem: how long does a train 110 m long running at the speed of 90 km / hr takes to cross a bridge 132 m length ?
Options: a ) 12.9 sec , b ) 9.68 sec , c ) 17.9 sec , d ) 16.8 sec , e ) 14.9 sec
Rationale: "speed = 90 * 5 / 18 = 25 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 25 = 9.68 sec . answer : b"
Answer: b
Problem: sum of the numbers from 1 to 29 is
Options: a ) 400 , b ) 430 , c ) 435 , d ) 405 , e ) none of these
Rationale: explanation : sum of first n natural numbers = 1 + 2 + 3 + . . . . . n = n ( n + 1 ) / 2 substitute n = 29 . so s 20 = 29 ã — 30 / 2 = 435 correct option : c
Answer: c
Problem: 20 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 75 %
Rationale: initially 80 % and 20 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) ∗ 80 so , the required % is [ ( 3 / 4 ) ∗ 80 / 100 ] ∗ 100 = 60 % answer : d
Answer: d
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 12 more photos than claire . how many photos has claire taken ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "explanation : l = r l = 3 c r = c + 12 we can substitute r for l in the second equation : r = 3 c . if r is equal to both 3 c and c + 12 , we can say 3 c = c + 12 , and solve for c . 3 c = c + 12 2 c = 12 c = 6 answer : ( a )"
Answer: a
Problem: a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 72 . find the number of notes of rs . 50 denomination .
Options: a ) 15 , b ) 21 , c ) 17 , d ) 37 , e ) 57
Rationale: "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 72 - x now , 50 * x + 500 * ( 72 - x ) = 10350 50 x + 36000 - 500 x = 10350 - 450 x = - 25650 x = 57 . no . of 50 rupees note = 57 . answer : option e"
Answer: e
Problem: mike earns $ 17.5 per hour and phil earns $ 10.5 per hour . approximately how much less , as a percentage , does phil earn than mike per hour ?
Options: a ) 25 % , b ) 32.5 % , c ) 37 % , d ) 37.5 % , e ) 40 %
Rationale: "what % less of 17.5 is 10.5 let it be x % less , then = 17.5 ( 1 - x / 100 ) = 10.5 1 - x / 100 = 10.5 / 17.5 x = 200 / 5 x = 40 % ans e"
Answer: e
Problem: it takes avery 3 hours to build a brick wall while tom can do it in 5 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140
Rationale: "avery takes 3 hours tom takes 2 hours efficiency of avery is 1 / 3 units / hr efficiency of tom is 1 / 5 units / hr combined efficiency of tom and avery is 1 / 3 + 1 / 5 = 8 / 15 units / hr since they worked for 1 hour they completed 8 / 15 units of work and 7 / 15 units of work is left which is to be completed by tom ( since avery left ) so time taken by tom to complete the remaining work will be 7 / 15 / 1 / 5 hours = > 7 / 3 * 60 = 140 minutes . . . answer will be ( e )"
Answer: e
Problem: a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 65 meters , what is the height of the building ( in meters ) ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "the height : length ratio will be equal in both cases . 18 / 45 = x / 65 x = 26 the answer is c ."
Answer: c
Problem: the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 85 and rs . 75 respectively . the sum is :
Options: a ) 1360 , b ) 637.5 , c ) 1600 , d ) 1800 , e ) none
Rationale: "sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 85 * 75 / ( 85 - 75 ) = rs . 637.5 . answer b"
Answer: b
Problem: of the 13 employees in a certain department , 1 has an annual salary of 38,000 , 2 have an annual salary of 45,700 each , 2 have an annual salary of 42,500 each , 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each . what is the median annual salary for the 13 employees ?
Options: a ) 38,000 , b ) 40,000 , c ) 42,500 , d ) 45,700 , e ) 48,500
Rationale: median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.7 so , answer is d .
Answer: d
Problem: a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many w 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 w of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c ."
Answer: c
Problem: if 36 men can do a piece of work in 25 hours , in how many hours will 12 men do it ?
Options: a ) 22 , b ) 38 , c ) 60 , d ) 88 , e ) 75
Rationale: "explanation : let the required no of hours be x . then less men , more hours ( indirect proportion ) \ inline \ fn _ jvn \ therefore 12 : 36 : : 25 : x \ inline \ fn _ jvn \ leftrightarrow ( 12 x x ) = ( 36 x 25 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 25 } { 12 } = 75 hence , 12 men can do it in 75 hours . answer : e ) 75"
Answer: e
Problem: in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 10 and the other one , that is cheaper , costs $ 6 . the factory holds a $ 80 worth stock of 12 modules . how many of the modules in the stock are of the cheaper kind ?
Options: a ) 20 , b ) 25 , c ) 10 , d ) 30 , e ) 35
Rationale: "so the number of $ 6 modules must be 10 so that the leftover 2 modules are of $ 10 which will give a total value $ 80 . 10 * 6 + 2 * 10 = 60 + 20 = 80 answer : c"
Answer: c
Problem: what is the value of ( 5 ) ^ - 5 ?
Options: a ) 1 / 3125 , b ) 1 / 3000 , c ) 1 / 658 , d ) 1 / 500 , e ) 1 / 75
Rationale: "5 ^ - 5 = 1 / ( 5 ) ^ 5 = 1 / 3125 answer : a"
Answer: a
Problem: rahim bought 40 books for rs . 600 from one shop and 20 books for rs . 240 from another . what is the average price he paid per book ?
Options: a ) s . 14 , b ) s . 18 , c ) s . 12 , d ) s . 11 , e ) s . 10
Rationale: "average price per book = ( 600 + 240 ) / ( 40 + 20 ) = 840 / 60 = rs . 14 answer : a"
Answer: a
Problem: the salary of a , b , c , d , e is rs . 9000 , rs . 5000 , rs . 11000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8200 , c ) rs . 8500 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 9000 + 5000 + 11000 + 7000 + 9000 / 5 = rs . 8200 correct option : b"
Answer: b
Problem: at a local appliance manufacturing facility , the workers received a 40 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 83 % , b ) 28 % , c ) 20 % , d ) 17 % , e ) 12 %
Rationale: "let ' s say he works usually 40 hours and earns 100 per hour . 10 * 100 = 1000 10 * 140 = 1400 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 140 = 7.14 so he can reduce his work by 2.86 hours . which is > 28 % . answer b"
Answer: b
Problem: a grocer has a sale of rs . 7435 , rs . 7920 , rs . 7855 , rs . 8230 and rs . 7560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7500 ?
Options: a ) 500 , b ) 2000 , c ) 5000 , d ) 6000 , e ) 7000
Rationale: "total sale for 5 months = rs . ( 7435 + 7920 + 7855 + 8230 + 7560 ) = rs . 39000 . required sale = rs . [ ( 7500 x 6 ) - 39000 ] = rs . ( 45000 - 39000 ) = rs . 6000 answer : option d"
Answer: d
Problem: david obtained 96 , 95 , 82 , 97 and 95 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 95 , c ) 93 , d ) 165 , e ) 11
Rationale: "explanation : average = ( 96 + 95 + 82 + 97 + 95 ) / 5 = 465 / 5 = 93 . answer : c"
Answer: c
Problem: if x = 5 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.2 , c ) 0.01 , d ) 4 , e ) 8
Rationale: "quickly we can spot that answer is neither integer nor negative . eliminate a , de 6 + 4 = 10 by inversing and squaring 0.01 answer : c"
Answer: c
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8100 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) 2177 , b ) 2876 , c ) 4500 , d ) 2981 , e ) 6100
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8100 = 32400 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 400 salary of may is rs . 6500 salary of january = rs . 6100 . answer : e"
Answer: e
Problem: a invested some money in 10 % stock at 96 . if b wants to invest in an equally good 12 % stock , he must purchase a stock worth of :
Options: a ) rs . 80 , b ) rs . 115.20 , c ) rs . 120 , d ) rs . 125.40 , e ) none of these
Rationale: explanation : for an income of rs . 10 , investment = rs . 96 . for an income of rs . 12 , investment = ( 96 / 10 x 12 ) = 115.20 answer : b
Answer: b
Problem: if 2 x + y = 7 and x + 2 y = 5 , then 7 xy / 3 = ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 7 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 7 * 3 * 1 ) / 3 = 21 / 3 = 7 c"
Answer: c
Problem: a watch was sold at a loss of 8 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 1000 , b ) 2876 , c ) 1977 , d ) 1167 , e ) 2711
Rationale: "92 % 104 % - - - - - - - - 12 % - - - - 140 100 % - - - - ? = > rs . 1167 answer : d"
Answer: d
Problem: a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 4400 . what is the share of b ?
Options: a ) 1100 , b ) 800 , c ) 1400 , d ) 1200 , e ) none of them
Rationale: let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 4400 x ( 2 / 11 ) ) = rs . 800 . answer is b
Answer: b
Problem: j is 25 % less than p and 20 % less than t . t is e % less than p . what is the value of e ?
Options: a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2
Rationale: "usually we can solve every question of this type by choosing appropriate value of the variable and deriving the value of other related variables . let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( e / 100 ) ] * p i . e . 100 - e = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . e = 6.25 answer : option d"
Answer: d
Problem: walking at 5 / 6 th of its usual speed a cab is 12 mnts late . find its usual time to cover the journey ?
Options: a ) 25 m , b ) 45 m , c ) 32 m , d ) 50 m , e ) 60 m
Rationale: "new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 12 m ut / 5 = 12 m ut = 60 m answer is e"
Answer: e
Problem: 6 points lie on the circumference of a ellipse . what is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points ?
Options: a ) 4 , b ) 6 , c ) 5 , d ) 15 , e ) 20
Rationale: number of triangles can be formed out of 6 points = 6 c 3 = 20 number of quadrilaterals can be formed out of 6 points = 6 c 4 = 15 20 - 15 = 5 . answer = c
Answer: c
Problem: the denominator of a fraction is 1 less than twice the numerator . if the numerator and denominator are both increased by 1 , the fraction becomes 3 / 5 . find the fraction ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 4 / 7 , d ) 5 / 9 , e ) none of these
Rationale: let the numerator and denominator of the fraction be ' n ' and ' d ' respectively . d = 2 n - 1 ( n + 1 ) / ( d + 1 ) = 3 / 5 5 n + 5 = 3 d + 3 5 n + 5 = 3 ( 2 n - 1 ) + 3 = > n = 5 d = 2 n - 1 = > d = 9 hence the fraction is : 5 / 9 answer : d
Answer: d
Problem: set s consists of integers { 13 , 57 } . if two numbers are chosen from set s at random , what is the probability that the product of 2 numbers is more than 15 ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) 2 / 3
Rationale: number of ways you can choose 2 from 4 = 4 c 2 = 6 e = event of getting the 2 numbers product is more than 15 = ( 3,7 ) , ( 5,7 ) = 2 probability = 2 / 6 = 1 / 3 answer is b
Answer: b
Problem: a dealer offers a cash discount of 20 % and still makes a profit of 20 % when he further allows 10 articles to be sold at the cost price of 9 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ?
Options: a ) 50 % , b ) 55 % , c ) 60 % , d ) 66 + ( 2 / 3 ) % , e ) 80 %
Rationale: "given cash discount - 20 % profit - 20 % items sold - 10 price sold at = list price of 9 assume list price = $ 10 total invoice = $ 90 - 20 % cash discount = $ 72 let cost price of 10 items be x so total cost = 10 * x given the shopkeeper had a profit of 20 % 10 * x * 120 / 100 = 72 or x = $ 6 which means his products were listed at $ 10 which is a 66 + ( 2 / 3 ) % markup over $ 6 answer d"
Answer: d
Problem: in a certain warehouse , 40 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?
Options: a ) 8 , b ) 64 , c ) 48 , d ) 102 , e ) 144
Rationale: "if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 40 % of the packages weigh less than 75 pounds so , 40 % oft = number of packages that weigh less than 75 pounds 40 % of 240 = 96 , so 96 packages weigh less than 75 pounds of those 96 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 96 - 48 = 48 = c"
Answer: c
Problem: if 0.5 % of a = 95 paise , then the value of a is ?
Options: a ) rs . 190 , b ) rs . 17 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: "answer ∵ 0.5 / 100 of a = 95 / 100 ∴ a = rs . ( 95 / 0.5 ) = rs . 190 correct option : a"
Answer: a
Problem: a company produces 60000 bottles of water everyday . if a case can hold 5 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 12000 , b ) 4500 , c ) 5000 , d ) 8000 , e ) 9000
Rationale: "number of bottles that can be held in a case = 5 number of cases required to hold 60000 bottles = 60000 / 5 = 12000 cases . so the answer is a = 12000"
Answer: a
Problem: cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost e is what percent of the original cost ?
Options: a ) e = 200 , b ) e = 600 , c ) e = 800 , d ) e = 1600 , e ) 50
Rationale: "original cost e , 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 1 / 12 of the passengers on a ship are from north america , 1 / 4 are europeans , 1 / 9 are from africa , 1 / 6 are from asia and the remaining 42 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 96 , b ) 100 , c ) 104 , d ) 108 , e ) 112
Rationale: "1 / 12 + 1 / 4 + 1 / 9 + 1 / 6 = ( 3 + 9 + 4 + 6 ) / 36 = 11 / 18 let x be the number of passengers on the ship . 42 = ( 7 / 18 ) x x = 108 the answer is d ."
Answer: d
Problem: by selling an article at rs . 500 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) s . 600 , b ) s . 480 , c ) s . 300 , d ) s . 450 , e ) s . 550
Rationale: "sp = 500 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 500 * [ 100 / 125 ] = 400 loss = 25 % = 25 % of 400 = rs . 100 sp = cp - loss = 400 - 100 = rs . 300 answer : c"
Answer: c