regisss/math_qa huggingface dataset:
Problem: | x + 3 | – | 2 - x | = | 8 + x | how many solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "you have | x + 3 | - | 4 - x | = | 8 + x | first , look at the three values independently of their absolute value sign , in other words : | x + 3 | - | 4 - x | = | 8 + x | ( x + 3 ) - ( 4 - x ) = ( 8 + x ) now , you ' re looking at x < - 8 , so x is a number less than - 8 . let ' s pretend x = - 10 here to make things a bit easier to understand . when x = - 10 i . ) ( x + 3 ) ( - 10 + 3 ) ( - 7 ) ii . ) ( 4 - x ) ( 4 - [ - 10 ] ) ( double negative , so it becomes positive ) ( 4 + 10 ) ( 14 ) iii . ) ( 8 + x ) ( 8 + - 10 ) ( - 2 ) in other words , when x < - 8 , ( x + 3 ) and ( 8 + x ) are negative . to solve problems like this , we need to check for the sign change . here is how i do it step by step . i . ) | x + 3 | - | 4 - x | = | 8 + x | ii . ) ignore absolute value signs ( for now ) and find the values of x which make ( x + 3 ) , ( 4 - x ) and ( 8 + x ) = to zero as follows : ( x + 3 ) x = - 3 ( - 3 + 3 ) = 0 ( 4 - x ) x = 4 ( 4 - 4 ) = 0 ( 8 + x ) x = - 8 ( 8 + - 8 ) = 2 c"
Answer: c
Problem: from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 10 percent . the enrollment on january 1 , 1993 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "1.10 x = 45 - - > 11 / 10 * x = 45 - - > x = 45 * 10 / 11 = 450 / 11 = ~ 41 . answer : d ."
Answer: d
Problem: if a 2 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ?
Options: a ) 50 % , b ) 100 % , c ) 150 % , d ) 200 % , e ) 250 %
Rationale: "the area a of the large cube is 2 * 2 * 6 = 24 square cm . the area of the 8 small cubes is 8 * 6 = 48 = 2 a , an increase of 100 % . the answer is b ."
Answer: b
Problem: a group of 4 investment bankers and 5 clients recently frequented the bonbon ribs restaurant . the total bill for the meal , including 20 % gratuity , came to $ 756 . on average , how much did the meal of each individual cost before gratuity ?
Options: a ) $ 160 , b ) $ 70 , c ) $ 90 , d ) $ 80 , e ) $ 55
Rationale: 4 ibs and 5 clients - so total 9 people the bill $ 756 includes 20 % gratuity . . . so the actual cost of dinner was $ 630 now , the cost per person will be $ 630 / 9 which is $ 70 option b
Answer: b
Problem: a salesman ' s income consists of a commission and a base salary of $ 370 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
Options: a ) $ 150 , b ) $ 345 , c ) $ 365 , d ) $ 715 , e ) $ 730
Rationale: "total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2070 = $ 1430 from this , we subtract base salary for 2 weeks i . e $ 370 * 2 = $ 740 therefore , commission = $ 1430 - $ 740 = $ 690 for 2 weeks avg weekly commission = $ 345 answer b"
Answer: b
Problem: a car is running at a speed of 60 kmph . what distance will it cover in 8 sec ?
Options: a ) 100 m , b ) 136 m , c ) 180 m , d ) 200 m , e ) 250 m
Rationale: "speed = 60 kmph = 60 * 5 / 18 = 17 m / s distance covered in 8 sec = 17 * 8 = 136 m answer is b"
Answer: b
Problem: without stoppages , a train travels certain distance with an average speed of 300 km / h , and with stoppages , it covers the same distance with an average speed of 200 km / h . how many minutes per hour the train stops ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "due to stoppages , it covers 100 km less . time taken to cover 100 km = 100 â  „ 300 h = 1 â  „ 3 h = 1 â  „ 3 ã — 60 min = 20 min answer a"
Answer: a
Problem: a fruit drink is made of grapefruit , lemon , and orange juice , where 25 percent of the drink is grapefruit juice and 35 percent is lemon juice . if the drink is made with 20 ounces of orange juice , how many ounces is the drink total ?
Options: a ) 60 , b ) 80 , c ) 50 , d ) 100 , e ) 40
Rationale: let the total number of ounces in the drink be x % of orange = 25 % % of watermelon = 35 % % of grape = 100 % - 60 % = 40 % but this number is given as 20 ounces so 40 % of x = 20 and x = ( 20 ) ( 100 / 40 ) = ( 20 ) ( 5 / 2 ) x = 50 therefore there a total of 50 ounces in the drink . correct answer - c
Answer: c
Problem: ` ` how old are you , alchemerion ? ' ' asked one of the wizards appearances the wizards answer with a riddle , ` ` i am still very young as wizards go . i am only 3 times my son ' s age . my father is 40 year more than twice of my age . together the 3 of us are a 1240 year old ' ' . how old is alchemerion
Options: a ) 300 , b ) 320 , c ) 340 , d ) 360 , e ) 380
Rationale: let alchemerion be a let son be s let father be f a = 3 * s f = 40 + ( 2 * a ) therefore 1240 = ( s + f + a ) 1240 = ( a / 3 ) + ( 40 + ( 2 * a ) ) + a a = 360 answer : d
Answer: d
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 16 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 128 %
Rationale: "0,128 r = x / 100 * 0.1 r answer e"
Answer: e
Problem: if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance travelled by him is
Options: a ) 50 km , b ) 56 km , c ) 70 km , d ) 80 km , e ) 90 km
Rationale: let the actual distance travelled be x km . then x / 10 = ( x + 20 ) / 14 - - > 14 x = 10 x + 200 - - > 4 x = 200 - - > x = 50 km . answer : a .
Answer: a
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 300 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 200 ?
Options: a ) 1,108 , b ) 2,500 , c ) 2,108 , d ) 2,124 , e ) 2,256
Rationale: "we have $ 200 and we have to maximize the number of hot dogs that we can buy with this amount . let ' s try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money , which in this case is 300 for $ 22.95 . for the sake of calculation , let ' s take $ 23 . 23 x 8 gives 184 , i . e . a total of 300 x 8 = 2400 hot dogs . we are left with ~ $ 16 . similarly , let ' s use $ 3 for calculation . we can buy 5 20 - pack hot dogs ( 3 x 5 ) , a total of 20 x 5 = 100 hot dogs . so we have 2500 hot dogs . 2108 looks far - fetched ( since we are not likely to be left with > $ 1.55 ) . hence , ( b ) 2500 ( answer b )"
Answer: b
Problem: find the 25 % of rs . 300 .
Options: a ) s . 50 , b ) s . 70 , c ) s . 100 , d ) s . 80 , e ) s . 75
Rationale: "explanation : 25 % of 300 = > 25 / 100 * 300 = rs . 75 answer : e"
Answer: e
Problem: a reduction of 50 % in the price of apples would enable a man to obtain 50 more for rs . 50 , what is reduced price per dozen ?
Options: a ) 1 , b ) 3 , c ) 6 , d ) 7 , e ) 10
Rationale: "c 50 * ( 50 / 100 ) = 25 - - - 50 ? - - - 12 = > rs . 6"
Answer: c
Problem: a 1000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ?
Options: a ) 6 , b ) 12 , c ) 18 , d ) 24 , e ) 48
Rationale: "in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 500 by that net inflow to get the minutes ) - 6 min . answer a ."
Answer: a
Problem: working simultaneously and independently at an identical constant rate , 4 machines of a certain type can produce a total of x units of product p in 6 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 2 x units of product p in 3 days ?
Options: a ) 24 , b ) 18 , c ) 16 , d ) 12 , e ) 8
Rationale: "4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 2 x units in 3 days therefore , we need to get to 2 x / 3 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 2 x done in 3 days . 2 x / 3 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 2 x / 3 y = 2 x / 3 * 24 / x cancel 3 with 24 , and x with x and get - > 16 . answer choice c"
Answer: c
Problem: a bag of potatoes weighs 36 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 30 lb , c ) 10 lb , d ) 15 lb , e ) 36 lb
Rationale: sol . 36 ÷ 3 = 12 . answer : e
Answer: e
Problem: p , q and r together earn rs . 1800 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ?
Options: a ) s . 50 , b ) s . 70 , c ) s . 90 , d ) s . 100 , e ) s . 120
Rationale: explanation : amount earned by p , q and r in 1 day = 1800 / 9 = 200 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 200 = 50 = > amount earned by r in 1 day = 50 answer : option a
Answer: a
Problem: jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid , approximately how many liters of the 2 percent solution will be required ?
Options: a ) 18 , b ) 20 , c ) 24 , d ) 36 , e ) 42
Rationale: "use weighted average : 2 % and 12 % solutions mix to give 5 % solution . w 1 / w 2 = ( a 2 - avg ) / ( avg - a 1 ) = ( 12 - 5 ) / ( 5 - 2 ) = 7 / 3 you need 7 parts of 2 % solution and 3 parts of 12 % solution to get 10 parts of 5 % solution . if total 5 % solution is actually 60 litres , you need 7 * 6 = 42 litres of 2 % solution and 3 * 6 = 18 litres of 12 % solution . answer ( e )"
Answer: e
Problem: in a kilo meter race , if a gives b a 40 m start , a wins by 19 s . but if a gives b a 30 s start , b wins by 40 m . find the time taken by b to run 5,000 m ?
Options: a ) 150 s , b ) 450 s , c ) 750 s , d ) 825 s , e ) 925 s
Rationale: when b is given a 40 m start then b runs 960 m in t secs and a runs 1000 m in t - 19 secs . when b is given a 30 second start then b runs 1000 m in t secs and a runs 960 m in t - 30 secs . assume that the speed of a ( va ) and b ( vb ) is constant in both situations . then vb = 960 ÷ t = 1000 ÷ t , and va = 1000 ÷ ( t - 19 ) = 960 ÷ ( t - 30 ) so 960 t = 1000 t , and 1000 t - 30000 = 960 t - 18240 . then 40 t = - 40 t + 11760 , t = - t + 294 . substituting for t in 960 t = 1000 t gives : - 960 t + 282240 = 1000 t 1960 t = 282240 t = 144 b ' s speed is 960 / t = 960 / 144 = 6.67 metres per second . assuming the same constant speed to run 5000 metres then the time taken is 5000 / 6.67 = 750 seconds answer : c
Answer: c
Problem: 0.9999 + 0.1111 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.111 , e ) 1.1111
Rationale: "0.9999 + 0.1111 = 0.9999 + 0.111 + 0.0001 = ( 0.9999 + 0.0001 ) + 0.111 = 1 + 0.111 = 1.111 d"
Answer: d
Problem: exactly 18 % of the reporters for a certain wire service cover local politics in country x . if 40 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 44 % , d ) 70 % , e ) 84 %
Rationale: "let ' s assume there are 100 reporters - - > 18 reporters cover local politics . now , as 40 % of the reporters who cover all politics do not cover local politics then the rest 60 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 60 % of them equal to 18 ( # of reporters who cover local politics ) : 0.6 x = 18 - - > x = 30 , hence 30 reporters cover politics and the rest 100 - 30 = 70 reporters do not cover politics at all . answer : d ."
Answer: d
Problem: when 200 is divided by positive integer x , the remainder is 5 . what is the remainder when 395 is divided by x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 5
Rationale: "if 200 / x leaves a reminder 5 then ( 200 - 5 ) i . e . 195 is divisible by x so ( 200 + 195 ) / x leaves a reminder rem ( 200 / x ) + rem ( 195 / x ) = > 5 + 0 = 5 answer : e"
Answer: e
Problem: xy = 1 then what is ( 7 ^ ( x + y ) ^ 2 ) / ( 7 ^ ( x - y ) ^ 2 )
Options: a ) 2401 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 7 ^ 4 = 2401 answer a"
Answer: a
Problem: if a ( a + 2 ) = 80 and b ( b + 2 ) = 80 , where a ≠ b , then a + b =
Options: a ) - 3 , b ) - 4 , c ) - 6 , d ) - 8 , e ) - 2
Rationale: i . e . if a = 8 then b = - 10 or if a = - 10 then b = 8 but in each case a + b = - 10 + 8 = - 2 answer : e
Answer: e
Problem: a man sitting in a train which is traveling at 40 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 50 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 72 kmph
Rationale: "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 40 ) kmph = 72 kmph . answer : e"
Answer: e
Problem: evaluate : 45 - 12 * 3 * 2 = ?
Options: a ) 62 , b ) 52 , c ) 37 , d ) 12 , e ) 22
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 45 - 12 * 3 * 2 = 45 - 8 = 37 correct answer c"
Answer: c
Problem: a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 55 paise per sq m is
Options: a ) rs . 209.20 , b ) rs . 309.20 , c ) rs . 409.20 , d ) rs . 509.20 , e ) none of these
Rationale: explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 55 / 100 ) = rs . 409.20 answer : c
Answer: c
Problem: let p be a prime number greater than 2 and let n = 14 p . how many even numbers divide n ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: answer : a . there is exactly one . the prime factorization of 14 is 14 = 2 * 7 , so n = 2 * 7 * p = 7 * 2 * p = 7 * 2 p , so 2 p is the only even number that divides n .
Answer: a
Problem: compound interest of rs . 5000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) .
Options: a ) rs . 473 , b ) rs . 374 , c ) rs . 495 , d ) rs . 788 , e ) none of the above
Rationale: "10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 5000 [ 1 + ( 5 / 100 ) ] ^ 3 - 5000 = 5000 [ ( 21 / 20 ) ^ 3 - 1 ] = 5000 ( 9261 - 8000 ) / 8000 = 5 * 1261 / 8 = 788 answer : d"
Answer: d
Problem: a train starts full of passengers . at the first station , it drops one - third of the passengers and takes 280 more . at the second station , it drops one - half of the new total and takes 12 more . on arriving at the third station , it is found to have 248 passengers . find the number of passengers in the beginning .
Options: a ) 240 , b ) 248 , c ) 280 , d ) 288 , e ) 290
Rationale: let x be no . of passengers at beginning at , 1 st station is drops 1 / 3 rd so remaining 2 / 3 rd are in train only plus 280 i . e . , 2 x / 3 + 280 at 2 nd stop 1 / 2 of new total and 12 more i . e . , ( 2 x / 3 + 280 ) / 2 + 12 = 248 on solving above equation we get x as 288 answer : d
Answer: d
Problem: the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 52.0 billion from $ 69.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 20.8 , b ) 24.6 , c ) 31.8 , d ) 32.5 , e ) 33.8
Rationale: "$ 69 - $ 52 = 17 $ ( 17 / 69 ) * 100 = 24.6 % answer : b"
Answer: b
Problem: what will be the compound interest on rs . 35000 after 3 years at the rate of 12 % per annum
Options: a ) rs 13123.20 , b ) rs 14103.48 , c ) rs 12172.48 , d ) rs 14172.48 , e ) none of these
Rationale: "explanation : ( 35000 × ( 1 + 12 / 100 ) 3 ) = > 35000 × 28 / 25 × 28 / 25 × 28 / 25 = > 49172.48 so compound interest will be 49172.48 - 35000 = rs 14172.48 option d"
Answer: d
Problem: in what ratio must wheat at rs . 3.20 pe rkg be mixed with wheat at rs . 2.90 per kg so that the mixture be worth rs . 3.08 per kg
Options: a ) 3 : 4 , b ) 3 : 2 , c ) 3 : 5 , d ) 3 : 7 , e ) 2 : 3
Rationale: if 2 ingredients are mixed , then the required ratio is given by , the rule of allegation c . p of a unit quantity of cheaper ( c ) c . p . of a unit quantity of dearer ( d ) mean price ( m ) d - m m - c  required ratio is cheaper quantity : dearer quantity = ( d - m ) : ( m - c ) answer with explanation : given i . c . p of a unit quantity of i kind ( p ) = 3.20 ii . c . p of a unit quantity of ii kind ( p ) = 2.90 iii . mean price ( p ) = 3.08 iv . d – m = 3.08 – 2.90 = 0.18 v . m – c = 3.20 – 3.08 = 0.12  required ratio = 0.18 : 0.12 = 3 : 2 answer : b
Answer: b
Problem: a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 10 days before the completion of the work . in how many days was the work completed ?
Options: a ) 12.5 days , b ) 16 days , c ) 18 days , d ) 11 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 10 days = 10 * ( 1 / 24 + 1 / 30 ) = 3 / 4 remaining work = 1 / 4 the number of days required for this initial work = 2.5 days . the total number of days required = 10 + 2.5 = 12.5 days . answer : a"
Answer: a
Problem: if a 2 + b 2 + c 2 = 213 and ab + bc + ca = 6 , then a + b + c is
Options: a ) 14 , b ) 20 , c ) 15 , d ) 32 , e ) 64
Rationale: "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 213 and ab + bc + ca = 6 , ( a + b + c ) ^ 2 = 213 + 2 ( 6 ) = 225 = 15 ^ 2 therefore : a + b + c = 15 answer : c"
Answer: c
Problem: if a - b = 6 and a 2 + b 2 = 48 , find the value of ab .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 6 , e ) 19
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 48 - 36 = 12 ab = 6 . answer : d"
Answer: d
Problem: a certain article of clothing was discounted during a special sale to 2 / 5 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 33.33 % , c ) 25 % , d ) 16.66 % , e ) 12.5 %
Rationale: "say the original retail price of the item was $ 200 . the price after the first sale = 3 / 5 * $ 200 = $ 120 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 120 - 100 ) / 120 = 1 / 3 = 16.66 % . answer : d ."
Answer: d
Problem: a committee is reviewing a total of 30 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?
Options: a ) 22 / 21 , b ) 20 / 21 , c ) 23 / 21 , d ) 25 / 21 , e ) 28 / 21
Rationale: "say x = y = 10 . in this case we would have : 30 x = 300 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 3 black - and - white films and all 60 color films , thus total of 63 films were selected . color films thus compose 60 / 63 = 20 / 21 of the selected films . answer : b"
Answer: b
Problem: after paying a 10 percent tax on all income over $ 3000 , a person had a net income of $ 12000 . what was the income before taxes ?
Options: a ) $ 13300 , b ) $ 13000 , c ) $ 12900 , d ) $ 10000 , e ) $ 9000
Rationale: let x be the income over 3000 then ( x - x / 10 ) + 3000 = 12000 = > x = 10000 therefore income before taxes = 10000 + 3000 = 13000 option ( b )
Answer: b
Problem: sam invested rs . 8000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 3200.0 , b ) 11520.0 , c ) 8820.0 , d ) 7354.0 , e ) 16537.11
Rationale: "p = rs . 8000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 8000 * ( 1 + 5 / 100 ) 2 ] = ( 8000 * 21 / 20 * 21 / 20 ) = rs . 8820.00 answer : c"
Answer: c
Problem: half a number plus 5 is 11 . what is the number ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "solution let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 11 ( 1 / 2 ) x + 5 - 5 = 11 - 5 ( 1 / 2 ) x = 6 2 × ( 1 / 2 ) x = 6 × 2 x = 12 answer c"
Answer: c
Problem: a can complete a certain job in 19 days . b is 90 % more efficient than a . in how many days can b complete the same job ?
Options: a ) 6 , b ) 6.25 , c ) 7 , d ) 7.5 , e ) 10
Rationale: "let , total work unit = 190 units a can finish in 19 days = 190 unit work i . e . a can finish in 1 days = 10 unit work i . e . b can finish in 1 days = 10 + ( 90 / 100 ) * 10 = 19 unit work days in which b will complete the work alone = 190 / 19 = 10 days answer : option e"
Answer: e
Problem: if 20 men can build a water fountain 56 metres long in 7 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 40 m , b ) 42 m , c ) 47 m , d ) 49 m , e ) 50 m
Rationale: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 7 : 3 : : 56 : x therefore ( 20 x 7 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 140 = 42 hence , the required length is 42 m . answer : b"
Answer: b
Problem: jaime earned enough money by selling seashells at 20 cents each to buy several used paperback books at 55 cents each . if he spent all of the money he earned selling seashells to buy the books , what is the least number of seashells he could have sold ?
Options: a ) 5 , b ) 10 , c ) 22 , d ) 25 , e ) 30
Rationale: "let ' s test answer c : 22 seashells . . . with 22 seashells , jamie would have 22 ( 20 ) = 440 cents . this would allow him to buy 8 books for 440 cents total , so this is the correct answer . c"
Answer: c
Problem: how many positive integers less than 248 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 41 , c ) 42 , d ) 53 , e ) 64
Rationale: "244 / 4 = 61 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 61 - 20 = 41 answer : b"
Answer: b
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 210 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 41 , c ) 68 , d ) 88 , e ) none
Rationale: "explanation we have : l = 20 ft and lb = 210 sq . ft . so , b = 10.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 21 ) ft = 41 ft . answer b"
Answer: b
Problem: in the coordinate plane a slope of the line k is 4 times the x - intercept of the line k . what is the y - intercept of the line k ?
Options: a ) - 4 , b ) 4 , c ) - 1 / 4 , d ) 1 / 4 , e ) 2
Rationale: as 4 y = mx + c , from 4 y = 0 m + m we get y = 1 / 4 . hence , the correct answer choice is d .
Answer: d
Problem: find the smallest four - digit number which is a multiple of 112 .
Options: a ) 896 , b ) 1008 , c ) 1120 , d ) 1024 , e ) none of these
Rationale: "the smallest four digit number is 1000 . if 1000 is divided by 112 , the remainder is 104 . 112 - 104 = 8 , if 8 is added to 1000 , it will become the smallest four digit number and a multiple of 112 . answer : b"
Answer: b
Problem: the difference between the place values of two sevens in the numerical 69758472 is
Options: a ) 0 , b ) 6993 , c ) 699930 , d ) 996330 , e ) none of them
Rationale: "required difference = ( 700000 - 70 ) = 699930 . answer is c"
Answer: c
Problem: a set s = { x , - 8 , - 5 , - 3 , 3 , 6 , 9 , y } with elements arranged in increasing order . if the median and the mean of the set are the same , what is the value of | x | - | y | ?
Options: a ) 2 , b ) 0 , c ) - 1 , d ) can not be determined , e ) 1
Rationale: "median of the set = ( - 3 + 3 ) / 2 = 0 as per statement , mean of the set = 0 mean of the set | y | - | x | + 18 - 16 = 0 ( where x is negative n y is positive ) | y | - | x | = - 2 so the absolute difference between two numbers is 2 answer a"
Answer: a
Problem: the market value of a certain machine decreased by 30 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 10,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 4,000 , c ) $ 3,200 , d ) $ 2,400 , e ) $ 800
Rationale: "b . market value in 1982 = $ 10000 market value in 1983 = $ 10000 - ( $ 10000 x 30 / 100 ) = 10000 - 3000 = $ 7000 market value in 1984 = market value in 1983 - ( 30 % of $ 10000 ) = 7000 - 3000 = $ 4000"
Answer: b
Problem: the value of log 2 16 is
Options: a ) 1 / 8 , b ) 4 , c ) 8 , d ) 16 , e ) 17
Rationale: "solution let log 216 = n . then , 2 n = 16 = 24 ‹ = › n = 4 . answer b"
Answer: b
Problem: dividing by 3 ⁄ 7 and then multiplying by 5 ⁄ 6 is the same as dividing by what number ?
Options: a ) 35 ⁄ 18 , b ) 16 ⁄ 5 , c ) 20 ⁄ 9 , d ) 9 ⁄ 20 , e ) 5 ⁄ 16
Rationale: "say x / 3 / 7 * 5 / 6 = x * 7 / 3 * 5 / 6 = x * 35 / 18 a"
Answer: a
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 13 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 19 , b ) 17 , c ) 13 , d ) 10 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 13 x = 13 answer : c"
Answer: c
Problem: excluding stoppages , the speed of a bus is 50 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7 min , b ) 6 min , c ) 9 min , d ) 10 min , e ) 11 min
Rationale: "due to stoppages , it covers 5 km less . time taken to cover 5 km = ( 5 / 50 ) x 60 = 6 min answer : b"
Answer: b
Problem: by selling 16 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 28 , b ) 25 , c ) 24 , d ) 23 , e ) 21
Rationale: "80 % - - - 16 120 % - - - ? 80 / 120 * 16 = 24 answer : c"
Answer: c
Problem: the ratio of spinsters to cats is 2 to 9 . if there are 42 more cats than spinsters , how many spinsters are there ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let 2 x be the number of spinsters . then 9 x is the number of cats . 9 x - 2 x = 42 x = 6 and the number of spinsters is 2 ( 6 ) = 12 . the answer is d ."
Answer: d
Problem: find the smallest number in a gp whose sum is 38 and product 1728
Options: a ) 12 , b ) 20 , c ) 8 , d ) all of these , e ) none of these
Rationale: "in gp : - a / r + a + ar . . . . = 38 a ( 1 + r + r ^ 2 ) = 38 r . . . . . . eq 1 product a ^ 3 = 1728 a = 12 now put this value in eq 1 12 ( 1 + r + r ^ 2 ) = 38 r r = 2 / 3 and 3 / 2 . . so sallest number is 8 answer : c"
Answer: c
Problem: what no . should be subtracted from x ^ 3 + 4 x 2 − 7 x + 12 x ^ 3 + 4 x ^ 2 − 7 x + 12 , if it is to be perfectly divisible by x + 3 x + 3 ?
Options: a ) 38 , b ) 42 , c ) 46 , d ) 49 , e ) 62
Rationale: according to remainder theorem when dfracf ( x ) x + adfracf ( x ) x + a , then the remainder is f ( − a ) f ( − a ) . in this case , as x + 3 x + 3 divides x 3 + 4 x 2 − 7 x + 12 – kx 3 + 4 x 2 − 7 x + 12 – k perfectly ( kk being the number to be subtracted ) , the remainder is 0 when the value of xx is substituted by - 3 . i . e . , ( − 3 ) 3 + 4 ( − 3 ) 2 − 7 ( − 3 ) + 12 − k = 0 ( − 3 ) 3 + 4 ( − 3 ) 2 − 7 ( − 3 ) + 12 − k = 0 or − 27 + 36 + 21 + 12 = k − 27 + 36 + 21 + 12 = k or k = k = 42 b
Answer: b
Problem: 76 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 13.25 , b ) 38.25 , c ) 33.25 , d ) 34.25 , e ) 31.25
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 76 = 33.25 answer : c"
Answer: c
Problem: in a division sum , the quotient is 40 , the divisor 72 and the remainder 64 , find the dividend ?
Options: a ) 2674 , b ) 2944 , c ) 2464 , d ) 2924 , e ) 2994
Rationale: explanation : 40 * 72 + 64 = 2944 answer : b
Answer: b
Problem: a store sells chairs and tables . if the price of 3 chairs and 1 table is 60 % of the price of 1 chair and 3 tables , and the price of 1 table and 1 chair is $ 80 , 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 ) 68 , b ) 84 , c ) 72 , d ) 60 , e ) 64
Rationale: "let c = chair ; t = table 3 c + 1 t = 0.6 ( 1 c + 3 t ) or c ( 3 - 0.6 ) = 1.8 t - 1 t or 2.4 c = 0.8 t therefore c = 0.8 / 2.4 t = 1 / 3 t ic + 1 t = 80 or 1 / 3 t + 1 t = 80 therefore t = 80 * 3 / 4 = 60 d"
Answer: d
Problem: the probability that a man will be alive for 10 more yrs is 1 / 4 & the probability that his wife will alive for 10 more yrs is 1 / 3 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 2 , b ) 1 , c ) 2 / 3 , d ) 3 / 5 , e ) 3 / 8
Rationale: sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 2 ans . ( a )
Answer: a
Problem: how many positive even integers less than 100 contain digits 4 or 7 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "one digit numbers : 4 two digit numbers : 4 at tens place : 40 , 42,44 , 46,48 7 at tens place : 70 , 72,74 , 76,78 4 at units place : 14 , 24,34 , 54,64 , 84,94 ( duplicates removed ) if 7 is at units place , the number cant be even total : 1 + 5 + 5 + 7 = 18 answer c"
Answer: c
Problem: a car traveled from san diego to san francisco at an average speed of 48 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 32 . , c ) 36 , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 48 x total distance traveled = 2 * 48 x = 96 x total time taken = x + 2 x = 3 x average speed = 96 x / 3 x = 32 answer : b"
Answer: b
Problem: amount of bacteria present time amount 1 : 00 p . m . 8.0 grams 4 : 00 p . m . x grams 7 : 00 p . m . 12.4 grams data for a certain biology experiment are given in the table above . if the amount of bacteria present increased by the same fraction during each of the two 3 - hour periods shown , how many grams of bacteria were present at 4 : 00 p . m . ?
Options: a ) 12.0 , b ) 12.1 , c ) 12.2 , d ) 10.0 , e ) 10.4
Rationale: the question says that bacteria increased by same fraction , not by same amount in 2 intervals of 3 hours . let x represent the amount of bacteria present at 4 : 00 pm . since the fractional increase must remain constant from 1 to 4 pm as it is from 4 pm to 7 pm : fractional increase from 1 pm to 4 pm = x / 8.0 fractional increase from 4 pm to 7 pm = 12.4 / x x \ 8 = 12.4 \ x x ^ 2 = 12.4 * 8 x = 10 answer : d
Answer: d
Problem: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.60 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 4 , d ) 7 : 9 , e ) none of these
Rationale: "solution required ratio = 70 : 90 = 7 : 9 answer d"
Answer: d
Problem: i bought two books ; for rs . 300 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 175 , b ) 280 , c ) 189 , d ) 278 , e ) 268
Rationale: "x * ( 85 / 100 ) = ( 300 - x ) 119 / 100 x = 175 answer : a"
Answer: a
Problem: p works 25 % more efficiently than q and q works 50 % more efficiently than r . to complete a certain project , p alone takes 50 days less than q alone . if , in this project p alone works for 60 days and then q alone works for 130 days , in how many days can r alone complete the remaining work ?
Options: a ) 50 days , b ) 83.6 days , c ) 100 days , d ) 150 days , e ) 80 days
Rationale: "p works 25 % more efficiently than q : something that takes q 5 days , takes p 4 days q works 50 % more efficiently than r : something that takes r 7.5 days , takes q 5 days p alone takes 50 days less than q : for every 4 days p works , q has to work an extra day . hence p alone can do it in 200 days and q alone in 250 days and hence r alone in 380 days p works for 60 days - - > 60 / 200 work done = > 30 % q works for 130 days - - > 130 / 250 work done = > 52 % 22 % work left . . . r alone will take 22 % * 380 = 83.6 days answer is ( b )"
Answer: b
Problem: a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 15 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 450 . , b ) 459 . , c ) 432 . , d ) 502 . , e ) 522 .
Rationale: "pastry is divided in 15 customers equally . so , total number of pastry must be a multiple of 15 only option a satisfies the condition , and hence is the answer"
Answer: a
Problem: for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 8 + 3 and * 8 + 8 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "generally * p or p ! will be divisible by all numbers from 1 to p . therefore , * 8 would be divisible by all numbers from 1 to 8 . = > * 8 + 3 would give me a number which is a multiple of 3 and therefore divisible ( since * 8 is divisible by 3 ) in fact adding anyprimenumber between 1 to 8 to * 8 will definitely be divisible . so the answer is none ( a ) ! supposing if the question had asked for prime numbers between * 8 + 3 and * 8 + 11 then the answer would be 1 . for * 8 + 3 and * 8 + 13 , it is 2 and so on . . . a"
Answer: a
Problem: the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each . the radius of the sphere is :
Options: a ) 4 cm , b ) 6 cm , c ) 8 cm , d ) 10 cm , e ) 9 cm
Rationale: "explanation : curved surface area of sphere = 4 / π r 2 surface area of cylinder = 2 π rh = > 4 / π r 2 = 2 π rh = > r 2 = 6 ∗ 12 / 2 = > r 2 = 36 = > r = 6 note : diameter of cylinder is 12 so radius is taken as 6 . option b"
Answer: b
Problem: during the first week of performances of a certain play , 5400 tickets were sold , all at reduced price . during the remaining weeks of performances , 5 times as many tickets were sold at full price as were sold at reduced price . if the total number of tickets e sold was 25200 , how many of them were sold at full price ?
Options: a ) 21000 , b ) 19800 , c ) 16500 , d ) 15800 , e ) 8700
Rationale: given : the question tells us about the number of tickets sold in the first week at reduced price = 5400 . it also tells us that during the remaining weeks , the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price . the total tickets sold was 25200 , and we are asked to find the number of tickets that where sold at full price . approach : the question asks us to find the number of ticket sold at full price . we know that the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price in remaining weeks . hence , assuming tickets sold at reduced price in remaining weeks to be x would give us the no . of tickets sold at full price to be 5 x . tickets sold in first week + tickets sold in remaining weeks = total no . of tickets soldi . e . tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold we know the no . of tickets sold during first week and the total no . of tickets sold . we will use this relation to get to our answer . working out : tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold substituting values in the equation , we get 5400 + 5 x + x = 25200 x = 3300 tickets sold at full price = 5 x = 16500 answer : option c
Answer: c
Problem: a cricket bat is sold for $ 900 , making a profit of $ 100 . the profit percentage would be
Options: a ) 24 % , b ) 12.5 % , c ) 30 % , d ) 36 % , e ) 40 %
Rationale: "100 / ( 900 - 100 ) = 100 / 800 = 0.125 = 12.5 % . answer : b"
Answer: b
Problem: a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 279 metres long in 20 seconds . the length of the train ( in metres ) is :
Options: a ) 186 , b ) 176 , c ) 175 , d ) 96 , e ) none of these
Rationale: "explanation : let the length of train be l m . acc . to question ( 279 + l ) / 20 = l / 8 2232 + 8 l = 20 l l = 2232 / 12 = 186 m answer a"
Answer: a
Problem: mary ' s income is 60 % more than tim ' s income and tim ' s income is 10 % less than juan ' s income . what % of juan ' s income is mary ' s income .
Options: a ) 144 % , b ) b . 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "even i got 96 % j = 100 t = 100 * 0.9 = 90 m = 90 * 1.6 = 144 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 144 * 100 / 100 = 144 ans : a"
Answer: a
Problem: let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 75 th number in this set ?
Options: a ) 597 , b ) 608 , c ) 613 , d ) 616 , e ) 621
Rationale: "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 75 th number = 8 * ( 75 - 1 ) + 5 = 597 answer = a"
Answer: a
Problem: the perimeter of a square is equal to the radius of a circle having area 39424 sq cm , what is the area of square ?
Options: a ) 1225 sq cm
b ) 441 sq cm
c ) 784 sq cm
d ) can ’ t say
e ) none of these
Rationale: let the side of square = a cm and radius of circle = r cm given , 4 a = r also area of square = pi * r ^ 2 = 39424 , r ^ 2 = 12544 or r = 112 so a = r / 4 = 112 / 4 = 28 hence area of square = a ^ 2 = 28 ^ 2 = 784 cm ^ 2 answer : c
Answer: c
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 54 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 60
Rationale: "the total number of books is 75 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 54 books , thus the number of un - returned books is 75 - 54 = 21 books . 0.35 x = 21 x = 60 the answer is e ."
Answer: e
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 86 . how much was lent at 5 % ?
Options: a ) 388 , b ) 2998 , c ) 277 , d ) 500 , e ) 400
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 86 5 x / 100 + 90 – 6 x / 100 = 86 x / 100 = 4 = > x = 400 . answer : e"
Answer: e
Problem: what is the smallest no . that should be added to 236 to make it exactly divisible by 9 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "if a number is divisible by 9 , the sum of its digits must be a multiple of 9 . here , 2 + 3 + 6 = 11 , the next multiple of 9 is 18 . 7 must be added to 236 to make it divisible by 9 d"
Answer: d
Problem: each of the positive integers a , b , and c is a 3 - digit integer . if each of the digits 1 through 9 appears in one of these 3 integers , what is the maximum possible value of the sum of a , b , and c ?
Options: a ) 2445 , b ) 2331 , c ) 2874 , d ) 2801 , e ) 2256
Rationale: according to the stem we should use the digits 1 through 9 to construct 3 three - digit integers , so that their sum is as big as possible . to maximize the sum , maximize the hundreds digits of a , b , and c , so make them 9 , 8 , and 7 . next , minimize tens digits . make them 6 , 5 , and 4 . use the remaining digits ( 3 , 2 , and 1 ) for units digits . so , a would be 963 , b would be 852 and c would be 741 . 741 + 852 + 963 = 2256 . answer : e .
Answer: e
Problem: the profits of qrs company rose 50 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
Options: a ) 15 % , b ) 32 % , c ) 40 % , d ) 62 % , e ) 80 %
Rationale: "assume 100 in march , then 150 in april as 50 % increase , then 120 in may as 20 % decrease from april , and then 180 in june which is 150 % of 120 . so overall increase is from 100 to 180 is 80 % answer e"
Answer: e
Problem: a certain bag contains 100 balls â € ” 20 white , 30 green , 10 yellow , 37 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 20 + 30 + 10 ) / 100 = 60 / 100 = 0.6 . answer is c"
Answer: c
Problem: what is the next number : 2 , 17 , 257 , __
Options: a ) 2977 , b ) 3837 , c ) 4097 , d ) 4847 , e ) 5387
Rationale: "4 ^ 0 + 1 = 2 4 ^ 2 + 1 = 17 4 ^ 4 + 1 = 257 4 ^ 6 + 1 = 4097 the answer is c ."
Answer: c
Problem: calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 15 % and its breadth is decreased by 10 % ?
Options: a ) 3.5 percent increase , b ) 9.5 percent increase , c ) 1.5 percent increase , d ) 3.9 percent increase , e ) 3.5 percent increase
Rationale: "let l and b be 100 each 100 * 100 = 10000 l increase by 15 % = 115 b decrease by 10 % = 90 115 * 90 = 10350 3.5 percent increase answer : e"
Answer: e
Problem: in order to obtain an income of rs . 450 from 10 % stock at rs . 108 , one must make an investment of
Options: a ) 5363 , b ) 6240 , c ) 4860 , d ) 1987 , e ) 2732
Rationale: "to obtain rs . 10 , investment = rs . 108 . to obtain rs . 450 , investment = = rs . 4860 . answer : c"
Answer: c
Problem: in a ratio which is equal to 4 : 6 , if the antecedent is 20 , then the consequent is ?
Options: a ) 72 , b ) 85 , c ) 30 , d ) 51 , e ) 45
Rationale: "we have 4 / 6 = 20 / x 4 x = 20 * 6 x = 30 consequent = 30 answer is c"
Answer: c
Problem: the area of a rectangular plot is 20 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 10 metres , b ) 5 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these
Rationale: "l × b = 20 × b ∴ l = 20 m and l – b = 10 ∴ b = 20 – 10 = 10 m answer a"
Answer: a
Problem: 78654 * 9999
Options: a ) 784598562 , b ) 765858254 , c ) 784569825 , d ) 786461346 , e ) none of these
Rationale: "explanation : 78654 * ( 10000 - 1 ) = 786540000 - 78654 = 786461346 option d"
Answer: d
Problem: the weight of a glass of jar is 40 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 2 / 3
Rationale: "let weight of jar filled with beans = 100 g weight of jar = 40 g weight of coffee beans = 60 g weight of jar and remaining beans = 60 g weight of remaining beans = 20 g fraction remaining = 20 / 60 = 1 / 3 answer is b ."
Answer: b
Problem: one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 75,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 80000 , b ) 60000 , c ) 50000 , d ) 70000 , e ) 90000
Rationale: "let savings in n . s . c and p . p . f . be rs . x and rs . ( 175000 - x ) respectively . then , = 1 / 3 x = 1 / 2 ( 175000 - x ) = x / 3 + x / 2 = 87500 = 5 x / 6 = 87500 = x = 87500 x 6 / 5 = 105000 savings in public provident fund = rs . ( 175000 - 105000 ) = rs . 70000 answer is d ."
Answer: d
Problem: how many positive integers less than 120 are there such that they are multiples of 13 or multiples of 12 but not both ?
Options: a ) 13 , b ) 19 , c ) 15 , d ) 16 , e ) 17
Rationale: "for 13 : 13 . . . 117 = 13 * 9 = 117 for 12 : 12 . . . 120 = 12 * 10 = 120 but there is one integer 13 * 12 . so n = ( 9 ) + ( 10 ) = 19 b"
Answer: b
Problem: a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 96 inches and the width is 72 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ?
Options: a ) a 64
b ) b 22
c ) c 27
d ) d 40
e ) e 50
Rationale: l = 96 / 12 = 8 ft w = 72 / 12 = 6 ft area of paper = 48 area of cube = 8 * side ^ 2 side of cube = 4 v of cube = 64
Answer: a
Problem: if the operation € is defined for all x and y by the equation x € y = 2 * x * y , then 9 € ( 4 € 5 ) =
Options: a ) 80 , b ) 720 , c ) 760 , d ) 840 , e ) 860
Rationale: "working inside out , ( 4 € 5 ) = 2 * 4 * 5 = 40 9 € 40 = 2 * 9 * 40 = 720 hence , answer is b"
Answer: b
Problem: jack and jill are marathon runners . jack can finish a marathon ( 43 km ) in 4.5 hours and jill can run a marathon in 4.3 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 43 / 45 , c ) 4 / 5 , d ) 5 / 4 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 43 / ( 9 / 2 ) = 86 / 9 average speed of jill = 43 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 86 / 9 ) / 10 = 86 / 90 = 43 / 45 answer b"
Answer: b
Problem: two pipes a and b can fill a tank in 6 and 12 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "part filled by a in 1 min . = 1 / 6 part filled by b in 1 min . = 1 / 12 part filled by ( a + b ) in 1 min . = 1 / 6 + 1 / 12 = 1 / 4 . both the pipes can fill the tank in 4 minutes . answer : a"
Answer: a
Problem: if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 34
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "p ã · 44 = 432 = > p = 432 * 44 = 19008 p / 34 = 19008 / 34 = 559 , remainder = 2 a"
Answer: a
Problem: a car traveled 420 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 6 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 16 , c ) 21 , d ) 24 , e ) 27
Rationale: "let the speed in highway be h mpg and in city be c mpg . h = c + 6 h miles are covered in 1 gallon 420 miles will be covered in 420 / h . similarly c miles are covered in 1 gallon 336 miles will be covered in 336 / c . both should be same ( as car ' s fuel capacity does not change with speed ) = > 336 / c = 420 / h = > 336 / c = 420 / ( c + 6 ) = > 336 c + 336 * 6 = 420 c = > c = 336 * 6 / 84 = 24 answer d ."
Answer: d
Problem: 65 bags of nuts are to be divided among 13 students . each bag contains 15 nuts . how many nuts will each student receive ?
Options: a ) 75 , b ) 65 , c ) 43 , d ) 52 , e ) 78
Rationale: 65 ÷ 13 = 5 bags per student 5 x 15 = 75 nuts per student correct answer a
Answer: a