regisss/math_qa huggingface dataset:
Problem: tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 50 people bought tickets to the concert , what was the total revenue from ticket sales ?
Options: a ) $ 600 , b ) $ 740 , c ) $ 860 , d ) $ 980 , e ) $ 1,140
Rationale: "price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 20 tickets = 20 * 20 = 400 revenue generated from sales of 50 tickets = 120 + 340 + 400 = 860 $ answer c"
Answer: c
Problem: x + ( 1 / x ) = 1.5 find x ^ 2 + ( 1 / x ^ 2 )
Options: a ) 2.25 , b ) 3.25 , c ) 4.25 , d ) 5.25 , e ) 0.25
Rationale: "squaring on both sides ( x + 1 / x ) ^ 2 = 1.5 ^ 2 x ^ 2 + 1 / x ^ 2 = 2.25 - 2 x ^ 2 + 1 / x ^ 2 = 0.25 answer : e"
Answer: e
Problem: the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 36 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ?
Options: a ) a . 40 , b ) b . 100 , c ) c . 400 , d ) d . 1,000 , e ) e . 10,000
Rationale: "the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 36 pi r = 3 so area = 4 . pi . r ^ 2 = 36 . pi = 36 x 3.14 = 100 ( approx ) b"
Answer: b
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 40 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 30 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , c is the answer"
Answer: c
Problem: at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 35 liters of forest green to change it to verdant green ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 4 / 3 , d ) 35 / 3 , e ) 10 / 3
Rationale: "35 liter of forset green have 20 liter of blue and 15 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 20 / ( 15 + x ) = ¾ 45 + 3 x = 80 = > x = 35 / 3 answer : d"
Answer: d
Problem: find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 12 x + 3 = 0 ?
Options: a ) 6 , b ) 7 , c ) 23 , d ) 17 , e ) 42
Rationale: "a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 12 / 1 = - 12 ab = 3 / 1 = 3 hence a / b + b / a = [ ( - 12 ) 2 - 2 ( 3 ) ] / 3 = 126 / 3 = 42 . e )"
Answer: e
Problem: p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 60 days to complete the same work . then q alone can do it in
Options: a ) 20 , b ) 24 , c ) 25 , d ) 27 , e ) 30
Rationale: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 60 work done by p , q and r in 1 day = 1 / 10 + 1 / 60 = 7 / 60 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 7 / 60 = > work done by p in 1 day = 7 / 120 = > work done by q and r in 1 day = 7 / 120 hence work done by q in 1 day = 7 / 120 â € “ 1 / 60 = 1 / 24 so q alone can do the work in 24 days answer is b ."
Answer: b
Problem: the total age of a and b is 12 years more than the total age of b and c . c is how many year younger than a ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 15
Rationale: "given that , a + b = 12 + b + c ⇒ a - c = 12 therefore , c is younger than a by 12 years answer is c ."
Answer: c
Problem: there are 1000 students in a school and among them 25 % of them attends chess class . 50 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?
Options: a ) 1 , b ) 10 , c ) 125 , d ) 50 , e ) 20
Rationale: "25 % of 1000 gives 250 . so 250 attends chess and 50 % of 250 gives 125 so 125 enrolled for swimming answer : c"
Answer: c
Problem: the temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 ( 2 ^ - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 60 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 125 , b ) 95 , c ) 80 , d ) 61.8 , e ) 50
Rationale: answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant “ a ” . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 60 minutes after it was poured is : f = 120 ( 2 ^ - 60 / 10 ) + 60 f = 120 * 1 / 64 + 60 f = 15 / 8 + 60 f = 495 / 8 = 61.8 d
Answer: d
Problem: the edges of three iron cubes are 6 cm ; 8 cm ; 10 cm respectively . a new cube was made by melting them . find the edge of the new cube ?
Options: a ) 17
b ) 19
c ) 16
d ) 12
e ) 14
Rationale: 63 + 83 + 103 = a 3 = > a = 12 answer : d
Answer: d
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 76 , b ) 76.5 , c ) 85 , d ) 80 , e ) none of these
Rationale: "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 65 + 20 ) kg = 85 kg . answer : c"
Answer: c
Problem: if a and b get profits of rs . 5,000 and rs . 2,000 respectively at the end of year then ratio of their investments are
Options: a ) 4 : 1 , b ) 1 : 4 , c ) 5 : 2 , d ) 2 : 3 , e ) 2 : 5
Rationale: "ratio = 5000 / 2000 = 5 : 2 answer : c"
Answer: c
Problem: someone on a skateboard is traveling 5 miles per hour . how many feet does she travel in 45 seconds ? ( 1 mile = 5280 feet )
Options: a ) 380 ft , b ) 400 ft , c ) 410.05 ft , d ) 329.85 ft , e ) 420.85 ft
Rationale: "per second = > 5 * 5280 ft / 60 * 60 = 7.33 ft 45 seconds = > 7.33 * 45 = 329.85 ft answer : d"
Answer: d
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 70 per component . shipping costs for delivering the components are $ 4 per unit . further , the manufacturer has costs of $ 14,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 250 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) 132 , b ) 138 , c ) 144 , d ) 128 , e ) 116
Rationale: "$ 14500 is a fixed cost each component is $ 74 ( $ 70 to produce , $ 4 to ship ) manufacturer will be producing and selling 250 components so therefore the equation to find price would be 250 * p = 14500 + ( 250 * 70 ) + ( 250 * 4 ) p = ( 14500 + 17500 + 1000 ) / 250 p = 132 answer : a"
Answer: a
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 20 seconds . the ratio of their speeds is ?
Options: a ) 3 / 7 , b ) 3 / 2 , c ) 3 / 5 , d ) 3 / 1 , e ) 3 / 3
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 20 = = > 27 x + 17 y = 20 x + 20 y = = > 7 x = 3 y = = > x / y = 3 / 7 . answer : a"
Answer: a
Problem: a bucket contains 2 mixtures a and b in the ratio 7 : 5 . if 9 liters of the mixture is replaced by 9 liters of liquid b , then the ratio of the two liquids becomes 7 : 9 . how much of the liquid a was there in the bucket ?
Options: a ) 15 liters , b ) 21 liters , c ) 12 liters , d ) 18 liters , e ) 25 liters
Rationale: 1 st ratio = 7 : 5 2 nd ratio = 7 : 9 difference of cross products ratio = 7 * 9 - 7 * 5 = 28 common factor of the 1 st ratio = ( quantity replaced / sum of terms in 1 st ratio ) + ( quantity replaced * term a in 2 nd ratio / difference ) = ( 9 / 7 + 5 ) + ( 9 * 7 / 28 ) = 3 quantity of a = 7 * 3 = 21 liters answer is b
Answer: b
Problem: jane makes toy bears . when she works with an assistant , she makes 53 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 70 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 61.2 bears per 36 hours a week or 1.7 bears / hr ( [ 40 bears * 1.53 ] / [ 40 hrs * . 90 ] ) . [ ( 1.7 - 1 ) / 1 ] * 100 % = 70 % answer : b"
Answer: b
Problem: two numbers are in the ratio of 1 : 2 . if 5 be added to both , their ratio changes to 3 : 5 . the greater number is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the ratio be x : y , given x / y = 1 / 2 , ( x + 5 ) / ( y + 5 ) = 3 / 5 = > x = 10 and y = 20 answer : a"
Answer: a
Problem: if 60 % of 3 / 5 of a number is 72 , then the number is ?
Options: a ) 80 , b ) 100 , c ) 75 , d ) 90 , e ) none of these
Rationale: "let the number be x . then 60 % of 3 / 5 of x = 72 60 / 100 * 3 / 5 * x = 72 x = ( 72 * 25 / 9 ) = 200 required number = 200 . correct option : e"
Answer: e
Problem: the cost to park a car in a certain parking garage is $ 12.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?
Options: a ) $ 1.09 , b ) $ 2.69 , c ) $ 2.25 , d ) $ 2.37 , e ) $ 2.50
Rationale: "total cost of parking for 9 hours = 12 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 12 + 7 * 1.75 = 24.25 thus the average parking price = 24.25 / 9 = 2.69 $ b is the correct answer ."
Answer: b
Problem: in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability t this college graduate has a graduate degree ?
Options: a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43
Rationale: "in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability t of cgd / ( cg ) - > 3 / 19 answer d"
Answer: d
Problem: walking with 4 / 5 of my usual speed , i arrive at the bus stop 6 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ?
Options: a ) 20 min , b ) 22 min , c ) 15 min , d ) 18 min , e ) 24 min
Rationale: "let t = usual time = distance / usual speed t + 6 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 24 the answer is e ."
Answer: e
Problem: with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity t of the pool ?
Options: a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
Rationale: "d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters ."
Answer: d
Problem: convert 500 miles to km ?
Options: a ) 600 km , b ) 700 km , c ) 800 km , d ) 900 km , e ) 1000 km
Rationale: "800 km 500 * 1.6 = 800 answer : c"
Answer: c
Problem: audrey 4 hours to complete a certain job . ferris can do the same job in 3 hours . audrey and ferris decided to collaborate on the job , working at their respective rates . while audrey worked continuously , ferris took 4 breaks of equal length . if the two completed the job together in 2 hours , how many minutes long was each of ferris ’ breaks ?
Options: a ) 5 , b ) 7 , c ) 15 , d ) 20 , e ) 25
Rationale: "audery and ferris collective work rate : 1 / 4 + 1 / 3 = 7 / 12 collective work time = 12 / 7 = 1.7 hrs job was actually done in = 2 ( includes breaks ) breaks = actual time taken - collective work time = 2 - 1.7 = . 3 hrs = 1 / 2 so ferrais took 4 breaks = . 3 / 4 = . 07 hrs = 7 m so answer is b ) 10 mins"
Answer: b
Problem: each week a restaurant serving mexican food uses the same volume of chili paste , which comes in either 25 - ounce cans or 15 - ounce cans of chili paste . if the restaurant must order 30 more of the smaller cans than the larger cans to fulfill its weekly needs , then how manysmallercans are required to fulfill its weekly needs ?
Options: a ) 60 , b ) 70 , c ) 75 , d ) 100 , e ) 120
Rationale: "let x be the number of 25 ounce cans . therefore ( x + 30 ) is the number of 15 ounce cans . total volume is same , therefore 25 x = 15 ( x + 30 ) 10 x = 450 x = 45 therefore , number of 15 ounce cans = 45 + 30 = 75 ans - c"
Answer: c
Problem: a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 160 . find the unknown rate of two blankets ?
Options: a ) 420 , b ) 550 , c ) 490 , d ) 450 , e ) 457
Rationale: "10 * 160 = 1600 3 * 100 + 5 * 150 = 1050 1600 – 1050 = 550 answer : b"
Answer: b
Problem: a 300 meter long train crosses a platform in 30 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 227 , b ) 266 , c ) 230 , d ) 288 , e ) 200
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 30 = 50 / 3 3 ( x + 300 ) = 1500 è x = 200 m . answer : e"
Answer: e
Problem: how many different values of positive integer x , for which | x + 6 | < x , are there ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
Rationale: "answer d i opted to put the random value option . i used 0 , 6 , - 6 and the the extreme of 20 and - 20 . . i was able to solve it in 1 : 09 d"
Answer: d
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . if the faster train passes the slower train in 36 seconds , what is the length of each train ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 75 , e ) 40
Rationale: "assume the length of each train = x total distance covered for overtaking the slower train = x + x = 2 x relative speed = 46 - 36 = 10 km / hr = ( 10 × 10 ) / 36 = 100 / 36 m / s time = 36 seconds 2 x / ( 100 / 36 ) = 36 = > ( 2 x × 36 ) / 100 = 36 = > x = 50 meter answer is c ."
Answer: c
Problem: convert the 9 / 36 m / s into kilometers per hour ?
Options: a ) 0.9 kmph , b ) 9.9 kmph , c ) 1.3 kmph , d ) 1.2 kmph , e ) 5.7 kmph
Rationale: "9 / 36 m / s = 9 / 36 * 18 / 5 = 9 / 10 = 0.9 kmph . answer : a"
Answer: a
Problem: in what time will a train 120 m long cross an electric pole , it its speed be 160 km / hr ?
Options: a ) 2.5 sec , b ) 2.9 sec , c ) 2.7 sec , d ) 8.7 sec , e ) 8.5 sec
Rationale: "speed = 160 * 5 / 18 = 44 m / sec time taken = 120 / 44 = 2.7 sec . answer : c"
Answer: c
Problem: all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes are there whose two adjacent faces are coloured red ?
Options: a ) 0 , b ) 8 , c ) 16 , d ) 24 , e ) 4
Rationale: "there are 64 small cubes , hence one side side of the big cube is 3 √ 64 = 4 cm number of small cubes having two adjacent faces coloured red = ( x - 2 ) x no . of edges = ( 4 - 2 ) x 12 = 24 answer : d"
Answer: d
Problem: a 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 320 m , b ) 350 m , c ) 650 m , d ) none of these , e ) can not be determined
Rationale: "solution speed = ( 300 / 18 ) m / sec = ( 50 / 3 ) m / sec . length of the platform be x metres . then = x + 300 / 39 = 50 / 3 m / sec = 3 ( x + 300 ) = 1950 . = 350 m answer b"
Answer: b
Problem: marketing executives for a certain chewing gum company projected a 30 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 25 % . what percent of the projected revenue was the actual revenue ?
Options: a ) 53 % , b ) 57.7 % , c ) 62.5 % , d ) 64 % , e ) 75 %
Rationale: "last year revenue = 100 ( assume ) ; this year revenue = 75 ; projected revenue = 130 . actual / projected * 100 = 75 / 130 * 100 = 57.7 % . answer : b ."
Answer: b
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 190 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) 50 sec
Rationale: "explanation : speed = 45 km / hr = 45 × ( 10 / 36 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 190 = 550 meter time taken to cross the platform = 550 / ( 25 / 2 ) = 550 × 2 / 25 = 44 seconds answer : option c"
Answer: c
Problem: find large number from below question the difference of two numbers is 2500 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 3345 , b ) 1250 , c ) 1540 , d ) 2997 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 2500 = 6 x + 15 5 x = 2485 x = 497 large number = 497 + 1365 = 2997 d"
Answer: d
Problem: 248 : 3 : : 328 : ?
Options: a ) 7 , b ) 5 , c ) 4 , d ) 6 , e ) none of the above
Rationale: "248 - - - - 24 / 8 . . . 3 328 - - - 32 / 8 . . . 4 answer c"
Answer: c
Problem: which number should replace both the asterisks in ( * / 18 ) x ( * / 72 ) = 1 ?
Options: a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 48
Rationale: "let ( y / 18 ) x ( y / 72 ) = 1 y ^ 2 = 18 x 72 = 18 x 18 x 4 y = ( 18 x 2 ) = 36 the answer is c ."
Answer: c
Problem: the triplicate ratio of 1 : 5 is ?
Options: a ) 1 : 7 , b ) 1 : 8 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 125
Rationale: "1 ^ 3 : 5 ^ 3 = 1 : 125 answer : e"
Answer: e
Problem: in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 200 m . then , a wins by :
Options: a ) 60 m , b ) 100 m , c ) 43 m , d ) 20 m , e ) 23 m
Rationale: "to reach the winning post a will have to cover a distance of ( 500 - 200 ) m , i . e . , 300 m . while a covers 3 m , b covers 4 m . while a covers 300 m , b covers 4 x 300 / 3 m = 400 m . thus , when a reaches the winning post , b covers 400 m and therefore remains 100 m behind . a wins by 100 m . answer : b"
Answer: b
Problem: a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount q of paint , in gallons , that must be purchased in order to measure out the portions needed for the mixture ?
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4
Rationale: "given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture q , so not acceptable . so correct ans is 2.5 gallons . b"
Answer: b
Problem: a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 9 multiples of 14 , how many multiples of 7 are there in q ?
Options: a ) 20 , b ) 19 , c ) 18 , d ) 17 , e ) 16
Rationale: "lets q ' s first number be 14 as per question , q contains 9 multiples of 14 , so let q ' s last number be 126 . ( 14 ∗ 9 ) we have , a n = a + ( n − 1 ) d then 126 = 14 + ( n - 1 ) 7 solving for n , we get n = 17 answer : d"
Answer: d
Problem: express a speed of 66 kmph in meters per second ?
Options: a ) 10.33 mps , b ) 17 mps , c ) 97 mps , d ) 17.33 mps , e ) 18.33 mps
Rationale: "66 * 5 / 18 = 18.33 mps answer : e"
Answer: e
Problem: a man buys a cycle for rs . 1600 and sells it at a loss of 15 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1360 , c ) s . 1190 , d ) s . 1202 , e ) s . 1256
Rationale: "s . p . = 85 % of rs . 1600 = rs . 85 / 100 x 1600 = rs . 1360 answer : b"
Answer: b
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 8 cm and breadth 6 cm . find the circumference of a semicircle whose diameter is equal to the side of the square .
Options: a ) 23.56 , b ) 23.59 , c ) 23.55 , d ) 23.53 , e ) 11.0
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 8 + 6 ) = 28 cm parameter of the square = 28 cm i . e . 4 a = 28 a = 7 diameter of the semicircle = 7 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) 7 = 1 / 2 ( 22 / 7 ) ( 7 ) = 11 cm answer : e"
Answer: e
Problem: a tempo is insured to an extent of 5 / 7 of its original value . if the premium on it at the rate of 3 % amounts to $ 300 , the original value of the tempo is ?
Options: a ) 12500 , b ) 13280 , c ) 17520 , d ) 14000 , e ) 12560
Rationale: "let the original value of the tempo is $ x 3 % of 5 / 7 of x = 300 ( 3 / 100 ) * ( 5 / 7 ) x = 300 x = $ 14000 answer is d"
Answer: d
Problem: last year department store x had a sales total for december that was 3 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?
Options: a ) 1 / 4 , b ) 4 / 15 , c ) 3 / 14 , d ) 4 / 11 , e ) 4 / 5
Rationale: let avg for 11 mos . = 10 therefore , dec = 30 year total = 11 * 10 + 30 = 140 answer = 30 / 140 = 3 / 14 = c
Answer: c
Problem: if a - b = 3 and a ^ 2 + b ^ 2 = 29 , find the value of ab
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 19
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 29 - 9 = 20 = > ab = 10 . answer : a"
Answer: a
Problem: the ratio of the cost price and selling price is 4 : 5 . the profit percent is ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 50 % , e ) 15 %
Rationale: "let the c . p . = $ 4 x then s . p . = $ 5 x then , gain = 5 x - 4 x = $ x gain % = x / 4 x * 100 = 25 % answer is b"
Answer: b
Problem: farm tax is levied on the 50 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) none
Rationale: only trick n this question is to ignore 50 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 50 ) = 25 % and the answer is not there in the options . the correct answer is ( b ) .
Answer: b
Problem: the difference between the local value and the face value of 7 in the numeral 32675149 is
Options: a ) 69990 , b ) 69993 , c ) 70000 , d ) 77000 , e ) 78000
Rationale: "explanation : ( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 b )"
Answer: b
Problem: how many even 4 - digit numbers can be formed , so that the numbers are divisible by 4 and no two digits are repeated ?
Options: a ) 336 , b ) 784 , c ) 1120 , d ) 1804 , e ) 1936
Rationale: number is divisible by 4 if the last two digits form a number divisible by 4 . therefore last two digits can be : 00 ; 04 ; 08 ; 12 16 ; . . . 96 . basically multiples of 4 in the range 0 - 96 , inclusive . multiples of 4 in a range 0 - 96 , inclusive are last multiple in the range − first multiple in the range 4 + 1 = 25 last multiple in the range − first multiple in the range 4 + 1 = 25 but 3 numbers out of these 25 are not formed with distinct digits : 00 , 44 , and 88 . hence the numbers we are looking for can have only 22 endings . if there is 0 in the ending ( 04 , 08 , 20 , 40 , 60 , 80 - total 6 such numbers ) , then the first and second digit can take 8 and 7 choices each = 56 choices total . as there are 6 numbers with 0 in ending , hence total 6 * 56 = 336 . if there is no 0 in the ending ( total 22 - 6 with zero = 16 such numbers ) , then the first digit can take 7 choices ( 10 - 2 digits in the ending and zero , so total 3 digits = 7 , as 4 - digit number can not start with zero ) and the second digit can take 7 choices too ( 10 digits - 3 digits we ' ve already used ) = 7 * 7 = 49 choices total . as there are 16 numbers without zero in ending , hence total 16 * 49 = 784 . total : 336 + 784 = 1120 answer : c .
Answer: c
Problem: 317 x 317 + 283 x 283 = ?
Options: a ) 79698 , b ) 80578 , c ) 80698 , d ) 180578 , e ) none of them
Rationale: "= ( 317 ) ^ 2 + ( 283 ) ^ 2 = ( 300 + 17 ) ^ 2 + ( 300 - 17 ) ^ 2 = 2 [ ( 300 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 90000 + 289 ] = 2 x 90289 = 180578 answer is d"
Answer: d
Problem: two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 36 seconds , the speed of each train ( in km / hr ) is
Options: a ) 12 , b ) 36 , c ) 28 , d ) 20 , e ) 24
Rationale: explanation : distance covered = 120 + 120 = 240 m time = 36 s let the speed of each train = v . then relative speed = v + v = 2 v 2 v = distance / time = 240 / 36 = 6.667 m / s speed of each train = v = 6.667 / 2 = 3.33 m / s = 3.33 × 36 / 10 km / hr = 12 km / hr answer : option a
Answer: a
Problem: two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line . for instance , 3 and 7 rhyme around 5 . what integer r between 1 and 20 , inclusive , has the greatest number of distinct rhyming primes around it ?
Options: a ) 12 , b ) 15 , c ) 17 , d ) r = 18 , e ) 20
Rationale: since we are concerned with integers between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 1112 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 1113 ) , ( 717 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 1517 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 1317 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 1819 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 2023 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) .
Answer: d
Problem: pumps a , b , and c operate at their respective constant rates . pumps a and b , operating simultaneously , can fill a certain tank in 2 hours ; pumps a and c , operating simultaneously , can fill the tank in 3 / 2 hours ; and pumps b and c , operating simultaneously , can fill the tank in 2 hours . how many hours does it take pumps a , b , and c , operating simultaneously , to fill the tank .
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 , e ) 5 / 6
Rationale: a + b = 2 ; a + c = 3 / 2 , b + c = 2 ; add then 2 * ( a + b + c ) = 4 + 3 / 2 = 11 / 2 a + b + c = 11 / 4 hrs c
Answer: c
Problem: how many even number in the range between 8 to 100 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 32 , d ) 33 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 8,10 , 12,14 . . . 100 using ap formula , we can say 100 = 10 + ( n - 1 ) * 2 or n = 47 . for 6 , 12,18 , . . . 96 using ap formula , we can say 96 = 12 + ( n - 1 ) * 6 or n = 15 . hence , only divisible by 2 but not 3 = 47 - 15 = 32 . hence , answer c"
Answer: c
Problem: in a group of 100 people , 50 like reading books , 20 like both reading books and listening songs . how many like listening songs ?
Options: a ) 40 , b ) 50 , c ) 70 , d ) 60 , e ) none
Rationale: make a venn diagram , and enter your data . let the number of people who like listening songs be x x + 20 + 30 = 100 x = 50 so number who like listening songs = 20 + 50 = 70 answer c
Answer: c
Problem: a man rows his boat 90 km downstream and 72 km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 5 , c ) 7 , d ) 3 , e ) 2
Rationale: "speed downstream = d / t = 90 / 3 = 30 kmph speed upstream = d / t = 72 / ( 3 ) = 24 kmph the speed of the stream = ( 30 - 24 ) / 2 = 3 kmph answer : d"
Answer: d
Problem: there are 97 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 29 , b ) 49 , c ) 39 , d ) 59 , e ) 69
Rationale: editing my solution : number of switches = 97 number of switches turned on by a : 3 , 6 , . . . 96 = 32 number of switches turned on by b : 5 , 10 , . . . . 95 = 19 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 32 - 6 ) + ( 19 - 6 ) = 39 answer : c
Answer: c
Problem: the product of two consecutive odd no is - 1 , then what is the value of the sum of them .
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "two odd numbers are - 1 and + 1 . - 1 + 1 = 0 answer : c"
Answer: c
Problem: to fill a tank , 10 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two - fifth of its present ?
Options: a ) 25 , b ) 50 , c ) 75 , d ) 100 , e ) 125
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 10 x . new capacity of bucket = 2 / 5 x therefore , required number of buckets = ( 10 x ) / ( 2 x / 5 ) = ( 10 x ) x 5 / 2 x = 50 / 2 = 25 answer is a ."
Answer: a
Problem: if 30 oxen can plough 1 / 7 th of a field in 2 days , how many days 18 oxen will take to do the remaining work ?
Options: a ) 30 days , b ) 20 days , c ) 15 days , d ) 18 days , e ) 21 days
Rationale: solution : we will use work equivalence method , 30 / 18 = ( 1 / 7 ) / ( 6 / 7 ) * x / 2 ; 5 / 3 = ( 1 / 6 ) * x / 2 ; or , x = 60 / 3 = 20 days . answer : option b
Answer: b
Problem: how many two - element subsets of { 6,7 , 8,9 } are there that do not contain the pair of elements 8 and 9 ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 6 , e ) 7
Rationale: required subsets are = { 6,7 } , { 6,8 } , { 6,9 } , { 7,8 } , { 7,9 } = 5 answer : a
Answer: a
Problem: one fourth of a solution that was 10 % sugar by weight was replaced by a second solution resulting in a solution that was 14 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 74 % , b ) 64 % , c ) 42 % , d ) 28 % , e ) 26 %
Rationale: say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.14 - - > x = 0.26 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.14 - - > x = 0.26 . answer : e .
Answer: e
Problem: two - fifth of one - third of 3 - seventh of a number is 15 . what is 40 % of that number ?
Options: a ) 72 , b ) 84 , c ) 136 , d ) 140 , e ) none of these
Rationale: explanation : let the number be x . then , 2 / 5 of 1 / 3 of 3 / 7 of x = 15 = > x = ( 15 * 5 / 3 * 3 * 5 / 2 ) = 525 / 2 40 % of 525 / 2 = ( 40 / 100 * 525 / 2 ) = 105 answer is e
Answer: e
Problem: when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 522.416 is divided by 0.0168 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 7
Rationale: "for the 1 st no . there are 3 digits after decimal for the 2 nd no . there are 5 digits after decimal total no . of decimals = 8 req . no . of digits = ( n - 1 ) = ( 8 - 1 ) = 7 answer : e"
Answer: e
Problem: there are 69 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 39 , e ) 32
Rationale: "lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 69 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 69 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 39 answer : d"
Answer: d
Problem: an employee ’ s annual salary was increased $ 25,000 . if her new annual salary now equals $ 90,000 , what was the percent increase ?
Options: a ) 15 % , b ) 162 ⁄ 3 % , c ) 20 % , d ) 38.46 % , e ) 24 %
Rationale: new annual salary = $ 90,000 salary increase = $ 25,000 . original salary = $ 90,000 - $ 25,000 . = $ 75,000 % increase = ( $ 25,000 / $ 65,000 ) * 100 = 38.46 % hence d .
Answer: d
Problem: 30 men can do a work in 40 days . when should 15 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 87 days , b ) 10 days , c ) 15 days , d ) 44 days , e ) 22 days
Rationale: total work to be done = 30 * 40 = 1200 let 15 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 15 * 40 ) = 1200 40 p = 600 = > p = 15 days answer : c
Answer: c
Problem: a car averages 70 mph for the first 4 hours of a trip and averages 60 mph for each additional hour . the average speed for the entire trip was 65 mph . how many hours long is the trip ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let the time for which car averages 60 mph = t 65 * ( t + 4 ) = 70 * 4 + 60 t = > 5 t = 20 = > t = 4 total duration of the trip = 4 + 4 = 8 answer a"
Answer: a
Problem: the speed of the boat in still water in 12 kmph . it can travel downstream through 39 kms in 3 hrs . in what time would it cover the same distance upstream ?
Options: a ) 3.5 hours , b ) 6 hours , c ) 4 hours , d ) 5 hours , e ) 6 hours
Rationale: "still water = 12 km / hr downstream = 39 / 3 = 13 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 13 / 2 = 11 km / hr so time taken in upstream = 39 / 11 = 3.5 hrs answer : a"
Answer: a
Problem: if n = 7 ^ 11 – 7 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: always divide the power ( incase 11 ) by 4 and use the remainder as the new power . the question now becomes 7 ^ 3 - 7 . now 7 ^ 3 has last digit 3 . since 7 ^ 11 ( or for that matter 7 ^ 3 ) is greater than 7 , we subtract 7 from 13 ( the 10 + 3 - - > 10 has come from carry over from the tenth place ) . thus 13 - 7 = 6 is the answer . option d
Answer: d
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 14 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 525 $ , d ) 456 $ , e ) 480 $
Rationale: "total cost = ( 1.75 * 14 ) + ( 0.65 * 14 * 55 ) = 24.5 + 500.5 = > 525 hence answer will be ( c ) 525"
Answer: c
Problem: in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 14 feet between each tree . how many trees can be planted if the road is 151 feet long ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 14 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 14 feet spaces will be t - 1 . then , the length of sidewalk required for 14 feet spaces will be 14 * ( t - 1 ) it is given that total lenght of sidewalk is 166 feet . or 14 ( t - 1 ) + t = 151 or 14 t - 14 + t = 151 or 15 t = 165 or t = 11 answer : - d"
Answer: d
Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability q that the next couple the maitre ' d seats will not order dessert ?
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Rationale: "could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . q = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %"
Answer: b
Problem: the product of two numbers is 120 and the sum of their squares is 289 . the sum of the number is :
Options: a ) 23 , b ) 20 , c ) 12 , d ) 128 , e ) 171
Rationale: "let the numbers be x and y . then , xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . answer a"
Answer: a
Problem: when tom works alone he chops 2 lb . salad in 3 minutes , and when tammy works alone she chops 3 lb . salad in 2 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tammy is what percent greater than the quantifying chopped by tom ? .
Options: a ) 44 % , b ) 125 % , c ) 105 % , d ) 225 % , e ) 400 %
Rationale: tom chops 4 lbs in 6 minutes tammy chops 9 lbs in 6 minutes so in the same amount of time , tammy chops 125 % more than tom , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . ans : b
Answer: b
Problem: the population of a town is 8000 . it decreases annually at the rate of 10 % p . a . what will be its population after 3 years ?
Options: a ) 5100 , b ) 5120 , c ) 5200 , d ) 5400 , e ) 5832
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 90 / 100 ã — 90 / 100 x 90 / 100 = 5832 answer : e"
Answer: e
Problem: a reduction of 30 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 2.8 , b ) 2.3 , c ) 2.5 , d ) 2.1 , e ) 4.3
Rationale: "100 * ( 30 / 100 ) = 30 - - - 10 ? - - - 1 = > rs . 3 100 - - - 70 ? - - - 3 = > rs . 4.3 answer : e"
Answer: e
Problem: what is the sum of all the even numbers between 31 and 99 , inclusive ?
Options: a ) 3,000 , b ) 2,562 , c ) 2,500 , d ) 2,180 , e ) 2,766
Rationale: "to figure this problem out , you just have to add all the even numbers , starting with 32 . 32 + 34 + 36 + 38 and so on , all the way up to 98 . you ' ll get 2,180 , so final answer : d"
Answer: d
Problem: a certain farmer pays $ 30 per acre per month to rent farmland . how much does the farmer pay per month to rent a rectangular plot of farmland that is 1080 feet by 605 feet ? ( 43,560 square feet = 1 acre )
Options: a ) $ 5,330 , b ) $ 3,360 , c ) $ 450 , d ) $ 360 , e ) $ 150
Rationale: basically the question an error . 1 acre = 43,560 square feet and if it is then the answer is 450 ( c )
Answer: c
Problem: according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 25 , by how much does the temperature in degrees celsius ( c ) increase ?
Options: a ) 9 , b ) 13.88 , c ) 47 , d ) 48 3 / 5 , e ) 59
Rationale: "you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 25 = 57 - - > c = 5 / 9 * 25 = 13.88 . increase = 13.88 degrees . answer : b ."
Answer: b
Problem: kamal obtained 76 , 60 , 72 , 65 and 82 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 71 , b ) 69 , c ) 72 , d ) 75 , e ) none
Rationale: "sol . average = 76 + 60 + 72 + 65 + 82 / 5 ) = ( 355 / 5 ) = 71 . answer a"
Answer: a
Problem: a person buys an article at rs . 550 . at what price should he sell the article so as to make a profit of 30 % ?
Options: a ) 600 , b ) 715 , c ) 772 , d ) 662 , e ) 521
Rationale: "cost price = rs . 550 profit = 30 % of 550 = rs . 165 selling price = cost price + profit = 550 + 165 = 715 answer : b"
Answer: b
Problem: an article with cost price of 280 is sold at 30 % profit . what is the selling price ?
Options: a ) 198 , b ) 364 , c ) 369 , d ) 207 , e ) 210
Rationale: "sp = 1.30 * 280 = 364 answer : b"
Answer: b
Problem: john can type a set of pages in 5 hours at a constant rate . if john types for 3 hours and jack does the rest of the job , who works at 2 / 5 constant rate of john . how long will it take for jack alone to do the rest of the job ?
Options: a ) 1 hrs , b ) 3 hrs , c ) 4 hrs , d ) 5 hrs , e ) 7 hrs
Rationale: john will do 3 / 5 in 3 hrs , so john does 3 / 5 of the work . . therefore , jack will do the remaining 2 / 5 th work alone . . as the speed of jack is 2 / 5 rate of john , jack will do the 2 / 5 th work in same time that john takes to complete full job . . . ans 5 d
Answer: d
Problem: a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 30 % , what should be the sale price of the mixed tea ?
Options: a ) 23.75 , b ) 22 , c ) 20.8 , d ) 19.2 , e ) none of these
Rationale: "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 30 ) / 100 × 16 = 20.8 answer c"
Answer: c
Problem: two persons a and b can complete a piece of work in 15 days and 30 days respectively . if they work together , what part of the work will be completed in 5 days ?
Options: a ) 1 / 8 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 5 / 3
Rationale: "a ' s one day ' s work = 1 / 15 b ' s one day ' s work = 1 / 30 ( a + b ) ' s one day ' s work = 1 / 15 + 1 / 30 = 1 / 10 the part of the work completed in 5 days = 5 ( 1 / 10 ) = 1 / 2 . answer : d"
Answer: d
Problem: the temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 ( 2 ^ - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 50 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 63.75 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: "answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant “ a ” . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 50 minutes after it was poured is : f = 120 ( 2 ^ - 50 / 10 ) + 60 f = 120 * 1 / 32 + 60 f = 15 / 4 + 60 f = 255 / 4 = 63.75 a"
Answer: a
Problem: water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 40 ° c , what is the temperature of the pot of water in ° f ?
Options: a ) 85 ° f , b ) 92 ° f , c ) 96 ° f , d ) 99 ° f , e ) 104 ° f
Rationale: "let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 40 ) / 5 + 32 = 104 ° f the answer is e ."
Answer: e
Problem: the number of natural numbers n such that ( n + 1 ) ^ 2 / ( n + 7 ) is an integer , is ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: we can use ( n + 1 ) ^ 2 greater than ( n + 7 ) which gives n > 2 , - 3 . . . . . . . . now there are four integers - 2 . - 1 , 01 in between - 3 and 2 . so answer is 4 . answer : a
Answer: a
Problem: total dinning bill of 8 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 11.84 , b ) 12.84 , c ) 23.84 , d ) 19.11 , e ) 10.12
Rationale: "dinner bill of 8 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 8 = $ 19.11 answer : d"
Answer: d
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 100 . what is the value of x ?
Options: a ) 50 , b ) 100 , c ) 200 , d ) 1,000 , e ) 2,000
Rationale: "y = 50 % of 50 % 0 f x = x / 4 and y / 100 of x = 100 y / 100 * 4 y = 100 y = 50 and x = 200 answer - c"
Answer: c
Problem: 3 / 4 of 1 / 2 of 2 / 5 of 5060 = ?
Options: a ) 392 , b ) 759 , c ) 753 , d ) 493 , e ) 540
Rationale: "b 759 ? = 5060 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 759"
Answer: b
Problem: the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 18 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.2 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) none of the above
Rationale: sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 18 = 402 hence , new average = 402 ⁄ 10 = 40.2 answer a
Answer: a
Problem: how many integers between 100 and 190 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 50
Rationale: "the total numbers between 100 and 190 , inclusive , is 91 . 3 * 34 = 102 and 3 * 63 = 189 so the number of multiples of 3 is 30 . 5 * 20 = 100 and 5 * 38 = 190 so the number of multiples of 5 is 19 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 12 = 180 so the number of multiples of 15 is 6 . thus the total number is 91 - 30 - 19 + 6 = 48 . the answer is d ."
Answer: d
Problem: $ 300 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is
Options: a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 120 , e ) $ 250
Rationale: "a : ( b + c ) = 2 : 3 a ' s share = 300 * 2 / 5 = $ 120 answer is d"
Answer: d
Problem: what is the cp of rs 100 stock at 4 discount , with 1 / 5 % brokerage ?
Options: a ) 96.9 , b ) 96.3 , c ) 96.2 , d ) 96.7 , e ) 96.21
Rationale: explanation : use the formula , cp = 100 – discount + brokerage % cp = 100 - 4 + 1 / 5 96.2 thus the cp is rs 96.2 . answer : c
Answer: c