regisss/math_qa huggingface dataset:
Problem: in one alloy there is 15 % chromium while in another alloy it is 8 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 8.8 % , b ) 9 % , c ) 10.1 % , d ) 8.6 % , e ) 8.4 %
Rationale: "the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.15 * 15 + 0.08 * 35 = 5.05 kg , so the percentage is 5.05 / 50 * 100 = 10.1 % . answer : c ."
Answer: c
Problem: working alone , sawyer finishes cleaning half the house in a third of the time it takes nick to clean the entire house alone . sawyer alone cleans the entire house in 6 hours . how many hours will it take nick and sawyer to clean the entire house if they work together ?
Options: a ) 1.5 , b ) 2 , c ) 2.4 , d ) 3 , e ) 3.6
Rationale: answer is 3.6 hours . sawyer does the complete house in 6 hours while nick does it in 9 hours . 1 / ( 1 / 6 + 1 / 9 ) = 3.6 answer is e
Answer: e
Problem: if x is 30 percent greater than 88 , then x =
Options: a ) 68 , b ) 70.4 , c ) 86 , d ) 114.4 , e ) 108
Rationale: "x = 88 * 1.3 = 114.4 so the answer is d ."
Answer: d
Problem: find value for x from below equation ? x + 1 = 5
Options: a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2
Rationale: 1 . subtract 1 from both sides : x + 1 - 1 = 5 - 1 2 . simplify both sides : x = 4 c
Answer: c
Problem: what least number should be added to 1015 , so that the sum is completely divisible by 25 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 10 , e ) 5
Rationale: "1015 ã · 25 = 40 with remainder = 15 15 + 10 = 25 . hence 10 should be added to 1015 so that the sum will be divisible by 25 answer : option d"
Answer: d
Problem: the population of a city increases @ 4 % p . a . there is an additional annual increase of 4 % of the population due to the influx of job seekers , find the % increase in population after 2 years ?
Options: a ) 14.64 % , b ) 15.64 % , c ) 16.64 % , d ) 17.64 % , e ) 18.64 %
Rationale: total annual increament in population = 4 + 4 = 8 % let the population be x population after 2 years = 1.08 x + . 0864 x population increase = 1.08 x + . 0864 x - x % increase = ( ( 1.08 x + . 0864 x - x ) / x ) * 100 = ( 1.08 + . 0864 - 1 ) * 100 = . 1664 * 100 = 16.64 % answer : c
Answer: c
Problem: the sum of even numbers between 1 and 31 is :
Options: a ) 240 , b ) 789 , c ) 520 , d ) 879 , e ) 456
Rationale: explanation : let sn = ( 2 + 4 + 6 + . . . + 30 ) . this is an a . p . in which a = 2 , d = 2 and l = 30 let the number of terms be n . then a + ( n - 1 ) d = 30 = > 2 + ( n - 1 ) x 2 = 30 n = 15 . sn = n / 2 ( a + l ) = 15 / 2 x ( 2 + 30 ) = ( 15 x 16 ) = 240 . answer : a
Answer: a
Problem: a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton , how many kilos did he consume on the sixth hour ?
Options: a ) 38 , b ) 47 , c ) 50 , d ) 53 , e ) 62
Rationale: "suppose food eaten in first hour : x the ap is : x , x + 3 , x + 6 , . . . . [ number of terms ' n ' = 9 ] therefore , 9 / 2 [ 2 x + ( 9 - 1 ) * 3 ] = 450 . solving for x , x = 38 . now , 6 th term will be : x + ( 6 - 1 ) * d = 38 + 5 * 3 = 53 . hence 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 55 kg . what might be the weight of the new person ?
Options: a ) 56 kg , b ) 90 kg , c ) 75 kg , d ) data inadequate , e ) none of these
Rationale: "c 75 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 55 + 20 ) kg = 75 kg ."
Answer: c
Problem: income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 17000 , then find his savings ?
Options: a ) 3600 , b ) 3400 , c ) 3608 , d ) 3602 , e ) 3603
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 17000 = > x = 3400 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3400 . answer : b"
Answer: b
Problem: a store reduced the price of all items in the store by 8 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?
Options: a ) 80.0 , b ) 80.9 , c ) 81.0 , d ) 81.1 , e ) 82.8
Rationale: consider price of the all items as $ 100 after a initial reduction of 8 % price becomes = 0.92 * 100 = $ 92 after the final reduction of 10 % price becomes = 0.9 * 92 = $ 82.8 price of all items on second day is 82.8 % of price on first day correct answer option e
Answer: e
Problem: out of 470 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?
Options: a ) 80 , b ) 150 , c ) 100 , d ) 180 , e ) 220
Rationale: "n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 470 - 50 = 420 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 420 = 80 . answer is a"
Answer: a
Problem: in a class of 60 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?
Options: a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 54
Rationale: "formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 60 54 + not = 60 not = 60 - 54 = 6 so answer is a"
Answer: a
Problem: tom and linda stand at point a . linda begins to walk in a straight line away from tom at a constant rate of 4 miles per hour . one hour later , tom begins to jog in a straight line in the exact opposite direction at a constant rate of 9 miles per hour . if both tom and linda travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes tom to cover half of the distance that linda has covered and the amount of time it takes tom to cover twice the distance that linda has covered ?
Options: a ) 60 , b ) 72 , c ) 84 , d ) 90 , e ) 216
Rationale: e is the answer . . . . d = ts where d = distance , t = time and s = speed to travel half distance , ( 2 + 4 t ) = 9 t = = > t = 2 / 5 = = > 24 minutes to travel double distance , 2 ( 2 + 4 t ) = 9 t = = > 4 = = > 240 minutes difference , 216 minutes e
Answer: e
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 30 percent , but profits were 10 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 70 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "0,07 r = x / 100 * 0.1 r answer a"
Answer: a
Problem: p is able to do a piece of work in 15 days and q can do the same work in 20 days . if they can work together for 4 days , what is the fraction of work left ?
Options: a ) 8 / 15 , b ) 7 / 15 , c ) 1 / 15 , d ) 3 / 15 , e ) none of these
Rationale: explanation : p ' s 1 - day work = 1 / 15 q ' s 1 - day work = 1 / 20 work done by ( p + q ) in 1 day = 1 / 15 + 1 / 20 = 7 / 60 . work done by them in 4 days = ( 7 / 60 ) * 4 = 7 / 15 . work left = 1 - ( 7 / 15 ) = 8 / 15 . answer is a
Answer: a
Problem: of the five - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 24440 , b ) 36440 , c ) 72440 , d ) 181440 , e ) 216440
Rationale: "of the five - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for p - 9 ways ; choosing the digit for q - 8 ways ; choosing the digit for r - 7 ways ; choosing the digit for s - 6 ways ; # of permutations of 3 digits in ppqrs - 5 ! / 2 ! total : 9 * 8 * 7 * 6 * 5 ! / 2 ! = 181440 . answer : d ."
Answer: d
Problem: when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 30 % water ?
Options: a ) 1.2 kg , b ) 1.5 kg , c ) 1.4 kg , d ) 1.9 kg , e ) none of these
Rationale: "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 70 % ( 100 - 30 ) . therefore 0.5 x amount of flower - nectar = 0.70 x amount of honey = 0.70 x 1 kg therefore amount of flower - nectar needed = ( 0.70 / 0.51 ) kg = 1.4 kgs answer : c"
Answer: c
Problem: for any integer m greater than 1 , $ m denotes the product of all the integers from 1 to m , inclusive . how many prime numbers are there between $ 7 + 2 and $ 7 + 10 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: $ is basically a factorial of a number . so , we are asked to find the number of primes between 7 ! + 2 and 7 ! + 10 , inclusive . from each number 7 ! + k were 2 ≤ k ≤ 102 ≤ k ≤ 10 we can factor out k , thus there are no pries in the given range . for example : 7 ! + 2 = 2 ( 3 * 4 * 5 * 6 * 7 + 1 ) - - > a multiple of 2 , thus not a prime ; 7 ! + 3 = 3 ( 2 * 4 * 5 * 6 * 7 + 1 ) - - > a multiple of 3 , thus not a prime ; . . . 7 ! + 10 = 10 ( 3 * 4 * 6 * 7 + 1 ) - - > a multiple of 10 , thus not a prime . answer : a .
Answer: a
Problem: excluding stoppages , the speed of a train is 50 kmph and including stoppages it is 30 kmph . of how many minutes does the train stop per hour ?
Options: a ) 82 , b ) 17 , c ) 12 , d ) 24 , e ) 18
Rationale: "explanation : t = 20 / 50 * 60 = 24 answer : option d"
Answer: d
Problem: find the constant k so that : - x 2 - ( k + 9 ) x - 8 = - ( x - 2 ) ( x - 4 )
Options: a ) 11 , b ) 12 , c ) 15 , d ) 14 , e ) 19
Rationale: - x 2 - ( k + 9 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 9 ) x - 8 = - x 2 + 6 x - 8 - ( k + 9 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 15 : solve the above for k correct answer c
Answer: c
Problem: a 230 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 230 , b ) 270 , c ) 260 , d ) 256 , e ) 298
Rationale: "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 2340 ) / 9 = 500 / 9 = > x = 270 . answer : b"
Answer: b
Problem: a candidate who gets 40 % of the marks fails by 40 marks . but another candidate who gets 60 % marks gets 20 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 100 marks , b ) 200 marks , c ) 160 marks , d ) 371 marks , e ) 827 marks
Rationale: "40 % - - - - - - - - - - - - 40 60 % - - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - - - 20 % - - - - - - - - - - - - - 60 40 % - - - - - - - - - - - - - - ? 120 + 40 = 160 marks answer : c"
Answer: c
Problem: two numbers are in the ratio of 1 : 2 . if 10 be added to both , their ratio changes to 3 : 5 . the greater number is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 40
Rationale: "let the ratio be x : y , given x / y = 1 / 2 , ( x + 10 ) / ( y + 10 ) = 3 / 5 = > x = 20 and y = 40 answer : e"
Answer: e
Problem: the length of the bridge , which a train 100 metres long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 230 , b ) 240 , c ) 245 , d ) 250 , e ) 275
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 100 + x ) / 30 = 25 / 2 = > 2 ( 100 + x ) = 750 = > x = 275 m . answer : option e"
Answer: e
Problem: a train running at the speed of 90 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 288 , b ) 225 , c ) 277 , d ) 272 , e ) 150
Rationale: "speed = 90 * 5 / 18 = 25 m / sec length of the train = speed * time = 25 * 9 = 225 m answer : b"
Answer: b
Problem: rs . 850 is divided so that 4 times the first share , twice the 2 nd share and twice the third share amount to the same . what is the value of the first share ?
Options: a ) s 400 , b ) s 500 , c ) s 850 , d ) s 540 , e ) s 170
Rationale: "a + b + c = 850 4 a = 2 b = 2 c = x a : b : c = 1 / 4 : 1 / 2 : 1 / 2 = 1 : 2 : 2 1 / 5 * 850 = rs 170 answer : e"
Answer: e
Problem: we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 550 . how many green hats did we buy ?
Options: a ) a ) 36 , b ) b ) 40 , c ) c ) 41 , d ) d ) 42 , e ) e ) 44
Rationale: "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 550 . 6 ( 85 - g ) + 7 g = 550 . 510 - 6 g + 7 g = 550 . g = 550 - 510 = 40 . the answer is b ."
Answer: b
Problem: solve for x and check : 6 x = 54
Options: a ) 12 , b ) 15 , c ) 5 , d ) 9 , e ) none of these
Rationale: "solution : dividing each side by 6 , we obtain ( 6 x / 6 ) = ( 54 / 6 ) therefore : x = 9 check : 6 x = 54 ( 6 * 9 ) = 54 54 = 54 answer : d"
Answer: d
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 12 percent solution will be required ?
Options: a ) 18 , b ) 20 , c ) 24 , d ) 36 , e ) 42
Rationale: let a = amount of 2 % acid and b = amount of 12 % acid . now , the equation translates to , 0.02 a + . 12 b = . 05 ( a + b ) but a + b = 60 therefore . 02 a + . 12 b = . 05 ( 60 ) = > 2 a + 12 b = 300 but b = 60 - a therefore 2 a + 12 ( 60 - a ) = 300 = > 10 a = 420 hence a = 42 . , b = 60 - 42 = 18 answer : a
Answer: a
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?
Options: a ) 16 , b ) 17 , c ) 12 , d ) 16 , e ) 16
Rationale: "t = 9 / 45 * 60 12 answer : c"
Answer: c
Problem: one - fourth of a number is greater than one - fifth of the number succeeding it by 1 . find the number .
Options: a ) 24 , b ) 42 , c ) 36 , d ) 48 , e ) 50
Rationale: number is 24 as 1 / 4 th of 24 = 6 1 / 5 th of 25 ( 24 + 1 ) = 5 6 = 5 + 1 answer : a
Answer: a
Problem: working at their respective constant rates , machine a makes 100 copies in 20 minutes and machine b makes 150 copies in 10 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?
Options: a ) 250 , b ) 425 , c ) 675 , d ) 700 , e ) 600
Rationale: "machine a can produce 100 * 30 / 20 = 150 copies and , machine b can produce 150 * 30 / 10 = 450 copies total producing 600 copies . e is the answer"
Answer: e
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 160 kilometers ?
Options: a ) 8 gallons , b ) 4 gallons , c ) 6 gallons , d ) 5.5 gallons , e ) 10 gallons
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 160 kilometers ? 160 / 40 = 4 * 1 gallon = 4 gallons correct answer b"
Answer: b
Problem: a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .
Rationale: 25 % of 2 litres = 0.5 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 2.9 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 29 % answer : d
Answer: d
Problem: cole drove from home to work at an average speed of 75 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 6 hours , how many minutes did it take cole to drive to work ?
Options: a ) 84 , b ) 136 , c ) 172 , d ) 210 , e ) 478
Rationale: "first round distance travelled ( say ) = d speed = 75 k / h time taken , t 2 = d / 75 hr second round distance traveled = d ( same distance ) speed = 105 k / h time taken , t 2 = d / 105 hr total time taken = 6 hrs therefore , 6 = d / 75 + d / 105 lcm of 75 and 105 = 525 6 = d / 75 + d / 105 = > 6 = 7 d / 525 + 5 d / 525 = > d = 525 / 2 km therefore , t 1 = d / 75 = > t 1 = 525 / ( 2 x 75 ) = > t 1 = ( 7 x 60 ) / 2 - - in minutes = > t 1 = 210 minutes . d"
Answer: d
Problem: the average of temperatures at noontime from monday to friday is 30 ; the lowest one is 20 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 10
Rationale: "average = 30 , sum of temperatures = 30 * 5 = 150 as the min temperature is 20 , max would be 150 - 4 * 20 = 30 - - > the range = 30 ( max ) - 20 ( min ) = 10 answer : e"
Answer: e
Problem: find the c . i . on a sum of rs . 10000 for 6 months at 20 % per annum , interest being compounded halfyearly ?
Options: a ) 3010 , b ) 2010 , c ) 1000 , d ) 3100 , e ) 2100
Rationale: "c . i . = 10000 ( 11 / 10 ) ^ 1 - 10000 = 1000 answer : c"
Answer: c
Problem: if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 40 minutes ?
Options: a ) 80 , b ) 100 , c ) 160 , d ) 240 , e ) 300
Rationale: "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 40 minutes the population increases by 40 x 4 = 160 people . answer . c ."
Answer: c
Problem: the average of 10 result is 42 . average of the first 7 of them is 30 and that of the last 7 is 80 . find the 8 th result ?
Options: a ) 35 , b ) 37 , c ) 70 , d ) 75 , e ) 50
Rationale: "sum of all the 10 results = 10 * 42 = 420 sum of the first 7 of them = 7 * 30 = 210 sum of the last 7 of them = 7 * 80 = 560 so , the 8 th number = 420 + 210 - 560 = 70 . c"
Answer: c
Problem: a certain boxer has agreed to pay his opponent a fee of 3 % of his total purse for every pound over the specified weight limit he weighs in . if the boxer pays his opponent a fee of $ 26250 after weighing in 7 pounds over the specified limit , what was the boxer ' s purse ?
Options: a ) $ 65,625 , b ) $ 105,000 , c ) $ 125,000 , d ) $ 183,750 , e ) $ 1 , 050,000
Rationale: . 03 * 7 = . 21 26250 / . 21 = $ 125,000 answer : c
Answer: c
Problem: what is the maximum number q of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
Options: a ) 36
b ) 32
c ) 24
d ) 21
e ) 15
Rationale: 27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get q = 24 cubes . ans . c
Answer: c
Problem: - 64 x 29 + 165 = ?
Options: a ) 2436 , b ) 2801 , c ) - 2801 , d ) - 1601 , e ) none of them
Rationale: "given exp . = - 64 x ( 30 - 1 ) + 165 = - ( 64 x 30 ) + 64 + 165 = - 1830 + 229 = - 1601 answer is d"
Answer: d
Problem: if ( c - a ) / ( c - b ) = 1 , then ( 5 b - 4 a ) / ( c - a ) =
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 2.5
Rationale: "let ' s say c = 3 , b = 1 , a = 1 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 0.5 answer a ( hopefully ) ) )"
Answer: a
Problem: two trains of length 100 m and 120 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 11 sec , b ) 70 sec , c ) 21 sec , d ) 20 sec , e ) 19 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 100 + 120 = 220 m . the time required = d / s = 220 / 20 = 11 sec . answer : a"
Answer: a
Problem: in an examination , a student scores 3 marks for every correct answer and loses 2 marks for every wrong answer . if he attempts all 100 questions and secures 300 marks , the number of questions he attempts correctly , is :
Options: a ) 150 , b ) 250 , c ) 400 , d ) 300 , e ) 100
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 100 â € “ x ) . 3 x â € “ 2 ( 100 â € “ x ) = 300 or 5 x = 500 or x = 100 . answer : e"
Answer: e
Problem: what is the % change in the area of a rectangle when its length increases by 30 % and its width decreases by 30 % ?
Options: a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 9 % decrease , e ) insufficient data
Rationale: "( 13 / 10 ) * ( 7 / 10 ) = 91 / 100 of original area 91 / 100 is a 9 % decrease from 100 / 100 - > d"
Answer: d
Problem: what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) rs . 3944
b ) rs . 3942
c ) rs . 3987
d ) rs . 3929
e ) rs . 3938
Rationale: let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 58 = rs . 3944 . answer : a
Answer: a
Problem: points a , b , c , and d , in that order , lie on a line . if ab = 3 cm , ac = 4 cm , and bd = 9 cm , what is cd , in centimeters ?
Options: a ) 1 , b ) 8 , c ) 3 , d ) 4 , e ) 5
Rationale: "putting a value to each point , lets use the following : a - 0 b - 3 ( ab = 3 ) c - 4 ( ac = 4 ) d - 12 ( bd = 9 ) cd is 12 - 4 = 8 . ans b"
Answer: b
Problem: robert is travelling on his cycle andhas calculated to reach point a at 2 pm . if he travels at 10 kmph , he will reach there at 12 pm if he travels at 15 kmph . at what speed musthe travel to reach a at 1 pm ?
Options: a ) 8 kmph , b ) 10 kmph , c ) 12 kmph , d ) 14 kmph , e ) 16 kmph
Rationale: "let the distance travelled by x km . then , x - x = 2 10 15 3 x - 2 x = 60 x = 60 km . time taken to travel 60 km at 10 km / hr = 60 hrs = 6 hrs . 10 so , robert started 6 hours before 2 p . m . i . e . , at 8 a . m . required speed = 60 kmph . = 12 kmph . 5 c"
Answer: c
Problem: find the value of m 32519 x 9999 = m ?
Options: a ) 724533811 , b ) 353654655 , c ) 545463251 , d ) 725117481 , e ) 325157481
Rationale: "32519 x 9999 = 32519 x ( 10000 - 1 ) = 32519 x 10000 - 32519 x 1 = 325190000 - 32519 = 325157481 e"
Answer: e
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 252 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 252 per week 36 x = 252 x = 7 correct option : e"
Answer: e
Problem: a can run 4 times as fast as b and gives b a start of 66 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 88 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 75 m
Rationale: speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 66 m he gains 66 * ( 4 / 3 ) i . e 88 m answer : a
Answer: a
Problem: how many multiples of 5 are there between 5 to 105 ?
Options: a ) 9 , b ) 18 , c ) 17 , d ) none of these , e ) 19
Rationale: "explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 , 85 , 90 , 95 , 100 . answer : e"
Answer: e
Problem: a and b go around a circular track of length 600 m on a cycle at speeds of 30 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 360 sec , c ) 178 sec , d ) 187 sec , e ) 189 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 600 / ( 30 * 5 / 18 ) , 600 / ( 54 * 5 / 18 ) } = 360 sec . answer : b"
Answer: b
Problem: the ratio of male to female in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one of the males and one of the females in the class ?
Options: a ) a ) 160 degree
b ) b ) 168 degree
c ) c ) 191 degree
d ) d ) 72 degree
e ) e ) 204 degree
Rationale: let the common ratio be x . . so m = 2 x and f = 3 x and total = 5 x 1 of m = 2 x and 1 of f = 3 x . . total preferring that carrer = 5 x now 5 x = 360 , so x = 360 / 5 = 72 . . so x * 8 / 3 = 72 * 8 / 3 = 192 d
Answer: d
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 20 % ?
Options: a ) 228 , b ) 480 , c ) 512 , d ) 288 , e ) 276
Rationale: sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 25 % = 25 % of 640 = rs . 128 sp = cp - loss = 640 - 128 = rs . 512 answer : c
Answer: c
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 9540 , what is the length of the plot in metres ?
Options: a ) 20 , b ) 200 , c ) 300 , d ) 400 , e ) 100
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 9540 [ 4 l - 40 ] = 9540 / 26.50 = 360 4 l = 400 l = 400 / 4 = 100 meters . answer : e"
Answer: e
Problem: what is the greatest of 3 consecutive integers whose sum is 36 ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "36 / 3 = 12 the three numbers are 11 , 12 , and 13 . the answer is b ."
Answer: b
Problem: each of the 43 points is placed either inside or on the surface of a perfect sphere . if 16 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ?
Options: a ) 3 , b ) 11 , c ) 13 , d ) 23 , e ) 38
Rationale: "maximum number of points on the surface is 16 % * 43 = 6.88 . . . or 6 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 6 points , so at best we can form 3 pairs ( 6 ) . so , answer is ( a )"
Answer: a
Problem: xavier starts from p towards q at a speed of 60 kmph and after every 12 mins increases his speed by 10 kmph . if the distance between p and q is 60 km , then how much time does he take to cover the distance ?
Options: a ) 48 , b ) 59 , c ) 60 , d ) 56 , e ) 50
Rationale: "first 12 min = 60 * 12 / 60 = 12 km 2 nd 12 min = 70 * 12 / 60 = 14 km 3 rd 12 min = 80 * 12 / 60 = 16 km 4 th 12 min = 90 * 12 / 60 = 18 km total time 12.4 = 48 min a"
Answer: a
Problem: a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 6000 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 42000 , d ) 34000 , e ) none of these
Rationale: explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 6000 = > total profit = 6000 * 7 = 42000 . answer : option c
Answer: c
Problem: the average of 5 quantities is 11 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 21.5 , b ) 10.6 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: "answer : a ( 5 x 11 - 3 x 4 ) / 2 = 21.5"
Answer: a
Problem: 10 % of a number is added to 45 , the result is the same number . find the number ?
Options: a ) 50 , b ) 288 , c ) 270 , d ) 129 , e ) 281
Rationale: "( 10 / 100 ) * x + 45 = x 9 x = 450 x = 50 answer : a"
Answer: a
Problem: if 4 x + y + z = 80 , 2 x - y - z = 4003 x + y - z = 20 for integers of x , y and z , find x = ?
Options: a ) 10 , b ) 20 , c ) 15 , d ) 26 , e ) 18
Rationale: 4 x + y + z = 80 - - - - - - - - - - 1 ) 2 x - y - z = 40 - - - - - - - - - - - - - 2 ) 3 x + y - z = 20 - - - - - - - - - - - - 3 ) from 1 ) and 2 ) 6 x = 120 x = 20 answer is b
Answer: b
Problem: calculate how much time could be saved if the train would run at its usual speed , given that it ran at 5 / 7 of its own speed and got to its destination in 15 hours ?
Options: a ) 1.29 hrs , b ) 2.29 hrs , c ) 4.29 hrs , d ) 5.29 hrs , e ) 3.29 hrs
Rationale: "new speed = 5 / 7 of usual speed new time = 5 / 7 of usual time 5 / 7 of usual time = 15 hrs usual time = 15 * 5 / 7 = 10.71 hrs time saved = 15 - 10.71 = 4.29 hrs answer is c"
Answer: c
Problem: find the average of first 10 multiples of 7
Options: a ) 35.5 , b ) 37.5 , c ) 38.5 , d ) 40.5 , e ) none of these
Rationale: "explanation : = 7 ( 1 + 2 + 3 + . . . + 10 ) 10 = 7 ( 10 ( 10 + 1 ) ) 10 × 2 = 7 ( 110 ) 10 × 2 = 38.5 answer : option c"
Answer: c
Problem: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 9 : 17 . the first number ?
Options: a ) 36 , b ) 86 , c ) 27 , d ) 86 , e ) 27
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 9 : 17 x = 12 = > 3 x = 36 answer : a"
Answer: a
Problem: john makes $ 30 a week from his job . he earns a raise and now makes $ 40 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 18 % , d ) 21 % , e ) 33.33 %
Rationale: "increase = ( 10 / 30 ) * 100 = 33.33 % . e"
Answer: e
Problem: a truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minutes . the ratio of their speeds is ?
Options: a ) 1 : 2 , b ) 3 : 4 , c ) 2 : 5 , d ) 3 : 7 , e ) 1 : 3
Rationale: ratio of speeds = ( 550 / 60 ) 18 / 5 : 60 * 33 / 45 = 33 : 44 = 3 : 4 answer is b
Answer: b
Problem: a particular library has 150 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 122 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "the total number of books is 150 . 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 122 books , thus the number of un - returned books is 150 - 122 = 28 books . 0.35 x = 28 x = 80 the answer is c ."
Answer: c
Problem: a batsman in his 12 th innings makes a score of 48 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 26 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 48 ∴ x = 26 answer a"
Answer: a
Problem: the average of 1 st 3 of 4 numbers is 7 and of the last 3 are 5 . if the sum of the first and the last number is 13 . what is the last numbers ?
Options: a ) 4 , b ) 5 , c ) 3.5 , d ) 7 , e ) 8
Rationale: "a + b + c = 21 b + c + d = 15 a + d = 13 a – d = 6 a + d = 13 2 d = 7 d = 3.5 answer : c"
Answer: c
Problem: the size of a flat - screen television is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 24 - inch flat - screen television than a square 17 - inch flat - screen television ?
Options: a ) 143.5 , b ) 154 , c ) 160 , d ) 148.75 , e ) 142.25
Rationale: "if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 24 - inch flat - screen television the diagonal ( hypotenuse ) = 24 so , we can apply the pythagorean theorem to get x ² + x ² = 24 ² simplify : 2 x ² = 24 ² divide both sides by 2 to get : x ² = 24 ² / 2 since the area of the square = x ² , we can see that the area of this square is 24 ² / 2 square 17 - inch flat - screen television the diagonal ( hypotenuse ) = 17 so , we can apply the pythagorean theorem to get x ² + x ² = 17 ² simplify : 2 x ² = 17 ² divide both sides by 2 to get : x ² = 17 ² / 2 since the area of the square = x ² , we can see that the area of this square is 17 ² / 2 difference in areas = 24 ² / 2 - 17 ² / 2 = 288 - 144.5 i . e = 143.5 a"
Answer: a
Problem: the average weight of 8 persons 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 kg , b ) 76.5 kg , c ) 85 kg , d ) 90 kg , e ) none
Rationale: "sol . total weight increased = ( 8 × 2.5 ) kg = 20 kg . weight of new person = ( 65 + 20 ) kg = 85 kg . answer c"
Answer: c
Problem: a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 6 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?
Options: a ) 3 / 8 , b ) 1 / 2 , c ) 11 / 16 , d ) 5 / 8 , e ) 3 / 4
Rationale: "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 6 / 8 * c : ( b + c ) / 2 = ( 6 / 8 ) * c b = ( 1 / 2 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 1 / 2 * c ) / 2 = ( 1 / 4 ) * c median = ( a + c ) / 2 = ( 1 / 4 * c + c ) / 2 = ( 5 / 4 ) * c / 2 = ( 5 / 8 ) * c ( answer d )"
Answer: d
Problem: line q has the equation 5 y – 3 x = 75 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )
Options: a ) 48 , b ) 52 , c ) 56 , d ) 60 , e ) 64
Rationale: "5 y - 3 x = 75 and so y = 3 x / 5 + 15 when x = 0 , then y = 15 . when y = 0 , then x = - 25 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 25 , 0 ) , 0 = - 5 ( - 25 ) / 3 + c the y - intercept is c = - 125 / 3 < - 41 . thus the perpendicular line s can have y - intercepts from - 41 up to 14 . the number of possible lines is 41 + 14 + 1 = 56 the answer is c ."
Answer: c
Problem: a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 5 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
Options: a ) $ 1100 , b ) $ 1240 , c ) $ 1360 , d ) $ 1480 , e ) $ 1550
Rationale: "the total surface area is 2 ( 2 * 3 + 3 * 5 + 2 * 5 ) = 62 square feet the total cost is 62 * $ 20 = $ 1240 the answer is b ."
Answer: b
Problem: two concentric circles form a ring . the inner and outer circumference of the ring are 352 / 7 m and 528 / 7 m respectively . find the width of the ring .
Options: a ) 2
b ) 4
c ) 5
d ) 6
e ) 78
Rationale: explanation : let the inner and outer radii be r and r meters then , \ inline { \ color { black } 2 \ prod r } = 352 / 7 = > r = ( 352 / 7 ) * ( 7 / 22 ) * ( 1 / 2 ) = 8 m \ inline { \ color { black } 2 \ prod r } = 528 / 7 = > r = ( 528 / 7 ) * ( 7 / 22 ) * ( 1 / 2 ) = 12 m width of the ring = r - r = 12 - 8 = 4 m answer : b ) 4
Answer: b
Problem: a shopkeeper sold an article for rs 2564.36 . approximately what was his profit percent if the cost price of the article was rs 2300
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 12 %
Rationale: "explanation : gain % = ( 264.36 * 100 / 2300 ) = 11.49 % = 12 % approx option e"
Answer: e
Problem: in a recent election , geoff received 0.5 percent of the 6000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3000 more votes to win the election , what is the value of x ?
Options: a ) 50 , b ) 50.5 , c ) 56 , d ) 60 , e ) 63
Rationale: word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 30 votes he needs 3571 more votes so : 30 + 3000 = 3030 now what ' s the problem wants ? ? a x % . . . . . . . . 3030 is what % of total votes 6000 . . . . . . . . translating : 3030 = x / 100 * 6000 - - - x = 50.5 % . . . . . . . . . . b
Answer: b
Problem: a certain electric - company plan offers customers reduced rates for electricity used between 8 p . m . and 8 a . m . weekdays and 24 hours a day saturdays and sundays . under this plan , the reduced rates w apply to what fraction of a week ?
Options: a ) 1 / 2 , b ) 5 / 8 , c ) 9 / 14 , d ) 16 / 21 , e ) 9 / 10
Rationale: "number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates w / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c"
Answer: c
Problem: the sum of two consecutive number is 115 . which is the larger number ?
Options: a ) 42 , b ) 58 , c ) 44 , d ) 45 , e ) 46
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 115 2 x + 1 = 115 2 x = 114 x = 57 therefore larger number is x + 1 = 58 answer : b"
Answer: b
Problem: three pipes a , b and c can fill a tank from empty to full in 20 minutes , 20 minutes and 30 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution p in the liquid in the tank after 3 minutes ?
Options: a ) 3 / 8 , b ) 2 / 8 , c ) 6 / 7 , d ) 3 / 5 , e ) 2 / 5
Rationale: "part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 20 + 1 / 20 + 1 / 30 ) = 6 / 15 part filled by a in 3 minutes = 3 / 20 required ratio = 3 / 20 * 15 / 6 = 3 / 8 answer : a"
Answer: a
Problem: if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 36 then sum is
Options: a ) s . 5000 , b ) s . 5100 , c ) s . 5800 , d ) s . 6000 , e ) s . 3600
Rationale: "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 36 3600 answer : e"
Answer: e
Problem: the ratio of ducks and frogs in a pond is 31 : 39 respectively . the average number of ducks and frogs in the pond is 152 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 152 , c ) 156 , d ) 169 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 31 : 39 . average of ducks and frogs in pond , = 152 . so , total number of ducks and frogs in the pond , = 2 * 152 = 304 . therefore , number of frogs , = ( 304 * 39 ) / 70 = 169 . answer : option d"
Answer: d
Problem: x is a positive number which when increased by 17 is equal to 60 times the reciprocal of the number . find value of x ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: let the number be x . then , x + 17 = 60 x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 a
Answer: a
Problem: a man invests rs . 6,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 3000 , e ) none of these
Rationale: "explanation : interest on rs . 6000 at 5 % per annum = ( 6000 × 5 × 1 ) / 100 = rs . 300 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 6000 + x ) × 6 × 1 / 100 . = > 300 + 2 x / 25 = ( 6000 + x ) × 6 × 1 / 100 . = > 30000 + 8 x = ( 6000 + x ) × 6 . = > 30000 + 8 x = 36000 + 6 x . = > 2 x = 6000 . = > x = 3000 . answer : d"
Answer: d
Problem: the lcm of two numbers is 2310 and hcf is 47 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 715 , b ) 825 , c ) 330 , d ) 582 , e ) 517
Rationale: first number * second number = lcm * hcf other number = 2310 * 47 / 210 = 11 * 47 = 517 answer : e
Answer: e
Problem: a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 70 percent greater than the wholesale price . if the retailer decreases the retail price by 30 percent this will have the same effect as increasing the wholesale price by what percent ?
Options: a ) 26 , b ) 37.5 , c ) 42 , d ) 19 , e ) 50
Rationale: "answer : d = 19 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 70 % increase makes retail price = 170 . now 30 % decrease - > ( 1 - 30 / 100 ) * 170 = 119 . now compared to the wholesale price of 100 , 19 % increase is what will have the same effect as increasing the wholesale price ."
Answer: d
Problem: machine p and machine q are each used to manufacture 220 sprockets . it takes machine p 10 hours longer to produce 220 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 2 , c ) 55 , d ) 95 , e ) 125
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 220 / x = 220 / 1.1 x + 10 1.1 ( 220 ) = 220 + 11 x 11 x = 22 x = 2 the answer is b ."
Answer: b
Problem: the diagonal of a square is twice the side of equilateral triangle then the ratio of area of the triangle to the area of square is ?
Options: a ) 3 √ 9
b ) 3 √ 8
c ) 3 √ 7
d ) 3 √ 5
e ) 3 √ 1
Rationale: let the side of equilateral triangle = 1 unit . we know that area of an equilateral triangle = 3 – √ 4 a 234 a 2 as side = 1 unit area of the equilateral triangle = 3 – √ 434 now diagonal of the square = 2 ( side of the equilateral triangle ) = 2 we know that area of the square = 12 d 212 d 2 where d = diagonal so area of the square = 12 ( 22 ) = 212 ( 22 ) = 2 ratio of the areas of equilateral triangle and square = 3 – √ 434 : 2 ⇒ ⇒ 3 √ 8 answer : b
Answer: b
Problem: the average mark of the students of a class in a particular exam is 65 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 14 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "let the number of students who wrote the exam be x . total marks of students = 75 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 65 x - ( 5 * 20 ) = 90 ( x - 5 ) 350 = 25 x = > x = 14 answer : a"
Answer: a
Problem: there are 24 students in a class . in how many different ways can a committee of 3 students be formed ?
Options: a ) 1250 , b ) 1800 , c ) 2024 , d ) 3256 , e ) 2864
Rationale: "24 c 3 = 24 * 23 * 22 / 6 = 2024 the answer is c ."
Answer: c
Problem: fred and sam are standing 35 miles apart and they start walking in a straight line toward each other at the same time . if fred walks at a constant speed of 2 miles per hour and sam walks at a constant speed of 5 miles per hour , how many miles has sam walked when they meet ?
Options: a ) 5 , b ) 9 , c ) 25 , d ) 30 , e ) 45
Rationale: relative distance = 35 miles relative speed = 2 + 5 = 7 miles per hour time taken = 35 / 7 = 5 hours distance travelled by sam = 5 * 5 = 25 miles = c
Answer: c
Problem: a camera lens filter kit containing 5 filters sells for $ 72.50 . if the filters are purchased individually , 2 of them are priced at $ 12.45 each , 2 at $ 14.05 each , 1 at $ 11.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 10.03 % , b ) 11.03 % , c ) 12.03 % , d ) 13.03 % , e ) 11 %
Rationale: cost of kit = $ 72.50 if filters are purchased individually - $ 12.45 * 2 + $ 14.05 * 2 + $ 11.50 = $ 64.50 amount saved = $ 72.50 - $ 64.50 = $ 8 required % age = ( $ 8 / $ 72.50 ) * 100 = 11.03 % so , the correct answer is b .
Answer: b
Problem: every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 1 / 2 of the juniors is equal to 2 / 3 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 4 / 7 , b ) 1 / 3 , c ) 5 / 3 , d ) 12 / 7 , e ) 17 / 20
Rationale: let total number of juniors = j total number of seniors = s ( 1 / 2 ) j = ( 2 / 3 ) s = > s = 3 / 4 j total number of students = j + s = ( 7 / 4 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 7 / 4 ) j ] = 4 / 7 answer a
Answer: a
Problem: in a certain alphabet , 10 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 6 , b ) 8 , c ) 14 , d ) 20 , e ) 28
Rationale: we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 10 + 24 = 34 ; next , we find the total # of letters without line : 40 - 34 = 6 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 6 - 0 = 6 . a
Answer: a
Problem: a certain manufacturer increased its gross profit on a product from 10 percent of the cost of the product to 15 percent of the cost by changing the selling price . if the new selling price was $ 92.00 and the cost of the product remained the same , what was the old selling price ?
Options: a ) $ 77.40 , b ) $ 80.00 , c ) $ 83.64 , d ) $ 87.40 , e ) $ 88.00
Rationale: given that { cost of the product } * 1.15 = $ 92 - - > { cost of the product } = $ 80 . the old price was $ 80 * 1.1 = $ 88 . answer : e .
Answer: e
Problem: in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 65 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 47 %
Rationale: "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.65 = 39 democrats are expected to vote for candidate a ; 40 * 0.20 = 8 republicans are expected to vote for candidate a . thus total of 39 + 8 = 47 registered voters are expected to vote for candidate a , which is 47 % of the total number of registered voters . answer : e ."
Answer: e
Problem: the smallest number when increased by ` ` 2 ` ` is exactly divisible by 12 , 30 , 48 , 74 and 100 is :
Options: a ) 14439 , b ) 44398 , c ) 44400 , d ) 44402 , e ) 15005
Rationale: "lcm = 44400 44400 - 2 = 44398 answer : b"
Answer: b
Problem: how many integers between 1 and 1400 are divisible by 25 , and 35 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: lcm of the given numbers = 175 therefore , number of integers = 1400 / 175 = 8 answer is option e
Answer: e