regisss/math_qa huggingface dataset:
Problem: a cylindrical container with 6 meters diameter and a height of 8 meters is filled to capacity with water . if the water is then used to fill several smaller cylinders ( 2 meters radius and 5 meters height ) , how many smaller cylinders can be filled to capacity before the larger cylinder becomes empty ?
Options: a ) 5
b ) 4
c ) 3
d ) 2
e ) 1
Rationale: calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = π r 2 h larger cylinder volume = 226.19 smaller cylinder volume = 62.83 therefore the number of smaller cylinders can be filled to capacity = 226.19 / 62.83 = 3.6 answer is c only 3 smaller cylinders can be filled to capacity .
Answer: c
Problem: four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is. four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is
Options: a ) 12
b ) 32
c ) 42
d ) 52
e ) 58
Rationale: required area = 14 * 14 - ( 4 * 1 / 4 * 22 / 7 * 7 * 7 ) sq cm = 196 - 154 = 42 sq cm . answer : c
Answer: c
Problem: the roof of an apartment building is rectangular and its length is 5 times longer than its width . if the area of the roof is 720 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 48 .
Rationale: "answer is e : 48 let w be the width , so length is 5 w . therefore : w * 5 w = 720 , solving for , w = 12 , so 5 w - w = 4 w = 4 * 12 = 48"
Answer: e
Problem: jaclyn buys $ 10 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 237.5 , b ) 234 , c ) 289.5 , d ) 345 , e ) none of these
Rationale: explanation : i = ( p x r x t ) / 100 = 10000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 237.5 answer : a
Answer: a
Problem: two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 40 kmph respectively . in what time will they cross each other completely ?
Options: a ) 15 sec , b ) 19 sec , c ) 12 sec , d ) 10 sec , e ) 11 sec
Rationale: "explanation : d = 250 m + 250 m = 500 m rs = 80 + 40 = 120 * 5 / 18 = 100 / 3 t = 500 * 3 / 100 = 15 sec answer : option a"
Answer: a
Problem: at garage sale , all of the prices of the items sold were different . if the price of a radio sold at the garage sale was both the 15 th highest price and the 25 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 33 , b ) 34 , c ) 35 , d ) 39 , e ) 37
Rationale: "14 + 24 + 1 = 39 answer : d"
Answer: d
Problem: in a division sum , the quotient is 20 , the divisor 66 and the remainder 55 , find the dividend ?
Options: a ) 1375 , b ) 1376 , c ) 1875 , d ) 1365 , e ) 1345
Rationale: "explanation : 20 * 66 + 55 = 1375 answer : a"
Answer: a
Problem: a and b are two partially filled buckets of water . if 6 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 6 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 66 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: let bucket a be a and bucket b be b scenario 1 a - 6 = 1 / 3 ( b + 6 ) - - - - > 3 a - 18 = b + 6 scenario 2 b - 6 = 1 / 2 ( a + 6 ) - - - - - > 2 b - 12 = a + 6 from scenario 1 , b = 3 a - 24 substitute b with this information in stmt 2 2 ( 3 a - 24 ) - 12 = a + 6 - - - - - - > 6 a - 48 - 12 = a + 6 - - - - - - > 6 a - a = 60 + 6 - - - > 5 a = 66 a = 66 / 5 , answer choice a
Answer: a
Problem: what is the total cost of 2 sandwiches at $ 2.49 each and 4 sodas at $ 1.87 each ?
Options: a ) $ 3.36 , b ) $ 6.85 , c ) $ 8.46 , d ) $ 10.08 , e ) $ 12.46
Rationale: "answer = e 2 * 2.49 + 4 * 1.87 = 2 ( 2.50 - 0.01 ) + 4 ( 2.00 - 0.13 ) = 5 + 8 - 0.02 - 0.52 = 13 - 0.54 = 12.46"
Answer: e
Problem: the sum of ages of 4 children born 1 years different each is 38 years . what is the age of the elder child ?
Options: a ) 8 , b ) 11 , c ) 10 , d ) 16 , e ) 17
Rationale: "let the ages of children be x , ( x + 1 ) , ( x + 2 ) , ( x + 3 ) years . then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 38 4 x = 32 x = 8 . x + 3 = 8 + 3 = 11 answer : b"
Answer: b
Problem: what is the positive integer that can be added by 595 to make it a perfect square ?
Options: a ) 2 * 3 * 6
b ) 3 * 2 * 5
c ) 5 * 3 * 3
d ) 2 * 3
e ) 3 * 5 * 4
Rationale: 596 is added to a number that gives a perfect square nearest perfect square is 625 . so , 625 - 596 = 30 30 = 2 * 3 * 5 option b is answer
Answer: b
Problem: after a storm deposits 110 billion gallons of water into the city reservoir , the reservoir is 60 % full . if the original contents of the reservoir totaled 220 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 40 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 %
Rationale: when the storm deposited 110 billion gallons , volume of water in the reservoir = 220 + 110 = 360 billion gallons if this is only 60 % of the capacity of the reservoir , the total capacity of the reservoir = 330 / 0.6 = 550 billion gallons therefore percentage of reservoir that was full before the storm = ( 220 / 550 ) * 100 = 40 % option a
Answer: a
Problem: ( 6 ) 6.5 × ( 36 ) 4.5 ÷ ( 216 ) 4.5 = ( 6 ) ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "explanation : ( 6 ) 6.5 × ( 36 ) 4.5 ÷ ( 216 ) 4.5 = ( 6 ) 6.5 × [ ( 6 ) 2 ] 4.5 ÷ [ ( 6 ) 3 ] 4.5 = ( 6 ) 6.5 × ( 6 ) 9 ÷ ( 6 ) 13.5 = ( 6 ) ( 6.5 + 9 - 13.5 ) = ( 6 ) 2 answer : option b"
Answer: b
Problem: a rectangular grass field is 75 m * 55 m , it has a path of 3.2 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) s . 1350 , b ) s . 1327 , c ) s . 1328 , d ) s . 1364 , e ) s . 1927
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 3.2 * 2 ) 2 * 2.5 = > 682 682 * 2 = rs . 1364 answer : d"
Answer: d
Problem: a fill pipe can fill 1 / 2 of cistern in 20 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 5 min , b ) 10 min , c ) 15 min , d ) 20 min , e ) 25 min
Rationale: required time = 20 * 2 * 1 / 2 = 20 minutes answer is d
Answer: d
Problem: what is the average of 120 , 130 , 140 , 510 , 520 , 530 , 1115 , 1120 , and 1125 ?
Options: a ) 419 , b ) 551 , c ) 601 , d ) 590 , e ) 721
Rationale: "add 120 , 130 , 140 , 510 , 520 , 530 , 1115 , 1120 , and 1125 grouping numbers together may quicken the addition sum = 5310 5310 / 9 = 590 . d"
Answer: d
Problem: a bus travels from town a to town b . if the bus ' s speed is 50 km / hr , it will arrive in town b 42 min later than scheduled . if the bus increases its speed by 509509 m / sec , it will arrive in town b 30 min earlier than scheduled . find : a ) the distance between the two towns ; b ) the bus ' s scheduled time of arrival in b ; c ) the speed of the bus when it ' s on schedule .
Options: a ) 60 , b ) 37 , c ) 26 , d ) 28 , e ) 11
Rationale: first we will determine the speed of the bus following its increase . the speed is increased by 509509 m / sec = 50 ⋅ 60 ⋅ 6091000 = 50 ⋅ 60 ⋅ 6091000 km / hr = 20 = 20 km / hr . therefore , the new speed is v = 50 + 20 = 70 v = 50 + 20 = 70 km / hr . if xx is the number of hours according to the schedule , then at the speed of 50 km / hr the bus travels from a to b within ( x + 4260 ) ( x + 4260 ) hr . when the speed of the bus is v = 70 v = 70 km / hr , the travel time is x − 3060 x − 3060 hr . then 50 ( x + 4260 ) = 70 ( x − 3060 ) 50 ( x + 4260 ) = 70 ( x − 3060 ) 5 ( x + 710 ) = 7 ( x − 12 ) 5 ( x + 710 ) = 7 ( x − 12 ) 72 + 72 = 7 x − 5 x 72 + 72 = 7 x − 5 x 2 x = 72 x = 7 x = 72 x = 72 hr . so , the bus is scheduled to make the trip in 33 hr 3030 min . the distance between the two towns is 70 ( 72 − 12 ) = 70 ⋅ 3 = 21070 ( 72 − 12 ) = 70 ⋅ 3 = 210 km and the scheduled speed is 210 / 7 / 2 = 60 km / hr . answer : a
Answer: a
Problem: how many numbers from 10 to 100000 are exactly divisible by 9 ?
Options: a ) 900 , b ) 11110 , c ) 1100 , d ) 1200 , e ) 1400
Rationale: "10 / 9 = 1 and 100000 / 9 = 11111 = = > 11111 - 1 = 11110 . answer : b"
Answer: b
Problem: if 10 litres of an oil of rs . 40 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 48.66 , b ) rs . 51.03 , c ) rs . 54.17 , d ) rs . 55.33 , e ) none of the above
Rationale: "40 * 10 = 400 66 * 5 = 330 730 / 15 = 48.66 answer : a"
Answer: a
Problem: tom wants to buy items costing $ 25.35 , $ 70.69 , and $ 85.96 . he earns $ 6.50 an hour doing odd jobs . if ten percent of his income is put aside for other purposes , how many hours must he work to earn the money he needs for his purchases ? round your answer to the nearest whole hour .
Options: a ) 8 hours , b ) 48 hours , c ) 31 hours , d ) 18 hours , e ) 28 hours
Rationale: $ 6.50 x . 10 = $ . 65 is 10 % of his hourly income $ 6.50 - . 65 = $ 5.85 hourly amount available to spend $ 25.35 + $ 70.69 + $ 85.96 = $ 182 total needed $ 182 ÷ $ 5.85 = 31.11 . . . rounds to 31 hours correct answer c
Answer: c
Problem: a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 1.8 kilometer long bridge , at the same speed ?
Options: a ) 4 min , b ) 2 min , c ) 8 min , d ) 9 min , e ) 3 min
Rationale: s = 600 / 40 = 15 mps s = 1800 / 15 = 120 sec = 2 min . answer : b
Answer: b
Problem: a small college reduced its faculty by approximately 13 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 208 , c ) 224 , d ) 254 , e ) 302
Rationale: "f x is the original number of faculty members , then after 13 % reduction in faculty members number is . 87 x but we are given . 87 x = 195 x = 224 so the original number of faculty members is 224 correct answer - c"
Answer: c
Problem: the probability that a man will be alive for 10 more yrs is 3 / 4 & the probability that his wife will alive for 10 more yrs is 1 / 5 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 2 , b ) 1 , c ) 2 / 3 , d ) 1 / 5 , e ) 2
Rationale: "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 5 ans . ( d )"
Answer: d
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 2.9 , b ) 2.2 , c ) 2.5 , d ) 2.1 , e ) 2.3
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 100 - - - 80 ? - - - 2 = > rs . 2.5 answer : c"
Answer: c
Problem: a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter . )
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24
Rationale: "let ' s start with 4 minimum number of colors so single color code we can make 4 nos . now if we need to make 2 color combination out of 4 we can do so in 4 ! / 2 ! * 2 ! or 4 * 3 / 2 or 6 so total we can make 4 + 6 = 10 color combinations but we have 12 boxes so let ' s look at 5 we get 5 single color codes and out 5 color choices , we can choose 2 in 5 ! / 2 ! * 3 ! ways or 10 ways . so total we can have 5 + 10 = 15 color combinations . so , minimum number we need will be 5 ans is b . . . . . . ."
Answer: b
Problem: the present worth of a sum due sometime hence is rs . 576 and the banker ’ s gain is rs . 16 . the true discount is
Options: a ) rs . 36 , b ) rs . 72 , c ) rs . 48 , d ) rs . 96 , e ) none
Rationale: solution t . d = √ p . w xb . g = √ 576 x 16 = 96 . answer d
Answer: d
Problem: two trains are moving in the same direction at 90 kmph and 36 kmph . the faster train crosses a man in the slower train in 29 seconds . find the length of the faster train ?
Options: a ) 425 , b ) 435 , c ) 445 , d ) 455 , e ) 465
Rationale: "relative speed = ( 90 - 36 ) * 5 / 18 = 3 * 5 = 15 mps . distance covered in 29 sec = 29 * 15 = 435 m . the length of the faster train = 435 m . answer : b"
Answer: b
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 5 minutes , then the area of the park ( in sq . m ) is :
Options: a ) 153601 , b ) 153600 , c ) 153602 , d ) 60000 , e ) 153604
Rationale: "perimeter = distance covered in 5 min . = ( 12000 / 60 ) x 5 m = 1000 m . let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1000 or x = 100 . length = 300 m and breadth = 200 m . area = ( 300 x 200 ) m 2 = 60000 m 2 . answer : d"
Answer: d
Problem: the value of a machine depreciates at the rate of 10 % every year . it was purchased 3 years ago . if its present value is rs . 8748 , its purchase price was :
Options: a ) 12003 , b ) 12000 , c ) 12002 , d ) 12289 , e ) 12019
Rationale: "explanation : = rs . 12000 answer : b ) 12000"
Answer: b
Problem: solve for x the equation log 9 ( x 3 ) = log 2 ( 8 )
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: log 9 ( x 3 ) = log 2 ( 8 ) : given log 2 ( 23 ) = 3 : simplify right hand side of given equation . log 9 ( x 3 ) = 3 : rewrite the above equation log 9 ( x 3 ) = log 9 ( 93 ) : rewite 3 as a log base 9 . x 3 = 93 : obtain algebraic equation from eqaution d . x = 9 : solve above for x correct answer a
Answer: a
Problem: there are 6 more women than there are men on a local co - ed softball team . if there are a total of 16 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 6 / 16 , c ) 4 / 16 , d ) 5 / 11 , e ) 4 / 10
Rationale: "w = m + 6 w + m = 16 m + 6 + m = 16 2 m = 10 m = 5 w = 11 ratio : 5 : 11 ans : d"
Answer: d
Problem: salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 25 % vinegar , dressing p comprises what percentage of the new dressing ?
Options: a ) 75 % , b ) 60 % , c ) 40 % , d ) 25 % , e ) 20 %
Rationale: "let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.25 0.2 x = 0.15 x = 0.75 = 75 % the answer is a ."
Answer: a
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 135 grams of water ?
Options: a ) 120 , b ) 116 , c ) 112 , d ) 108 , e ) 104
Rationale: "( 16 / 18 ) * 144 = 120 grams the answer is a ."
Answer: a
Problem: a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 63 km downstream .
Options: a ) 3 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours
Rationale: "explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 63 / 21 = 3 hours option a"
Answer: a
Problem: john and jacob set out together on bicycle traveling at 15 and 12 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john two hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 15 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible )
Options: a ) 7 , b ) 7 1 / 3 , c ) 7 1 / 2 , d ) 4 , e ) 7 1 / 2
Rationale: "john ' s speed - 15 miles / hr jacob ' s speed - 12 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 15 x 2 / 3 = 10 miles . jacob continues to ride for a total of 2 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 2 hour 40 min ( i . e 8 / 3 hr ) = 12 x 8 / 3 = 32 miles . now , when john starts riding back , the distance between them is 22 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 15 - 12 = 3 miles / hr . thus , to cover 22 miles at 3 miles / hr , john will take 22 / 3 = 7 1 / 3 hours answer b"
Answer: b
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 600 m long ?
Options: a ) 266 sec , b ) 180 sec , c ) 776 sec , d ) 166 sec , e ) 997 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1800 m t = d / s t = 1800 / 10 t = 180 sec answer : b"
Answer: b
Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability v that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability v = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Problem: a rectangular plot 15 m × 10 m , has a path of grass outside it . if the area of grassy pathway is 54 m 2 , find the width of the path .
Options: a ) 4 m
b ) 3 m
c ) 2 m
d ) 1 m
e ) none of these
Rationale: let the width of the path = w m then , length of plot with path = ( 15 + 2 w ) m and breadth of plot with path = ( 10 + 2 w ) m therefore , area of rectangular plot ( without path ) = 15 × 10 = 150 m 2 and area of rectangular plot ( with path ) = 150 + 54 = 204 m 2 hence , ( 15 + 2 w ) × ( 10 + 2 w ) = 204 ⇒ 4 w 2 + 50 w – 54 = 0 ⇒ 2 w 2 + 25 w – 27 = 0 ⇒ ( w – 2 ) ( w + 27 ) = 0 thus w = 2 or – 27 ∴ with of the path = 2 m answer c
Answer: c
Problem: if a car had traveled 40 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 120 km , at what speed did it travel ?
Options: a ) 50 kmh , b ) 60 kmh , c ) 70 kmh , d ) 80 kmh , e ) 90 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 120 / x - 120 / ( x + 40 ) = 1 / 2 substitute the value of x from the options . - - > x = 80 - - > 120 / 80 - 120 / 120 = 3 / 2 - 1 = 1 / 2 answer : d"
Answer: d
Problem: a grocer has a sale of rs . 3435 , rs . 3927 , rs . 3855 , rs . 4230 and rs . 3562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 3500 ?
Options: a ) s . 1991 , b ) s . 2991 , c ) s . 3991 , d ) s . 4991 , e ) s . 5991
Rationale: "explanation : total sale for 5 months = rs . ( 3435 + 3927 + 3855 + 4230 + 3562 ) = rs . 19009 . required sale = rs . [ ( 3500 x 6 ) â € “ 19009 ] = rs . ( 21000 â € “ 19009 ) = rs . 1991 . answer a"
Answer: a
Problem: what is the probability of getting a number less than 4 when a die is rolled ?
Options: a ) 5 / 5 , b ) 1 / 2 , c ) 5 / 1 , d ) 5 / 7 , e ) 5 / 2
Rationale: "total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) i . e . , n ( s ) = 6 e = getting a number less than 4 = { 1 , 2 , 3 } hence , n ( e ) = 3 the probability = 3 / 6 = 1 / 2 . answer : b"
Answer: b
Problem: a 270 m long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 second . what is the length of the other train ?
Options: a ) 150 m , b ) 230 m , c ) 290 m , d ) 310 m , e ) 420 m
Rationale: relative speed = 120 + 80 = 200 * 5 / 18 = 500 / 9 m / s let the length of the other train be x meters x + 270 / 9 = 500 / 9 x = 230 m answer is b
Answer: b
Problem: two trains of equal length , running with the speeds of 60 and 40 kmph , take 40 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 sec , b ) 16 sec , c ) 13 sec , d ) 67 sec , e ) 8 sec
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 40 d = 40 * 100 / 18 = 2000 / 9 rs = 60 + 40 = 100 * 5 / 18 t = 2000 / 9 * 18 / 500 = 8 sec answer : e"
Answer: e
Problem: a dog takes 2 leaps for every 3 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 1 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 4 : 5 , e ) 6 : 5
Rationale: "explanation : dog : hare = ( 2 * 3 ) leaps of hare : 3 leaps of hare = 6 : 5 . answer : e ) 6 : 5"
Answer: e
Problem: in a group of pigs and hens , the number of legs are 22 more than twice the number of heads . the number of pigs is
Options: a ) 5 , b ) 7 , c ) 10 , d ) 12 , e ) 11
Rationale: explanation : let the number of pigs be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 22 4 x + 2 y = 2 x + 2 y + 22 2 x = 22 x = 11 answer : e
Answer: e
Problem: x + y = 19 , and x + 3 y = 1 . find the value of x + 2 y
Options: a ) 20 , b ) 18 , c ) 11 , d ) 10 , e ) 5
Rationale: add these two equations 2 x + 4 y = 20 divide by 2 ( to get x + 2 y ) answer will be d . 10
Answer: d
Problem: in the fifth grade at parkway elementary school there are 470 students . 300 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 135 . , c ) 81 . , d ) 91 . , e ) 108 .
Rationale: "total students = 470 boys = 300 , girls = 170 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 170 - 35 = 135 . correct option : b"
Answer: b
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length ?
Options: a ) 18.9 sec , b ) 88.9 sec , c ) 22.9 sec , d ) 30.00 sec , e ) 72.0 sec
Rationale: "d = 110 + 390 = 500 m s = 60 * 5 / 18 = 50 / 3 t = 500 * 3 / 50 = 30 sec answer : d"
Answer: d
Problem: a can finish a work in 24 days , b in 9 days and c in 12 days . b and c start the work but are forced to leave after 3 days . when a done the work ?
Options: a ) 10 days , b ) 12 days , c ) 13 days , d ) 9 days , e ) 14 days
Rationale: "b + c = = > 1 / 9 + 1 / 12 = 7 / 36 b , c = in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 24 work is done by a in 1 day 5 / 12 work is done a 24 * 5 / 12 = 10 days answer a"
Answer: a
Problem: in a recent election , james received 1.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 901 , b ) 989 , c ) 990 , d ) 971 , e ) 1,001
Rationale: "james = ( 1.5 / 100 ) * 2000 = 30 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 30 = 971 answer : option d"
Answer: d
Problem: jolene entered an 18 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 10 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
Options: a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24
Rationale: if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 726.24 . answer : b .
Answer: b
Problem: walking 4 / 3 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 16 , c ) 27 , d ) 28 , e ) 20
Rationale: "speed ratio = 1 : 4 / 3 = 3 : 4 time ratio = 4 : 3 1 - - - - - - - - 4 4 - - - - - - - - - ? 16 m . answer : b"
Answer: b
Problem: which is the least number that must be subtracted from 1256 so that the remainder when divided by 7 , 12 , 16 is 4 ?
Options: a ) 242 , b ) 232 , c ) 236 , d ) 240 , e ) 244
Rationale: "first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 4 will be { 336 + 4 , 336 x 2 + 4 , 336 x 3 + 4 , . . . } the largest such number less than or equal to 1256 is 336 x 3 + 4 or 1012 to obtain this you need to subtract 244 . e"
Answer: e
Problem: if n is the smallest integer such that 108 times n is the square of an integer , what is the value of n ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 12 , e ) 24
Rationale: "108 can written as = 2 * 2 * 3 * 3 * 3 - - > 2 ^ 2 * 3 ^ 3 - - - ( 1 ) so for 108 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 2 to make the power of 2 in ( 1 ) even option a is correct"
Answer: a
Problem: of the 500 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 40 percent of the employees prefer city y and 60 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?
Options: a ) 65 , b ) 100 , c ) 115 , d ) 130 , e ) 325
Rationale: "300 prefer x ( group 1 ) ; 200 prefer y ( group 2 ) . city y needs 375 people : letall 200 who prefer y ( entire group 2 ) be relocated there , the rest 175 will be those who prefer x from group 1 ; city x needs 125 people : 300 - 175 = 125 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 200 + 125 = 325 . answer : e ."
Answer: e
Problem: the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 11 . what is the last numbers ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "a + b + c = 18 b + c + d = 15 a + d = 11 a – d = 3 a + d = 11 2 d = 8 d = 4 answer : a"
Answer: a
Problem: if the cost price of 50 articles is equal to the selling price of 35 articles , then the gain or loss percent is ?
Options: a ) 16 , b ) 127 , c ) 12 , d ) 18 , e ) 43
Rationale: "percentage of profit = 15 / 35 * 100 = 43 % answer : e"
Answer: e
Problem: a batch of cookies was divided amomg 3 tins : 3 / 4 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 3 / 5 , e ) 9 / 7
Rationale: "this will help reduce the number of variables you have to deal with : g + b = 3 / 4 r = 1 / 3 b = 1 / 4 we can solve for g which is 1 / 2 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 1 / 2 + 1 / 3 ) = 1 / 2 x = 3 / 5 answer : d"
Answer: d
Problem: 10 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
Options: a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 1260
Rationale: "no . of ways of picking 2 biology books ( from 10 books ) = 10 c 2 = ( 10 * 9 ) / 2 = 45 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 45 * 28 = 1260 ( option e )"
Answer: e
Problem: a grocer has a sale of rs . 6400 , rs . 7000 , rs . 6800 , rs . 7200 and rs . 6500 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) rs . 4500 , b ) rs . 4700 , c ) rs . 4800 , d ) rs . 5000 , e ) rs . 5100
Rationale: "total sale for 5 months = rs . ( 6400 + 7000 + 6800 + 7200 + 6500 ) = rs . 33900 required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 33900 ) = rs . 5100 answer : e"
Answer: e
Problem: given that a is the average ( arithmetic mean ) of the first 5 positive multiples of 6 and b is the median of the first 12 positive multiples of 6 , what is the ratio of a to b ?
Options: a ) 3 : 4 , b ) 6 : 13 , c ) 5 : 6 , d ) 13 : 10 , e ) 4 : 3
Rationale: the first nine positive multiples of six are { 6 , 12 , 18 , 24,30 } the first twelve positive multiples of six are { 6 , 12 , 18 , 24 , 30 , 36,42 , 48 , 54 , 60 , 66 , 72 } both sets are evenly spaced , thus their median = mean : a = 18 and b = ( 36 + 42 ) / 2 = 39 - - > a / b = 18 / 39 = 6 / 13 . answer : b .
Answer: b
Problem: find the compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually .
Options: a ) rs . 610 , b ) rs . 612 , c ) rs . 614 , d ) rs . 616 , e ) none of these
Rationale: "explanation : amount = [ 7500 × ( 1 + 4100 ) 2 ] = ( 7500 × 2625 × 2625 ) = 8112 so compound interest = ( 8112 - 7500 ) = 612 answer : b"
Answer: b
Problem: how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 13 inches than that of a rectangular sheet of paper measuring 6.5 inches by 11 inches ?
Options: a ) 50 %
b ) 87 %
c ) 100 %
d ) 187 %
e ) 200 %
Rationale: let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 13 is twice 6.5 then the area will be double which means 100 % greater . the answer is c .
Answer: c
Problem: in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,9 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 9 , e ) 4 / 5
Rationale: "the area of the right triangle is ( 1 / 2 ) * 4 * 9 = 18 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 18 = 2 / 9 the answer is d ."
Answer: d
Problem: if a sum of money doubles itself in 5 years at simple interest , the ratepercent per annum is
Options: a ) 12 , b ) 12.5 , c ) 20 , d ) 13.5 , e ) 14
Rationale: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 5 ) = 20 option c"
Answer: c
Problem: elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 52 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 28 , e ) $ 29
Rationale: "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 52 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 52 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 52 i . e . x = 24 i . e . fixed monthly charge , y = 28 answer : option d"
Answer: d
Problem: a started a business with an investment of rs . 70000 and after 9 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 76000 , then the share of b is ?
Options: a ) 33008 , b ) 24000 , c ) 28000 , d ) 48000 , e ) 81122
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 3 ) = 7 : 12 total profit = rs . 76000 share of b = 12 / 19 ( 76000 ) = rs . 48000 answer : d"
Answer: d
Problem: how many 7 in between 1 to 110 ?
Options: a ) 18 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78 , 79,87 , 97,107 21 7 ' s between 1 to 110 answer : b"
Answer: b
Problem: a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3000 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 1800 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 120 so , a ’ s amount = 120 × 15 = rs . 1800 . answer : option c"
Answer: c
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 78000 , then the share of b is ?
Options: a ) a ) 34500 , b ) b ) 36099 , c ) c ) 36000 , d ) d ) 38007 , e ) e ) 42000
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 78000 share of b = 6 / 13 ( 78000 ) = rs . 36000 answer : c"
Answer: c
Problem: if an object travels 90 feet in 3 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 17.36 , b ) 20.45 , c ) 23.87 , d ) 26.92 , e ) 29.56
Rationale: "90 feet / 3 seconds = 30 feet / second ( 30 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 20.45 miles / hour ( approximately ) the answer is b ."
Answer: b
Problem: if 2 x + y = 7 and x + 2 y = 5 , then xy / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 xy / 3 = 3 * 1 / 3 = 1 a"
Answer: a
Problem: there are 21 students in a class . in how many different ways can a committee of 3 students be formed ?
Options: a ) 1180 , b ) 1330 , c ) 1540 , d ) 1760 , e ) 1920
Rationale: "21 c 3 = 21 * 20 * 19 / 6 = 1330 the answer is b ."
Answer: b
Problem: the average age of boys in a class is 16 years and that of the girls is 15 years . the average age for the whole class is
Options: a ) 15 years , b ) 15.5 years , c ) 16 years , d ) 17 years , e ) can not be computed
Rationale: "clearly , to find the average , we ought to know the numbers of boys , girls or students in the class , neither of which has been given . so the data provided is inadequate . answer : e"
Answer: e
Problem: of 800 surveyed students , 20 % of those who read book a also read book b and 25 % of those who read book b also read book a . if each student read at least one of the books , what is the difference between the number of students who read only book a and the number of students who read only book b ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 55 , e ) 100
Rationale: "say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 25 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.25 b - - > a = 1.25 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 800 = 1.25 b + b - 0.25 b - - > b = 400 , a = 1.25 b = 500 and { both } = 0.25 b = 100 . the number of students who read only book a is { a } - { both } = 500 - 100 = 400 ; the number of students who read only book b is { b } - { both } = 400 - 100 = 300 ; the difference is 400 - 300 = 100 . answer : e ."
Answer: e
Problem: what annual payment will discharge a debt of rs . 1090 due in 2 years at the rate of 5 % compound interest ?
Options: a ) 993.2 , b ) 586.21 , c ) 534.33 , d ) 543.33 , e ) 646.33
Rationale: explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1090 820 x + 1090 * 441 x = 586.21 so , value of each installment = rs . 586.21 answer : option b
Answer: b
Problem: a man sells a car to his friend at 15 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 22941.18 , b ) rs . 32941.18 , c ) rs . 52941.18 , d ) rs . 62941.18 , e ) none of these
Rationale: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 15 % . now s . p = rs . 45000 and loss = 15 % c . p . rs . [ 100 / 85 ã — 45000 ] = rs . 52941.18 correct option : c"
Answer: c
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 399 , b ) 272 , c ) 666 , d ) 277 , e ) 311
Rationale: "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1 = 666 answer : c"
Answer: c
Problem: how many 0 ' s are there in the binary form of 6 * 1024 + 4 * 64 + 2
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 9
Rationale: 6 * 1024 + 4 * 64 + 2 = 6144 + 256 + 2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2 . so 9 zeros are there . answer : e
Answer: e
Problem: what is 7 1 / 4 - 4 2 / 3 divided by 7 / 8 - 3 / 4 ?
Options: a ) 87 / 36 , b ) 36 / 17 , c ) 7 / 6 , d ) 62 / 3 , e ) 5 / 4
Rationale: "7 1 / 4 - 4 2 / 3 = 29 / 4 - 14 / 3 = ( 87 - 56 ) / 12 = 31 / 12 7 / 8 - 3 / 4 = ( 7 - 6 ) / 8 = 1 / 8 so 31 / 12 / 1 / 8 = 31 / 12 * 8 = 62 / 3 answer - d"
Answer: d
Problem: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 225 , then the mean profit for the last 15 days would be
Options: a ) rs . 200 , b ) rs . 350 , c ) rs . 475 , d ) rs . 425 , e ) none of these
Rationale: "average would be : 350 = ( 225 + x ) / 2 on solving , x = 475 . answer : c"
Answer: c
Problem: find out the c . i on rs . 8000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 489.66 , b ) 406.07 , c ) 406.04 , d ) 306.03 , e ) 306.01
Rationale: "a = 8000 ( 51 / 50 ) 3 = 8489.66 8000 - - - - - - - - - - - 489.66 answer : a"
Answer: a
Problem: jayes can eat 25 marshmallows is 20 minutes . dylan can eat 25 in one hour . in how much time will the two eat 150 marshmallows ?
Options: a ) 40 minutes . , b ) 1 hour and 30 minutes . , c ) 1 hour . , d ) 1 hour and 40 minutes . , e ) 2 hours and 15 minutes .
Rationale: rate = output / time jayes rate = 25 / 20 = 5 / 4 dylan rate = 25 / 60 = 5 / 12 combined rate = 5 / 4 + 5 / 12 = 20 / 12 combinedrate * combinedtime = combinedoutput 20 / 12 * t = 150 t = 90 mins = > 1 hr 30 min
Answer: c
Problem: how many even number in the range between 10 to 120 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 31 , d ) 37 , 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 , 10 , 12,14 . . . 120 using ap formula , we can say 120 = 10 + ( n - 1 ) * 2 or n = 56 . for 6 , 12,18 , . . . 120 using ap formula , we can say 120 = 12 + ( n - 1 ) * 6 or n = 19 . hence , only divisible by 2 but not 3 = 56 - 19 = 37 . hence , answer d"
Answer: d
Problem: in the biology lab of ` ` jefferson ' ' high school there are 0.037 * 10 ^ 5 germs , equally divided among 74000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: 0.037 * 10 ^ 5 can be written as 3700 74000 * 10 ^ ( - 3 ) can be written as 74 required = 3700 / 74 = 50 answer : e
Answer: e
Problem: the largest 4 digit number exactly divisible by 44 is ?
Options: a ) 9988 , b ) 9939 , c ) 9944 , d ) 9954 , e ) 9960
Rationale: "largest 4 - digit number = 9999 44 ) 9999 ( 227 9988 largest number : 9988 answer : a"
Answer: a
Problem: if a certain number is divided by 2 , the quotient , dividend , and divisor , added together , will amount to 62 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 40 , d ) 38 , e ) 59
Rationale: "let x = the number sought . then x / 2 + x + 2 = 62 . x = 40 . c"
Answer: c
Problem: a and b can do a work in 10 days and 15 days respectively . a starts the work and b joins him after 5 days . in how many days can they complete the remaining work ?
Options: a ) 6 days , b ) 2 days , c ) 8 days , d ) 4 days , e ) 3 days
Rationale: "work done by a in 5 days = 5 / 10 = 1 / 2 remaining work = 1 / 2 work done by both a and b in one day = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 remaining work = 1 / 2 * 6 / 1 = 3 days . answer : e"
Answer: e
Problem: for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 4 ” 2 ?
Options: a ) 5 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "4 ” 2 = 4 - 4 = 0 answer : e"
Answer: e
Problem: in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1100 employees , then the no . of female employees who are computer literate ?
Options: a ) 462 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: "solution : total employees , = 1100 female employees , 60 % of 1100 . = ( 60 * 1100 ) / 100 = 660 . then male employees , = 440 50 % of male are computer literate , = 220 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1100 ) / 100 = 682 computer literate . thus , female computer literate = 682 - 220 = 462 . answer : option a"
Answer: a
Problem: total 48 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 48 , b ) 47 , c ) 40 , d ) 42 , e ) 47
Rationale: "47 players answer : e"
Answer: e
Problem: in 130 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 20 m , b ) 25 m , c ) 22.5 m , d ) 26 m , e ) 12 m
Rationale: "distance covered by b in 9 sec . = 130 / 45 x 9 m = 26 m . a beats b by 26 metres . answer : option d"
Answer: d
Problem: at a certain university , 69 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?
Options: a ) 25 , b ) 37.5 , c ) 50 , d ) 52.5 , e ) 75
Rationale: "answer is 75 % total women = 69 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 21 % but question wants to know the percent of men that are tenured 21 % / 40 % = 52.5 % d"
Answer: d
Problem: in a dairy farm , 26 cows eat 26 bags of husk in 26 days . in how many days one cow will eat one bag of husk ?
Options: a ) 1 , b ) 40 , c ) 20 , d ) 26 , e ) 30
Rationale: "explanation : one bag of husk = 26 cows per day ⇒ 26 × 1 × 26 = 1 × 26 × x for one cow = 26 days answer : d"
Answer: d
Problem: the average age of a group of n people is 14 years old . one more person aged 34 joins the group and the new average is 16 years old . what is the value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "14 n + 34 = 16 ( n + 1 ) 2 n = 18 n = 9 the answer is c ."
Answer: c
Problem: the number 0.650 is how much greater than 1 / 8 ?
Options: a ) ½ , b ) 21 / 40 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500
Rationale: "let x be the difference then . 65 - 1 / 8 = x 65 / 100 - 1 / 8 = x x = 21 / 40 ans b"
Answer: b
Problem: if $ 1092 are divided between worker a and worker b in the ratio 5 : 8 , what is the share that worker b will get ?
Options: a ) 60.32 % , b ) 61.54 % , c ) 62.21 % , d ) 62.76 % , e ) 63.87 %
Rationale: "worker b will get 8 / 13 = 61.54 % the answer is b ."
Answer: b
Problem: a card is drawn from a pack of 52 cards the probability of getting queen of club or aking of a heart ?
Options: a ) 8 / 58 , b ) 9 / 25 , c ) 1 / 26 , d ) 6 / 25 , e ) 8 / 45
Rationale: "here n ( s ) = 52 let e be the event of getting queen of the club or king of kings n ( e ) = 2 p ( e ) = n ( e ) / n ( s ) = 2 / 52 = 1 / 26 answer ( c )"
Answer: c
Problem: 1000 men have provisions for 17 days . if 500 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.5 , c ) 11.3 , d ) 12.2 , e ) 12.1
Rationale: "1000 * 17 = 1500 * x x = 11.3 answer : c"
Answer: c
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 1 km , b ) 2 km , c ) 3 km , d ) 4 km , e ) 5 km
Rationale: "c 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 47 / 60 47 x / 60 = 47 / 60 = > x = 1 . total distance = 3 * 1 = 3 km ."
Answer: c
Problem: if x is an integer such that 0 < x < 7 , 0 < x < 15 , 5 > x > – 1 , 3 > x > 0 , and x + 2 < 4 , then x is
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "0 < x < 7 , 0 < x < 15 , 5 > x > – 1 3 > x > 0 x < 2 from above : 0 < x < 2 - - > x = 1 . answer : a ."
Answer: a
Problem: an error 5 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :
Options: a ) 10.01 , b ) 9.25 , c ) 10.25 , d ) 8.25 , e ) 6.25
Rationale: "explanation : 100 cm is read as 105 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 105 × 105 ) cm 2 = 10816 ( a 2 - a 1 ) = 11025 - 10000 = 1025 = > 1025 / 10000 * 100 = 10.25 answer : c"
Answer: c
Problem: 1 + 1
Options: a ) 9 , b ) 8 , c ) 3 , d ) 0 , e ) 2
Rationale: e
Answer: e
Problem: rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 150 . what is the share of rahul ?
Options: a ) $ 50 , b ) $ 40 , c ) $ 60 , d ) $ 100 , e ) $ 90
Rationale: "rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 150 * 2 / 5 = $ 60 answer is c"
Answer: c
Problem: a boat m leaves shore a and at the same time boat b leaves shore b . they move across the river . they met at 500 yards away from a and after that they met 300 yards away from shore b without halting at shores . find the distance between the shore a & b
Options: a ) 1000 yards , b ) 1200 yards , c ) 1400 yards , d ) 1600 yards , e ) 1800 yards
Rationale: if x is the distance , a is speed of a and b is speed of b , then ; 500 / a = ( x - 500 ) / b and ( x + 300 ) / a = ( 2 x - 300 ) / b , solving it , we get x = 1200 yards answer : b
Answer: b
Problem: a pineapple costs rs 7 each and a watermelon costs rs . 5 each . if i spend rs 38 on total what is the number of pineapple i purchased ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 2 , e ) 3
Rationale: explanation : the equation for this problem can be made as : 5 x + 7 y = 38 where x is the number of watermelons and y is the number of pineapples . now test for 2 , 3 and 4 : for y = 2 5 x + 14 = 38 x is not an integer for y = 3 5 x = 17 x not an integer for y = 4 x = 2 so 4 pineapples and 2 watermelons can be bought by 38 rs . answer : d
Answer: d
Problem: the sub - duplicate ratio of 25 : 16 is
Options: a ) 4 : 3 , b ) 1 : 2 , c ) 1 : 3 , d ) 5 : 4 , e ) 2 : 3
Rationale: "root ( 25 ) : root ( 16 ) = 5 : 4 answer : d"
Answer: d
Problem: in δ pqs above , if pq = 7 and ps = 8 , then
Options: a ) 9 / 4 , b ) 12 / 5 , c ) 56 / 9 , d ) 15 / 4 , e ) 20 / 3
Rationale: "there are two ways to calculate area of pqs . area remains same , so both are equal . 7 * 8 / 2 = pr * 9 / 2 pr = 56 / 9 c"
Answer: c
Problem: ajay can ride 50 km in 1 hour . in how many hours he can ride 1250 km ?
Options: a ) 10 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: "1 hour he ride 50 km he ride 1250 km in = 1250 / 50 * 1 = 25 hours answer is d"
Answer: d