regisss/math_qa huggingface dataset:
Problem: the moon revolves around the earth at a speed of approximately 0.9 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 61.2 , c ) 3240 , d ) 3,600 , e ) 3,672
Rationale: "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 0.9 * 3600 = 3240 kilometers per hour . option c is correct"
Answer: c
Problem: john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 60 miles per hour , what is v in miles per hour ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: "let distance be d . we can find the total time & equate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 60 = > v = 30 answer : a"
Answer: a
Problem: the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 150 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?
Options: a ) 30 , b ) 50 , c ) 70 , d ) 80 , e ) 90
Rationale: "let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 150 / ( 150 + x ) = 5 / 6 x = 30 the answer is a ."
Answer: a
Problem: divide rs . 1300 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) 346 , b ) 368 , c ) 375 , d ) 337 , e ) 325
Rationale: "a + b + c = 1300 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1300 = > 325 answer : e"
Answer: e
Problem: a boy is travelling from his home to school at 4 km / hr and reached 7 min late . next day he traveled at 8 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 2 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "let the distance be x t 1 = x / 4 hr t 2 = x / 8 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 4 - x / 8 = 1 / 4 x / 8 = 1 / 4 x = 2 km answer is a"
Answer: a
Problem: a , b and c , each working alone can complete a job in 2 , 4 and 6 days respectively . if all three of them work together to complete a job and earn $ 2500 , what will be c ' s share of the earnings ?
Options: a ) $ 1206.60 , b ) $ 1363.63 , c ) $ 1263.63 , d ) $ 1463.53 , e ) $ 1163.03
Rationale: "the dollars earned will be in the same ratio as amount of work done 1 day work of c is 1 / 6 ( or 2 / 12 ) 1 day work of the combined workforce is ( 1 / 2 + 1 / 4 + 1 / 6 ) = 11 / 12 c ' s contribution is 2 / 9 of the combined effort translating effort to $ = 6 / 11 * 2500 = $ 1363.63 hence : b"
Answer: b
Problem: according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 5 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 50 , d ) 60 , e ) 100
Rationale: orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 5 oz can = 300 oz / 5 oz = 60 answer d , 60 cans
Answer: d
Problem: each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 16 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 21
Rationale: if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 30 boxes , 6 are 10 - pound boxes and 24 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 16 , the ratio of 10 - pound boxes : 20 - pound boxes should be 2 : 3 . the number of 10 pound boxes remain the same so we still have 6 of them . to get a ratio of 2 : 3 , the number of 20 - pound boxes must be 9 . we need to remove 15 of the 20 - pound boxes . the answer is c .
Answer: c
Problem: two pipes can fill a tank in 18 minutes and 15 minutes . an outlet pipe can empty the tank in 54 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 30 minutes , b ) 17 minutes , c ) 15 minutes , d ) 6 minutes , e ) 12 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 15 - 1 / 54 = ( 15 + 18 - 5 ) / 270 = 28 / 270 = 14 / 135 so , the tank becomes full in 6 minutes . answer : d"
Answer: d
Problem: how many bricks each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall 8 m x 6 m x 22.5 m
Options: a ) 5600 , b ) 600 , c ) 6400 , d ) 7200 , e ) none of these
Rationale: "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 25 x 11.25 x 6 ) = 6400 answer : c"
Answer: c
Problem: a prize of $ 500 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?
Options: a ) $ 160 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 360
Rationale: total value of the prize = $ 500 number of people = 20 2 / 5 of 500 ( = $ 200 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 500 - 200 = $ 300 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 300 - 140 = $ 160 , hence a is the correct answer .
Answer: a
Problem: two trains , each 100 m long , moving in opposite directions , cross other in 8 sec . if one is moving twice as fast the other , then the speed of the faster train is ? a . 30 km / hr b . 45 km / hr
Options: a ) 11 , b ) 78 , c ) 60 , d ) 28 , e ) 81
Rationale: let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 8 = 3 x = > x = 25 / 3 . so , speed of the faster train = 50 / 3 = 50 / 3 * 18 / 5 = 60 km / hr . answer : c
Answer: c
Problem: a car going at 40 miles per hour set out on an 90 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ?
Options: a ) 45 , b ) 50 , c ) 53 , d ) 55 , e ) 90
Rationale: "let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 40 m per hour = 1.5 hours distance travelled by car a = 40 * 1.5 = 60 miles since car b catches up car a at 10 : 30 , time = 90 mins = 3 / 2 hour speed of car b = 60 / ( 3 / 2 ) = 90 miles per hour answer e"
Answer: e
Problem: how many bricks each measuring 30 cm x 12 cm x 10 cm , will be needed to build a wall 6 m x 4 m x 20.5 m
Options: a ) 5655 , b ) 1366 , c ) 6444 , d ) 7266 , e ) none of these
Rationale: explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 600 x 400 x 20.5 ) / ( 30 x 12 x 10 ) = 1366 answer : b
Answer: b
Problem: a , b and c can do a work in 6 , 8 and 12 days respectively doing the work together and get a payment of rs . 1800 . what is b ’ s share ?
Options: a ) 300 , b ) 245 , c ) 600 , d ) 743 , e ) 215
Rationale: c 600 wc = 1 / 6 : 1 / 8 : 1 / 12 = > 4 : 3 : 2 3 / 9 * 1800 = 600
Answer: c
Problem: how many positive integers less than 50 have a reminder 01 when divided by 4 ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "1 also gives the remainder of 1 when divided by 4 . so , there are total of 13 numbers . answer : a ."
Answer: a
Problem: the proportion of water to alcohol in solution a is 2 : 1 and the proportion of water to alcohol in solution b is 2 : 3 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 46.7 % , b ) 47.3 % , c ) 48.4 % , d ) 50.6 % , e ) 51.8 %
Rationale: "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 3 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 6 + 3 v / 10 = 14 v / 30 = 7 v / 15 . the concentration of alcohol is 7 / 15 = 46.7 % the answer is a ."
Answer: a
Problem: a worker makes a toy in every 2 h . if he works for 100 h , then how many toys will he make ?
Options: a ) 40 , b ) 54 , c ) 50 , d ) 39 , e ) none
Rationale: "no . of toys = 100 / 2 = 50 answer : c"
Answer: c
Problem: a book is bought for $ 32 and sold for $ 56 . what is the profit in percentage ?
Options: a ) 15 , b ) 35 , c ) 75 , d ) 25 , e ) 85
Rationale: 56 / 32 = 1.75 the answer is c .
Answer: c
Problem: an alloy weighing 24 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 24 , e ) 48
Rationale: "in 24 ounces , gold is 24 * ( 70 / 100 ) = 16.8 ounces . now we add x ounces of pure gold to make it 90 % gold . so 16.8 + x = ( 24 + x ) * 90 / 100 = > x = 48 . answer is e ."
Answer: e
Problem: the youngest of 4 children has siblings who are 3 , 5 , and 8 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 20 , what is the age of the youngest sibling ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "x + ( x + 3 ) + ( x + 5 ) + ( x + 8 ) = 80 4 x + 16 = 80 4 x = 64 x = 16 the answer is c ."
Answer: c
Problem: on a map the distance between two mountains is 310 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 34 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 14.83 , b ) 14.81 , c ) 14.91 , d ) 14.82 , e ) 14.12
Rationale: "explanation : since 310 inch = 136 km so 1 inch = 136 / 310 km so 34 inch = ( 136 ã — 34 ) / 310 = 14.91 km answer : c"
Answer: c
Problem: brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 100 meters . they next meet after sally has run 100 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 500
Rationale: "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 100 meters , thus second time she runs 2 * 100 = 200 meters . since second time ( when they run full circumference ) brenda runs 200 meters and sally runs 100 meters , thus the circumference is 200 + 100 = 300 meters . answer : b ."
Answer: b
Problem: for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 3 ” 3 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "3 ” 3 = 9 - 3 = 6 answer : a"
Answer: a
Problem: a river 3 m deep and 32 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 , b ) 3200 , c ) 3400 , d ) 2761 , e ) 2882
Rationale: "( 2000 * 3 * 32 ) / 60 = 3200 m 3 answer : b"
Answer: b
Problem: a factory produces 7500 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 4436 toys , b ) 5487 toys , c ) 6113 toys , d ) 1875 toys , e ) 1375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 7500 / 4 = 1875 toys correct answer d"
Answer: d
Problem: if a 7 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ?
Options: a ) 140 %
b ) 350 %
c ) 450 %
d ) 600 %
e ) 700 %
Rationale: the area a of the large cube is 7 * 7 * 6 = 294 square cm . the area of the 343 small cubes is 7 * 7 * 7 * 6 = 7 a , an increase of 600 % . the answer is d .
Answer: d
Problem: a student chose a number , multiplied it by 4 , then subtracted 142 from the result and got 110 . what was the number he chose ?
Options: a ) 58 , b ) 59 , c ) 60 , d ) 62 , e ) 63
Rationale: "let x be the number he chose , then 4 ⋅ x − 142 = 110 4 x = 252 x = 63 correct answer e"
Answer: e
Problem: a merchant purchased a jacket for $ 56 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 30 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 8 , c ) $ 4 , d ) $ 12 , e ) $ 15
Rationale: "actual cost = $ 56 sp = actual cost + mark up = actual cost + 30 % sp = 56 * 100 / 70 on sale sp = 80 / 100 ( 56 * 100 / 70 ) = 64 gross profit = $ 8 answer is b"
Answer: b
Problem: a and b can do a piece of work in 3 days , b and c in 4 days , c and a in 6 days . how long will c take to do it ?
Options: a ) 33 , b ) 77 , c ) 24 , d ) 55 , e ) 71
Rationale: "2 c = ¼ + 1 / 6 – 1 / 3 = 1 / 12 c = 1 / 24 = > 24 days answer : c"
Answer: c
Problem: how many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr
Options: a ) 25 seconds , b ) 28 seconds , c ) 30 seconds , d ) 35 seconds , e ) 40 seconds
Rationale: "explanation : relative speed = 63 - 3 = 60 km / hr = 60 * ( 5 / 18 ) = 50 / 3 m / sec time taken to pass the man will be 500 â ˆ — 3 / 50 = 30 seconds answer is c"
Answer: c
Problem: the current in a river is 3 mph . a boat can travel 21 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
Options: a ) 69 miles , b ) 88 miles , c ) 96 miles , d ) 102.8 miles , e ) 112 miles
Rationale: "upstream speed = 21 - 3 = 18 mph downstream speed = 21 + 3 = 24 mph d / 18 + d / 24 = 10 hours solving for d we get d = 102.8 answer : d"
Answer: d
Problem: if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 180 pounds . what is leo ' s current weight ?
Options: a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104
Rationale: l + k = 180 and so k = 180 - l l + 10 = 1.5 k = 1.5 ( 180 - l ) 2.5 l = 260 l = 104 the answer is e .
Answer: e
Problem: if the perimeter of a rectangular garden is 1200 m , its length when its breadth is 240 m is ?
Options: a ) 338 m , b ) 778 m , c ) 200 m , d ) 276 m , e ) 360 m
Rationale: "2 ( l + 240 ) = 1200 = > l = 360 m answer : e"
Answer: e
Problem: the volumes of two cones are in the ratio 1 : 35 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ?
Options: a ) 7 : 5 , b ) 2 : 9 , c ) 7 : 2 , d ) 2 : 2 , e ) 2 : 8
Rationale: "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 35 = ( 1 ) 2 h 1 / ( 2 ) 2 h 2 = > h 1 / h 2 = 7 / 5 i . e . h 1 : h 2 = 7 : 5 answer : a"
Answer: a
Problem: a jar of 144 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "144 = 16 * 9 = 18 * 8 there are 16 people in the group today . the answer is c ."
Answer: c
Problem: how many minutes does aditya take to cover a distance of 400 m , if he runs at a speed of 20 km / hr
Options: a ) 115 min , b ) 215 min , c ) 315 min , d ) 415 min , e ) none of these
Rationale: "explana ɵ on : we know that , time = distancespeedspeed = 20 km / hr = 20 ∗ 518 m / sec = 509 m / sec time = ( 400 ∗ 950 ) = 72 sec = 115 min answer : op ɵ on a"
Answer: a
Problem: a cyclist rides a bicycle 7 km at an average speed of 10 km / hr and again travels 10 km at an average speed of 7 km / hr . what is the average speed for the entire trip ?
Options: a ) 7.59 , b ) 7.79 , c ) 7.99 , d ) 8.19 , e ) 8.39
Rationale: distance = 17 km time = 7 / 10 + 10 / 7 = ( 49 + 100 ) / 70 = 149 / 70 hours average speed = ( 17 * 70 ) / 149 = 7.99 km / h the answer is c .
Answer: c
Problem: a train 240 m long passed a pole in 24 sec . how long will it take to pass a platform 650 m long ? a . 65
Options: a ) 28 sec , b ) 89 sec , c ) 85 sec , d ) 16 sec , e ) 15 sec
Rationale: speed = 240 / 24 = 10 m / sec . required time = ( 240 + 650 ) / 10 = 89 sec . answer : b
Answer: b
Problem: if the radius of a circle that centers at the origin is 5 , how many k points on the circle have integer coordinates ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20
Rationale: "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : k = c"
Answer: c
Problem: 1504 x 1504 = ?
Options: a ) 2262016 , b ) 2250000 , c ) 12000 , d ) 2262000 , e ) 2250016
Rationale: "1504 x 1504 = ( 1504 ) 2 = ( 1500 + 4 ) 2 = ( 1500 ) 2 + ( 4 ) 2 + ( 2 x 1500 x 4 ) = 2250000 + 16 + 12000 = 2250016 + 12000 = 2262016 a"
Answer: a
Problem: marcella has 23 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 21 , b ) 20 , c ) 19 , d ) 18 , e ) 15
Rationale: marcella has 23 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 23 pairs of shoes minus the 5 ' destroyed ' pairs yields 20 pairs that still fulfill the requirements . answer : d
Answer: d
Problem: a room 3 m 21 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 27636 , b ) 27640 , c ) 27647 , d ) 27713 , e ) 27675
Rationale: "explanation : area of the room = ( 321 x 777 ) cm 2 . size of largest square tile = h . c . f . of 321 cm and 777 cm = 3 cm . area of 1 tile = ( 3 x 3 ) cm 2 . number of tiles required = ( 321 × 777 ) / ( 3 × 3 ) = 27713 answer : option d"
Answer: d
Problem: a shopkeeper sold 15 articles at the cost price of 20 articles . then find the profit % or lost %
Options: a ) 30 % , b ) 31 % , c ) 20 % , d ) 33.33 % , e ) 40 %
Rationale: "here 15 articles selling price = 20 articles cost price so the difference = 20 - 15 = 5 % of profit = 5 * 100 / 15 = 33.33 % correct option is d"
Answer: d
Problem: the price of 2 saris and 4 shirts is rs . 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ?
Options: a ) rs . 2400 , b ) rs . 2490 , c ) rs . 2500 , d ) rs . 2550 , e ) rs . 2600
Rationale: let the price of a saree and a shirt be rs . x and rs . y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = rs . ( 12 x 200 ) = rs . 2400 . a
Answer: a
Problem: two numbers are in ratio 4 : 5 and their lcm is 180 . the smaller number is
Options: a ) 9 , b ) 15 , c ) 36 , d ) 45 , e ) none
Rationale: solution : let two numbers be 4 x and 5 x ; their lcm = 180 and hcf = x ; now , 1 st number * 2 nd number = lcm * hcf or , 4 x * 5 x = 180 * x ; or , 20 x = 180 ; or , x = 9 ; then , the smaller number = 4 * 9 = 36 . answer : option c
Answer: c
Problem: how many cubes of 25 cm edge can be put in a cubical box of 1 m edge .
Options: a ) 177 cm
b ) 100 cm
c ) 86 cm
d ) 64 cm
e ) 87 cm
Rationale: number of cubes = 100 â ˆ — 100 â ˆ — 100 / 25 â ˆ — 25 â ˆ — 25 = 64 note : 1 m = 100 cm answer : d
Answer: d
Problem: if an object travels at two feet per second , how many feet does it travel in one hour ?
Options: a ) 3488 , b ) 3778 , c ) 7200 , d ) 1800 , e ) 2881
Rationale: "explanation : if an object travels at 2 feet per second it covers 2 x 60 feet in one minute , and 2 x 60 x 60 feet in one hour . answer = 7200 answer : c ) 7200"
Answer: c
Problem: an apple orchard grows red and green apples . on the first day of harvest , 496 apples are collected . there are 3 times as many red apples as there are green apples . how many green apples were harvested ?
Options: a ) 99 , b ) 112 , c ) 118 , d ) 124 , e ) 130
Rationale: let x be the number of green apples . there were 496 total apples ; there are three times as many red apples as green apples . therefore , x + 3 x = 496 4 x = 496 x = 124 answer : d
Answer: d
Problem: what is the tenth digit to the right of the decimal point , in the decimal expansion of ( 1 / 5 ) ^ 10
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: actually 1 / 5 = 0.2 = 2 * 10 ^ - 1 so 2 ^ 10 * 10 ^ - 10 2 has sequence 24 , 86 . hence digit will be 4 answer is c
Answer: c
Problem: 100 liters of a mixture contains milk and water in the ratio 7 : 3 . if 10 liters of this mixture be replaced by 10 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 7 : 8 , b ) 8 : 3 , c ) 3 : 8 , d ) 8 : 7 , e ) 7 : 1
Rationale: "quantity of milk in 100 liters if mix = 100 * 7 / 10 = 70 liters quantity of milk in 110 liters of new mix = 80 + 10 = 80 liters quantity of water in it = 110 - 80 = 30 liters ratio of milk and water in new mix = 80 : 30 = 8 : 3 answer is b"
Answer: b
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 2 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 16 : 5 , b ) 14 : 5 , c ) 16 : 7 , d ) 19 : 5 , e ) none of these
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 2 = 5 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 / 4 + 7 / 2 = 19 / 4 = 4.75 litres as 6 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5 . answer : d"
Answer: d
Problem: a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 36 / 49 . how many marbles are in the bag ?
Options: a ) 24 , b ) 48 , c ) 84 , d ) 72 , e ) 80
Rationale: ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 36 / 49 - - > ( x - 12 ) ^ 2 = 36 / 49 x ^ 2 square rooting u have x - 12 / x = 6 / 7 or 7 x - 6 x = 84 or x = 84 c
Answer: c
Problem: 288 ã · ? ã — 15 + 270 = 405
Options: a ) 24 , b ) 25 , c ) 32 , d ) 39 , e ) 43
Rationale: "explanation : 288 ã · ? ã — 15 = 405 - 270 = 135 ( 288 ã — 15 ) / ? = 135 ? = ( 288 ã — 15 ) / 135 = 32 answer : option c"
Answer: c
Problem: how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 7 , and the digit 2 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 320
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 7 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 2 = 160 numbers with two 2 - s , 2 x 2 x 1 * 5 * 1 * 2 = 10 . thus there are 160 - 10 = 150 such numbers . answer : b ."
Answer: b
Problem: a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 8 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?
Options: a ) $ 54.00 , b ) $ 89.60 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 154.80
Rationale: "correct answer : b the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.08 ( $ 1120 ) = $ 89.60 . the correct answer is b ."
Answer: b
Problem: what is the remainder of g = 3 ^ 19 when divided by 10 ?
Options: a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9
Rationale: "i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , g = when divided by 10 , the remainder must be 7 . d"
Answer: d
Problem: what is the value of ( log 2 3 ) ( log 3 4 ) ( log 4 5 ) . . . ( log 63 64 ) ?
Options: a ) 1 / 6 , b ) 2 , c ) 5 / 2 , d ) 6 , e ) 32
Rationale: using the identity ( loga b ) ( logb c ) = loga c repeatedly , we obtain ( log 2 3 ) ( log 3 4 ) ( log 4 5 ) . . . ( log 63 64 ) = log 2 64 = 6 correct answer d
Answer: d
Problem: how many 2 x 2 x 2 cubes could fit in a box of 7 x 9 x 4 ?
Options: a ) 31 , b ) 32 , c ) 30 , d ) 33 , e ) 29
Rationale: the answer is a ) 31 . a 2 x 2 x 2 cube has an area of 8 . a 7 x 9 x 4 box has an area of 252 . if you divide 252 by 8 , you get 31.5 . since that means you can only fit 31 entire cubes in the box , the answer is 31 .
Answer: a
Problem: by selling a book for 300 , 20 % profit was earned . what is the cost price of the book ?
Options: a ) a ) 215 , b ) b ) 250 , c ) c ) 230 , d ) d ) 235 , e ) e ) 240
Rationale: "sp = 120 % of cp ; : . cp = 300 × 100 / 120 = 250 option ' b '"
Answer: b
Problem: the h . c . f . of two numbers is 15 and their l . c . m . is 420 . if one of the numbers is 375 , then the other is :
Options: a ) 12.21 , b ) 283 , c ) 16.8 , d ) 318 , e ) 32.4
Rationale: "other number = ( 15 x 420 ) / 375 = 16.8 . answer : c"
Answer: c
Problem: what is the sum of all the multiples of 10 between 0 and 85 ?
Options: a ) 500 , b ) 620 , c ) 450 , d ) 360 , e ) 440
Rationale: "the multiples of 10 between 0 and 85 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 . if these are all added together , the result is 360 . final answer : d"
Answer: d
Problem: find large number from below question the difference of two no . ' s is 1365 . on dividing the larger no . by the smaller , we get 6 as quotient and the 15 as remainder ?
Options: a ) 1456 , b ) 1563 , c ) 1546 , d ) 1643 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Problem: if | x + 2 | = 10 , what is the sum of all the possible values of x ?
Options: a ) - 16 , b ) - 13 , c ) - 4 , d ) - 2 , e ) 12
Rationale: "there will be two cases x + 2 = 10 or x + 2 = - 10 = > x = 8 or x = - 12 sum of both the values will be - 12 + 8 = - 4 answer : c"
Answer: c
Problem: in a group of cows and chickens , the number of legs was 18 more than twice the number of heads . the number of cows was :
Options: a ) 5 , b ) 7 , c ) 9 , d ) 12 , e ) 14
Rationale: "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 18 more than twice the number of heads . therefore , 2 × ( x + y ) + 18 = 4 x + 2 y . or , 2 x + 2 y + 18 = 4 x + 2 y . or , 2 x + 18 = 4 x [ subtracting 2 y from both sides ] . or , 18 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 18 = 2 x . or , x = 9 [ dividing by 2 on both sides ] . therefore , the number of cows = 9 . correct answer : c ) 9"
Answer: c
Problem: before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 3.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ?
Options: a ) 1 / 3 , b ) 1 / 30 , c ) 1 / 42 , d ) 2 , e ) 30
Rationale: pete covered 3.5 * 60 = 210 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 210 = 1 / 42 . answer : c .
Answer: c
Problem: what least number should be subtracted from 642 so that the remainder when divided by 5 , 7 , and 9 will leave in each case the same remainder 4 ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "the lcm of 5 , 7 , and 9 is 315 . the next multiple is 2 * 315 = 630 . 630 + { remainder } = 630 + 4 = 634 , which is 8 less than 642 . answer : c ."
Answer: c
Problem: 9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 6 miles per hour faster than the first runner ' s rate . how far apart , to the nearest mile , will they be after 1 / 2 hour ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 8 m / h - - > 4 m in 1 / 2 hr side 2 = 14 m / h - - > 7 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 7 ^ 2 d ^ 2 = 65 = ~ 8 answer option c"
Answer: c
Problem: a train 250 m long running at 72 kmph crosses a platform in 20 sec . what is the length of the platform ?
Options: a ) 150 m , b ) 200 m , c ) 250 m , d ) 270 m , e ) 300 m
Rationale: "d = 72 * 5 / 18 = 20 = 400 â € “ 250 = 150 m answer : a"
Answer: a
Problem: raman ' s salary was decreased by 50 % and subsequently increased by 50 % . how much percent does he loss .
Options: a ) 75 , b ) 65 , c ) 45 , d ) 25 , e ) 85
Rationale: explanation : let the origianl salary = rs . 100 it will be 150 % of ( 50 % of 100 ) = ( 150 / 100 ) * ( 50 / 100 ) * 100 = 75 so new salary is 75 , it means his loss is 25 % option d
Answer: d
Problem: if 80 % of a number is equal to four - third of another number , what is the ratio of first number to the second number ?
Options: a ) 5 : 3 , b ) 1 : 4 , c ) 3 : 7 , d ) 6 : 11 , e ) 2 : 3
Rationale: "let 80 % of a = 4 / 3 b then 80 a / 100 = 4 b / 3 4 a / 5 = 4 b / 3 a / b = 5 / 3 a : b = 5 : 3 answer is a"
Answer: a
Problem: two pipes can fill a tank in 18 minutes and 15 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 11 minutes , b ) 17 minutes , c ) 18 minutes , d ) 10 minutes , e ) 16 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 15 - 1 / 45 = ( 5 + 6 - 2 ) / 90 = 9 / 90 = 1 / 10 so , the tank becomes full in 10 minutes . answer : d :"
Answer: d
Problem: 223.124 x 11.98 ã · 6.001 + 11.11 = ?
Options: a ) 983.578 , b ) 459.121 , c ) 781.189 , d ) 656.112 , e ) 457.358
Rationale: "explanation : ? = 223.124 x 11.98 ã · 6.001 + 11.11 â ‰ ˆ ( 223.124 x 12 / 6 ) + 11.11 â ‰ ˆ 446.248 + 11.11 â ‰ ˆ 457.358 answer : option e"
Answer: e
Problem: pipe p can fill a tank in 6 hours , pipe q in 12 hours and pipe r in 24 hours . if all the pipes are open , in how many hours will the tank be filled ?
Options: a ) 2 hours , b ) 2.4 hours , c ) 3 hours , d ) 3.4 hours , e ) 4.5 hours
Rationale: "explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 6 + 1 / 12 + 1 / 24 ) = 7 / 24 all the three pipes together will fill the tank = 24 / 7 = 3.4 hours answer d"
Answer: d
Problem: 4 friends , peter , john , quincy , and andrew , are pooling their money to buy a $ 1200 item . peter has twice as much money as john . quincy has $ 20 more than peter . andrew has 15 % more than quincy . if they put all their money together and spend the $ 1200 , they will have $ 11 left . how much money does peter have ?
Options: a ) $ 320 , b ) $ 160 , c ) $ 200 , d ) $ 410 , e ) $ 325
Rationale: p = 2 j ; q = p + 20 ; a = 1.15 ( q ) p + j + q + r - 1200 = 11 p + 0.5 p + p + 20 + 1.15 ( p + 20 ) = 1211 p + 0.5 p + p + 20 + 1.15 p + 23 = 1211 p + 0.5 p + p + 1.15 p + 43 = 1211 p + 0.5 p + p + 1.15 p = 1168 3.65 p = 1168 p = 320 answer : a
Answer: a
Problem: a man travelled from the village to the post - office at the rate of 25 kmph and walked back at the rate of 4 kmph . if the whole journey took 5 hours 48 minutes , find the distance of the post - office from the village
Options: a ) 20 , b ) 87 , c ) 276 , d ) 198 , e ) 171
Rationale: explanation : average speed = ( 2 × a × b ) / ( a + b ) here a = 25 b = 4 average speed = 2 × 25 × 4 / ( 25 + 4 ) = 200 / 29 kmph . distance covered in 5 hours 48 minutes = speed × time distance = ( 200 / 29 ) × ( 29 / 5 ) = 40 kms distance covered in 5 hours 48 minutes = 40 kms distance of the post office from the village = ( 40 / 2 ) = 20 km . answer : a
Answer: a
Problem: 893.7 – 573.07 – 95.007 = ?
Options: a ) 225.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these
Rationale: "solution given expression = 893.7 - ( 573.07 + 95.007 ) = 893.7 - 668.077 = 225.623 . answer a"
Answer: a
Problem: one man traveled a distance of 61 km in 9 hrs . he traveled partly on footat 4 km / hr and partly on bicycle ta 9 km / hr . the distance traveled on foot is ?
Options: a ) 11 km , b ) 13 km , c ) 16 km , d ) 18 km , e ) 19 km
Rationale: let the distance travelled on foot be x km . then , distance travelled on bicycle = ( 61 - x ) km . so , x + ( 61 - x ) = 9 4 9 9 x + 4 ( 61 - x ) = 9 x 36 5 x = 80 x = 16 km . c
Answer: c
Problem: ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 64500 . what is his profit percent ?
Options: a ) 22 , b ) 77 , c ) 17.3 , d ) 99 , e ) 88
Rationale: "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 64500 profit ( % ) = ( 64500 - 55000 ) / 55000 * 100 = 17.3 % answer : c"
Answer: c
Problem: in the coordinate plane , points ( x , 3 ) and ( 5 , y ) are on line k . if line k passes through the origin and has slope 3 / 5 , then x + y =
Options: a ) 9 , b ) 8 , c ) 7 , d ) 5 , e ) 6
Rationale: "line k passes through the origin and has slope 3 / 5 means that its equation is y = 3 / 5 * x . thus : ( x , 3 ) = ( 3 , 5 ) and ( 5 , y ) = ( 3 , 5 ) - - > x + y = 3 + 5 = 8 . answer : b"
Answer: b
Problem: on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 30 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 14.28 %
Rationale: "0.1 m = 0.70 e = > e / m = 1 / 7 * 100 = 14.28 % so answer is e . m - # of motorists e - # of motorists exceeding speed"
Answer: e
Problem: a question paper has 2 parts , a & b , each containing 6 questions . if a student has to choose 4 from part a & 3 from part b , in how many ways can he choose the questions ?
Options: a ) 100 , b ) 200 , c ) 350 , d ) 150 , e ) 140
Rationale: "there 6 questions in part a out of which 4 question can be chosen as = 6 c 4 . similarly , 3 questions can be chosen from 6 questions of part b as = 6 c 3 . hence , total number of ways , = 6 c 4 * 6 c 3 = [ 6 ! / ( 2 ! 4 ! ) ] * [ 6 ! / ( 3 ! * 3 ! ) ] = { 15 } * { 6 * 5 * 4 * 3 / ( 3 * 2 * 1 ) } = 300 . d"
Answer: d
Problem: a man invests some money partly in 12 % stock at 132 and partly in 10 % stock at 80 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 11 : 8 , d ) 16 : 15 , e ) none
Rationale: "solution for an income of rs . 1 in 12 % stock at 132 , investment = rs . ( 132 / 12 ) = rs . 11 . for an income of rs . 1 in 10 % stock at 80 , investment = rs . ( 80 / 10 ) = rs . 8 . ∴ ratio of investments = 11 : 8 = 11 : 8 answer c"
Answer: c
Problem: george baked a total of 150 pizzas for 7 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 2
Rationale: "3 / 5 of the 150 pizzas cooked on saturday = 90 pizzas 3 / 5 of the remaining pizzas on sunday = 36 pizzas we ' re left with ( 150 - 90 - 36 ) = 24 pizzas for the remaining 5 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w th f 8 7 6 2 1 = 24 w = 6 b"
Answer: b
Problem: a train 200 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 15 sec
Rationale: "answer : c . speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 200 m at 50 / 3 m / sec = 200 * 3 / 50 sec = 12 sec"
Answer: c
Problem: at veridux corporation , there are 200 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 65
Rationale: "well , first let â € ™ s take care of the â € œ totals â €  . the numbers in the â € œ totals â €  row must add up . if 90 are females , the other 200 â € “ 90 = 110 must be males . similarly , the numbers in the â € œ totals â €  column must add up . if 40 are managers , then the other 200 â € “ 40 = 160 must be associates . now , in the â € œ associate â €  row , 135 + e = 160 , which means e = 25 â € ” the other 25 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the â € œ female â €  column : b + 25 = 90 , which means b = 65 . there are fifteen female managers in this company . thus , the answer = ( e ) ."
Answer: e
Problem: find the value of ( √ 1.21 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) is
Options: a ) 195 / 63 , b ) 145 / 63 , c ) 155 / 63 , d ) 125 / 63 , e ) 185 / 63
Rationale: "( √ 1.21 ) / ( √ 0.81 ) + ( √ 1.44 ) / ( √ 0.49 ) 11 / 9 + 12 / 7 = > ( 77 + 108 ) / 63 = > 185 / 63 answer is e ."
Answer: e
Problem: the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 49 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 49 has the form 4 k + 1 , so the units digit of 93 ^ 49 is 3 . the units digit of powers of 5 is always 5 . 3 + 5 = 8 , so the units digit is 8 . the answer is d ."
Answer: d
Problem: a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( 2 , 4 ) . what is the smallest possible area of that circle ?
Options: a ) 13 π , b ) 15.25 π , c ) 262 √ π , d ) 52 π , e ) 64 π
Rationale: "the distance between the two points is sqrt ( 61 ) . radius = sqrt ( 61 ) / 2 area = pi * ( sqrt ( 61 ) / 2 ) ^ 2 b . 15.25 π"
Answer: b
Problem: if the cost price of 20 articles is equal to the selling price of 15 articles , what is the % profit or loss made by the merchant ?
Options: a ) 25 % loss , b ) 33.33 % profit , c ) 20 % loss , d ) 20 % profit , e ) 5 % profit
Rationale: "let the cost price of 1 article be $ 1 . therefore , cost price of 20 articles = 20 * 1 = $ 20 the selling price of 15 articles = cost price of 20 articles = $ 15 . now , we know the selling price of 15 articles . let us find the cost price of 15 articles . cost price of 15 articles = 15 * 1 = $ 15 . therefore , profit made on sale of 15 articles = selling price of 15 articles - cost price of 15 articles = 20 - 15 = $ 5 . as the profit is in the positive , the merchant has made a profit of $ 5 . therefore , % loss = loss / cp * 100 % loss = 5 / 15 * 100 = 33.33 % profit . b"
Answer: b
Problem: how many positive integers less than 255 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 43 , e ) 64
Rationale: from here , it might be easier to go up in bounds of 60 , so we know that 61 - 120 gives 10 more numbers . 121 - 180 and 181 - 240 as well . this brings us up to 240 with 40 numbers . a cursory glance at the answer choices should confirm that it must be 42 , as all the other choices are very far away . the numbers 244 and 248 will come and complete the list that ’ s ( naughty or nice ) under 250 . answer choice d is correct here .
Answer: d
Problem: if 2 x + y = 10 , 2 y + z = 20 and 2 x + z = 30 . where x , y , and z are real number . what is the value of 2 x ?
Options: a ) 3 / 2 , b ) sqrt ( 15 ) , c ) sqrt ( 6 ) / 2 , d ) 15 , e ) 18
Rationale: "explanation : let , 2 x = a , 2 y = b and 2 z = c then from the question : 2 x + y = 2 x * 2 y = ab = 10 similarly , bc = 20 , ac = 30 ab / bc = 1 / 2 = > a / c = 1 / 2 and ac = 30 ( a / c ) * ac = 1 / 2 * 30 = 15 a = sqrt ( 15 ) answer : b"
Answer: b
Problem: in a factory , there are 50 % technicians and 50 % non - technicians . if the 50 % of the technicians and 50 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 50 % , b ) 57 % , c ) 52 % , d ) 22 % , e ) 42 %
Rationale: "total = 100 t = 50 nt = 50 50 * ( 50 / 100 ) = 25 50 * ( 50 / 100 ) = 25 25 + 25 = 50 = > 100 - 50 = 50 % answer : a"
Answer: a
Problem: three unbiased coins are tossed , what is the probability of getting at least 2 tails ?
Options: a ) 1 / 5 , b ) 1 / 7 , c ) 1 / 8 , d ) 1 / 2 , e ) 1 / 10
Rationale: "total cases are = 2 ^ 3 = 8 favoured cases = [ tth , tht , htt , ttt ] = 4 probability = 4 / 8 = 1 / 2 answer d"
Answer: d
Problem: 3 interviewers , x , y , and z are interviewing 40 applicants . only with 3 interviewers ' admission can an applicant be admitted . if interviewer x admitted 15 applicants , y admitted 17 applicants , and z admitted 20 applicants , at least how many applicants get the admission ?
Options: a ) 0 , b ) 2 , c ) 6 , d ) 8 , e ) 12
Rationale: if x admitted 15 are overlapping with y admission of 17 but z does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : a
Answer: a
Problem: tom traveled the entire 50 miles trip . if he did the first 15 miles of at a constant rate 20 miles per hour and the remaining trip of at a constant rate 45 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 60.40 mph , b ) 60.20 mph , c ) 55.32 mph , d ) 65.50 mph , e ) 70.25 mph
Rationale: "avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 15 + 35 ) / ( ( 15 / 20 ) + ( 35 / 45 ) ) = 50 * 180 / 149 = 60.40 mph a"
Answer: a
Problem: shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 60 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 80 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 58 , d ) 40 , e ) 46
Rationale: "nice question + 1 we have that x / 24 - ( 60 - x ) / 2 r = 40 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 58 hence answer is c"
Answer: c
Problem: a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 5 - inch increase in the length of the shoe . if the largest size of this shoe is 20 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?
Options: a ) 8.6 , b ) 9.8 , c ) 10.4 , d ) 11.2 , e ) 12.6
Rationale: "let x be the length of the size 8 shoe . then 0.2 x = 9 / 5 x = 9 inches the size 15 shoe has a length of 9 + 7 / 5 = 10.4 inches the answer is c ."
Answer: c
Problem: if the cost price of 60 articles is equal to the selling price of 50 articles , then what is the percent profit ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "let x be the cost price of one article . let y be the selling price of one article . 50 y = 60 x y = 1.2 x the answer is c ."
Answer: c
Problem: spheres a and b have their radil 40 cm and 10 cm respectively . the ratio of the surface area of a to the surface area of b is
Options: a ) 1 : 4
b ) 1 : 16
c ) 4 : 1
d ) 16 : 1
e ) none
Rationale: solution let the radil of a and b be r and r respectively . required ratio = 4 π r 2 / 4 π r 2 ‹ = › r 2 / r 2 ‹ = › ( r / r ) 2 ‹ = › ( 40 / 10 ) 2 ‹ = › 16 : 1 . answer d
Answer: d
Problem: a 6 - liter solution is 35 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?
Options: a ) 1.5 , b ) 1.8 , c ) 2.1 , d ) 2.4 , e ) 2.7
Rationale: "let x be the amount of pure alcohol required . 0.35 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 2.1 x = 1.8 liters the answer is b ."
Answer: b
Problem: 46 x 46 = ?
Options: a ) 2500 , b ) 2516 , c ) 1600 , d ) 36 , e ) 2116
Rationale: "46 x 46 = ( 46 ) 2 = ( 50 - 4 ) 2 = ( 50 ) 2 + ( 4 ) 2 - ( 2 x 50 x 4 ) = 2500 + 16 - 400 = 2516 - 400 = 2116 e )"
Answer: e
Problem: if a * b * c = 130 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) none of these
Rationale: "explanation : a ∗ b ∗ c / b ∗ c ∗ d = 130 / 65 = > a / d = 2 d ∗ e ∗ f / c ∗ d ∗ e = 250 / 1000 = > f / c = 14 a / d * f / c = 2 * 1 / 4 = 1 / 2 answer : a"
Answer: a
Problem: calculate the largest 5 digit number which is exactly divisible by 77 ?
Options: a ) 99111 , b ) 99946 , c ) 99869 , d ) 99792 , e ) 99654
Rationale: "largest 4 digit number is 99999 after doing 99999 ÷ 77 we get remainder 53 hence largest 5 digit number exactly divisible by 77 = 99999 - 53 = 99946 b"
Answer: b
Problem: working at a constant rate , p can finish a job in 4 hours . q , also working at a constant rate , can finish the same job in 20 hours . if they work together for 3 hours , how many more minutes will it take p to finish the job , working alone at his constant rate ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 21 , e ) 24
Rationale: "each hour they complete 1 / 4 + 1 / 20 = 3 / 10 of the job . in 3 hours , they complete 3 ( 3 / 10 ) = 9 / 10 of the job . the time for p to finish is ( 1 / 10 ) / ( 1 / 4 ) = ( 2 / 5 ) hour = 24 minutes the answer is e ."
Answer: e
Problem: two stations p and q are 290 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ?
Options: a ) 10 am , b ) 12 am , c ) 10.30 am , d ) 12.30 pm , e ) 2 pm
Rationale: "assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 290 = > 20 x + 25 ( x - 1 ) = 290 = > 45 x = 315 = > x = 7 means , they meet after 7 hours after 7 am , ie , they meet at 2 pm answer is e ."
Answer: e