regisss/math_qa huggingface dataset:
Problem: if n is an integer from 1 to 96 ( inclusive ) , what is the probability for n * ( n + 1 ) * ( n + 2 ) being divisible by 8 ?
Options: a ) 25 % , b ) 50 % , c ) 62.5 % , d ) 72.5 % , e ) 75 %
Rationale: ( a ) 25 % , to be divisible by 8 the number needs to have 3 2 s in it . only a multiple of 4 can provide that . number of numbers divisible by 4 = 96 / 4 = 24 . so p ( 8 ) = 24 / 96 = 25 % .
Answer: a
Problem: by selling an article for $ 90 , a person gains $ 15 . what is the gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 90 gain = $ 15 c . p . = 90 - 15 = 75 gain % = 15 / 75 * 100 = 20 % answer is d"
Answer: d
Problem: on multiplying a number b by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
Options: a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
Rationale: the only thing you actually know about the correct number b is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
Answer: d
Problem: if a computer program generates 3 - digit odd numbers using the numbers 9 , 7 , 0 , 8 , and 1 , and the digits can be repeated , what is the probability that the number formed from the program is a multiple of 3 ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: a
Answer: a
Problem: how many pounds of salt at 70 cents / lb must be mixed with 45 lbs of salt that costs 40 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 5 , b ) 9 , c ) 40 , d ) 50 , e ) 25
Rationale: "selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 40 cents / lb ( salt 1 ) with 70 cents / lb ( salt 2 ) to get a mixture costing 45 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 70 - 45 ) / ( 45 - 40 ) = 5 / 1 we know that weight of salt 1 is 45 lbs . weight of salt 2 must be 9 lbs . answer ( b )"
Answer: b
Problem: the length of a side of a hexagon is 5 inches . what is the perimeter ?
Options: a ) 116 , b ) 25 , c ) 30 , d ) 24 , e ) 15
Rationale: "hexagon . it means 6 equal sides . p = 5 + 5 + 5 + 5 + 5 + 5 = 10 + 10 + 10 = 30 inches answer c"
Answer: c
Problem: one fourth of a solution that was 12 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options: a ) 28 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.12 + 25 * x = 100 * 0.16 - - > x = 0.28 . answer : a .
Answer: a
Problem: a house wife saved $ 4 in buying an item on sale . if she spent $ 28 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 13 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: "actual price = 28 + 4 = $ 32 saving = 4 / 32 * 100 = 13 % approximately answer is b"
Answer: b
Problem: a can do a work in 3 days . b can do the same work in 6 days . both a & b together will finish the work and they got $ 1000 from that work . find their shares ?
Options: a ) 600,400 , b ) 500,500 , c ) 300,700 , d ) 800,200 , e ) 200,400
Rationale: "ratio of their works a : b = 3 : 6 ratio of their wages a : b = 1 : 2 a ' s share = ( 1 / 5 ) 1000 = 200 b ' s share = ( 2 / 5 ) 1000 = 400 correct option is e"
Answer: e
Problem: two friends deepak and rajeev have agreed to meet at a definite spot on a particular day between 9 pm and 10 pm . the first person to come waits for some time and leaves . if the other one does not turn up by that time . if deepak comes first , he waits for 45 minutes and if rajeev comes first , he waits for 15 minutes . what is the probability of meeting between deepak and rajeev if their arrival times are independent of eachother and each person arrives during the indicated period at random ?
Options: a ) 3 / 4 , b ) 11 / 16 , c ) 7 / 8 , d ) 3 / 16 , e ) 5 / 16
Rationale: deepak : 45 / 60 = 3 / 4 rajeev : 15 / 60 = 1 / 4 as these are independent events total probability = ( 3 / 4 ) * ( 1 / 4 ) = 3 / 16 answer : d
Answer: d
Problem: claire has a total of 90 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
Options: a ) 39 , b ) 50 , c ) 66 , d ) 57 , e ) 60
Rationale: g + h = 90 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 90 - h or 3 ( 90 - h ) + 4 h = 300 h = 300 - 270 = 30 then g = 96 - 30 = 66 c
Answer: c
Problem: what is the units digit of 2222 ^ ( 333 ) * 3333 ^ ( 444 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits . here ' s another way to organize the information . we ' re given [ ( 2222 ) ^ 333 ] [ ( 3333 ) ^ 222 ] we can ' combine ' some of the pieces and rewrite this product as . . . . ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) [ ( 2222 ) ^ 111 ] ( 2222 ) ( 3333 ) = a big number that ends in a 6 taking a number that ends in a 6 and raising it to a power creates a nice pattern : 6 ^ 1 = 6 6 ^ 2 = 36 6 ^ 3 = 216 etc . thus , we know that ( [ ( 2222 ) ( 3333 ) ] ^ 222 ) will be a gigantic number that ends in a 6 . 2 ^ 111 requires us to figure out thecycleof the units digit . . . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 so , every 4 powers , the pattern of the units digits repeats ( 2 , 4 , 8 , 6 . . . . . 2 , 4 , 8 , 6 . . . . ) . 111 = 27 sets of 4 with a remainder of 3 . . . . this means that 2 ^ 111 = a big number that ends in an 8 so we have to multiply a big number that ends in a 6 and a big number that ends in an 8 . ( 6 ) ( 8 ) = 48 , so the final product will be a gigantic number that ends in an 4 . final answer : c"
Answer: c
Problem: a shopkeeper labeled the price of his articles so as to earn a profit of 30 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 18 % , b ) 20 % , c ) 17 % , d ) 18 % , e ) none of these
Rationale: explanation : let the cp of the article = rs . 100 . then labeled price = rs . 130 . sp = rs . 130 - 10 % of 130 = rs . 130 - 13 = rs . 117 . gain = rs . 117 – rs . 100 = rs . 17 therefore , gain / profit percent = 17 % . answer : option c
Answer: c
Problem: what is the area inscribed by the lines y = 10 , x = 1 , y = 3 x + 1 on an xy - coordinate plane ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 3 , d ) d ) 6 , e ) e ) 12
Rationale: "first , let ' s graph the lines y = 10 and x = 1 at this point , we need to find the points where the line y = 3 x + 1 intersects the other two lines . for the vertical line , we know that x = 1 , so we ' ll plug x = 1 into the equation y = 3 x + 1 to get y = 3 ( 1 ) + 1 = 4 perfect , when x = 1 , y = 5 , so one point of intersection is ( 1,4 ) for the horizontal line , we know that y = 10 , so we ' ll plug y = 10 into the equation y = 3 x + 1 to get 10 = 3 x + 1 . solve to get : x = 3 so , when y = 10 , x = 3 , so one point of intersection is ( 3,10 ) now add these points to our graph and sketch the line y = 3 x + 1 at this point , we can see that we have the following triangle . the base has length 2 and the height is 6 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 2 ) ( 6 ) = 6 answer : d"
Answer: d
Problem: what is rate of interest if principal . amount be 400 , simple interest 100 and time 2 year .
Options: a ) 10 , b ) 12.5 , c ) 25 , d ) 12 , e ) 14.5
Rationale: "s . i = ( p * r * t ) / 100 100 = 800 r / 100 r = 100 / 8 = 12.5 % answer b"
Answer: b
Problem: harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 4 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 7 , d ) 1 / 2 , e ) 4 / 7
Rationale: "the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 4 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 4 x = 10 x august tips as a fraction of total tips = 4 x / 10 x = 2 / 5 . so b"
Answer: b
Problem: a train covers a distance of 12 km in 10 minutes . if it takes 7 seconds to pass a telegraph post , then the length of the train is
Options: a ) 100 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 170 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 7 ) m = 140 m answer : option c"
Answer: c
Problem: the ratio of the volumes of two cubes is 6859 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 1 : 21 , b ) 12 : 7 , c ) 1 : 15 , d ) 21 : 17 , e ) 13 : 13
Rationale: "ratio of the sides = ³ √ 6859 : ³ √ 1331 = 19 : 11 ratio of surface areas = 192 : 112 = 12 : 7 answer : b"
Answer: b
Problem: if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 14 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 400 , b ) 410 , c ) 460 , d ) 420 , e ) 430
Rationale: "( 3500 * 4 * 3 ) / 100 = > 420 answer : d"
Answer: d
Problem: a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 6 days . b can do the work alone in ?
Options: a ) 19 , b ) 36 , c ) 11 , d ) 19 , e ) 114
Rationale: "suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 6 6 / x = 1 / 6 = > x = 36 so , b takes 18 hours to finish the work . answer : b"
Answer: b
Problem: a train running at a speed of 36 km / h passes an electric pole in 14 seconds . in how many seconds will the whole train pass a 350 - meter long platform ?
Options: a ) 43 , b ) 45 , c ) 47 , d ) 49 , e ) 51
Rationale: "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 14 * 10 = 140 m . the time taken to pass the platform = ( 140 + 350 ) / 10 = 49 seconds the answer is d ."
Answer: d
Problem: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 110 mangoes .
Options: a ) 367 , b ) 380 , c ) 400 , d ) 406 , e ) 412
Rationale: "mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 110 mangoes = 110 * 3.33 = 367 . answer a"
Answer: a
Problem: there are two numbers . if 20 % of the first number is added to the second number , then the second number increases to its 5 - fourth . what is the ratio of the first number to the second number ?
Options: a ) 2 : 9 , b ) 3 : 8 , c ) 8 : 5 , d ) 5 : 4 , e ) 7 : 3
Rationale: let the two numbers be x and y . ( 2 / 10 ) * x + y = ( 5 / 4 ) * y ( 2 / 10 ) * x = ( 1 / 4 ) * y x / y = 10 / 8 = 5 / 4 the answer is d .
Answer: d
Problem: a train is 560 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 56 seconds , b ) 18 seconds , c ) 40 seconds , d ) 19 seconds , e ) 45 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 560 + 140 = 700 meter time = distance / speed = 700 * ( 2 / 25 ) = 56 seconds answer : a"
Answer: a
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1600 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 99 , c ) 88 , d ) 160 , e ) 12
Rationale: "given that the area of the square = 1600 sq . units = > side of square = √ 1600 = 40 units the radius of the circle = side of the square = 40 units length of the rectangle = 2 / 5 * 40 = 16 units given that breadth = 10 units area of the rectangle = lb = 16 * 10 = 160 sq . units answer : d"
Answer: d
Problem: the average age of 28 students in a group is 11 years . when teacher ’ s age is included to it , the average increases by one . what is the teacher ’ s age in years ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) can not be determined , e ) none of these
Rationale: "age of the teacher = ( 29 × 12 – 28 × 11 ) years = 40 years . answer c"
Answer: c
Problem: a man can row his boat with the stream at 10 km / h and against the stream in 6 km / h . the man ' s rate is ?
Options: a ) 2 kmph , b ) 7 kmph , c ) 98 kmph , d ) 6 kmph , e ) 4 kmph
Rationale: "ds = 10 us = 6 s = ? s = ( 10 - 6 ) / 2 = 2 kmph answer : a"
Answer: a
Problem: if the product of 12 integers is negative , at most how many of the integers can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 11
Rationale: "the product of 12 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 11 correct option : e"
Answer: e
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of d is less than the square root of d . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "clearly d a number is said to be prime saturated if the product of all the different positive prime factors of d is less than the square root of d . 96 has more number of smaller prime factor thats the clue ! ! = d"
Answer: d
Problem: the distance from steve ' s house to work is 28 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 28 km = > speed = 14 kmph c"
Answer: c
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 2 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: oa is definitely wrong . the answer should be e .
Answer: e
Problem: there are 20 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 190 , d ) 60 , e ) 90
Rationale: "20 players are there . two players play one game with one another . so 20 c 2 = 20 * 19 / 2 = 190 so option c is correct"
Answer: c
Problem: the sum of four consecutive even numbers is 36 . find the sum of the squares of these numbers ?
Options: a ) 296
b ) 252
c ) 344
d ) 388
e ) none of these
Rationale: let the four numbers be x , x + 2 , x + 4 and x + 6 . = > x + x + 2 + x + 4 + x + 6 = 36 = > 4 x + 12 = 36 = > x = 6 the numbers are 6 , 8 , 10 and 12 . sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344 . answer : c
Answer: c
Problem: p is 40 % more efficient than q . p can complete a work in 24 days . if p and q work together , how many days will it take to complete the same work ?
Options: a ) 8 , b ) 9 , c ) 11 , d ) 14 , e ) 15
Rationale: "the work done by p in 1 day = 1 / 24 let work done by q in 1 day = q q × ( 140 / 100 ) = 1 / 24 q = 100 / ( 24 × 140 ) = 10 / ( 24 × 14 ) the work done by p and q in 1 day = 1 / 24 + 10 / ( 24 × 14 ) = 24 / ( 24 × 14 ) = 1 / 14 p and q together can do the work in 14 days . the answer is d ."
Answer: d
Problem: if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance travelled by him is :
Options: a ) 50 km , b ) 56 km , c ) 70 km , d ) 80 km , e ) 46 km
Rationale: "let the actual distance travelled be x km . then , x / 10 = ( x + 20 ) / 14 14 x = 10 x + 200 4 x = 200 x = 50 km . answer : a"
Answer: a
Problem: ( 422 + 404 ) 2 − ( 4 × 422 × 404 ) = ?
Options: a ) none of these , b ) 342 , c ) 324 , d ) 312 , e ) can not be determined
Rationale: "explanation : given equation is in the form ( a + b ) 2 − 4 ab where a = 422 and b = 404 hence answer = ( a + b ) 2 − 4 ab = ( a − b ) 2 = ( 422 − 404 ) 2 = 182 = 324 , answer : option c"
Answer: c
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 98 of the area of the field . what is the length of the field ?
Options: a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 112
Rationale: "explanation : a / 98 = 8 * 8 = > a = 8 * 8 * 98 x * 2 x = 8 * 8 * 98 x = 56 = > 2 x = 112 answer : option e"
Answer: e
Problem: there are 50 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 1000 , b ) 3000 , c ) 1225 , d ) 6000 , e ) 9000
Rationale: "50 players are there . two players play one game with one another . so 50 c 2 = 50 * 49 / 2 = 1225 so option c is correct"
Answer: c
Problem: an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 1 / 4 % , then the amount invested at 11 % was ?
Options: a ) 12500 , b ) 37500 , c ) 29977 , d ) 26777 , e ) 19871
Rationale: "let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 37 / 4 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) = 37000 / 4 = 925000 x = 87500 sum invested at 9 % = rs . 87500 sum invested at 11 % = rs . ( 100000 - 87500 ) = rs . 12500 . answer : a"
Answer: a
Problem: a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed y of the train .
Options: a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61
Rationale: "let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = y ans = c"
Answer: c
Problem: a and b can do a piece of work in 10 days , b and c in 5 days , c and a in 15 days . how long will c take to do it ?
Options: a ) 77 days , b ) 55 days , c ) 12 days , d ) 33 days , e ) 11 days
Rationale: 2 c = 1 / 5 + 1 / 15 – 1 / 10 = 1 / 6 c = 1 / 12 = > 12 days answer : c
Answer: c
Problem: when 1 / 10 percent of 1,000 is subtracted from 1 / 10 of 1,000 , the difference is
Options: a ) 10 , b ) 100 , c ) 999 , d ) 99 , e ) 9
Rationale: "( 1 / 10 ) * 1000 - ( 1 / 10 ) % * 1000 = 100 - ( 1 / 1000 ) * 1000 = 100 - 1 = 99 the answer is d ."
Answer: d
Problem: a rectangular courtyard 3.78 meters long 5.25 meters wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ?
Options: a ) 14 cms
b ) 21 cms
c ) 42 cms
d ) none of these
e ) 56 cms
Rationale: explanation : 3.78 meters = 378 cm = 2 × 3 × 3 × 3 × 7 5.25 meters = 525 cm = 5 × 5 × 3 × 7 hence common factors are 3 and 7 hence lcm = 3 × 7 = 21 hence largest size of square tiles that can be paved exactly with square tiles is 21 cm . answer : b
Answer: b
Problem: if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number e of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see e = 5 or 1 will give you same equation . . ans d"
Answer: d
Problem: convert 1.3 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .
Rationale: "1.3 hectares in ares 1 hectare = 100 ares therefore , 1.3 hectares = 1.3 × 100 ares = 130 ares . answer - a"
Answer: a
Problem: on a certain road , 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 40 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 16.7 % , d ) 25 % , e ) 30 %
Rationale: "suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . again , suppose total no . of motorists who exceeded the speed limit are y . 40 % of y exceeded the speed limit but did n ' t received the ticket , i . e . 2 y / 5 . it means 3 y / 5 received the ticket . hence , 3 y / 5 = x / 10 or y / x = 1 / 6 or y / x * 100 = 1 / 6 * 100 = 16.7 % c"
Answer: c
Problem: there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 54 %
Options: a ) 18.75 , b ) 19.75 , c ) 20.75 , d ) 33 , e ) 22.75
Rationale: 60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 54 / 100 = 50.40 so x = 33.33 answer : d
Answer: d
Problem: a certain bus driver is paid a regular rate of $ 14 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 998 in total compensation , how many total hours did he work that week ?
Options: a ) 54 , b ) 51 , c ) 58 , d ) 55 , e ) 52
Rationale: "for 40 hrs = 40 * 14 = 560 excess = 998 - 560 = 438 for extra hours = . 75 ( 14 ) = 10.5 + 14 = 24.5 number of extra hrs = 438 / 24.5 = 17.8 = 18 approx . total hrs = 40 + 18 = 58 answer c"
Answer: c
Problem: when n is divided by 24 , the remainder is 6 . what is the remainder when 3 n is divided by 8 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 2
Rationale: "let n = 6 ( leaves a remainder of 6 when divided by 24 ) 3 n = 3 ( 6 ) = 18 , which leaves a remainder of 2 when divided by 8 . answer e"
Answer: e
Problem: a certain debt will be paid in 40 installments from january 1 to december 31 of a certain year . each of the first 20 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 20 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 442.5 , b ) 450 , c ) 465 , d ) 468 , e ) 475
Rationale: "total number of installments = 40 payment per installment for the first 20 installments = 410 payment per installment for the remaining 20 installments = 410 + 65 = 475 average = ( 20 * 410 + 20 * 475 ) / 40 = 442.50 answer a"
Answer: a
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 20 % profit on the first article and 20 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 177 , c ) 188 , d ) 166 , e ) 129
Rationale: "profit on first article = 20 % of 1000 = 200 . answer : a"
Answer: a
Problem: 20 men do a work in 20 days . how many men are needed to finish the work in 4 days ?
Options: a ) 50 , b ) 20 , c ) 30 , d ) 100 , e ) 15
Rationale: "men required to finish the work in 4 days = 20 * 20 / 4 = 100 answer is d"
Answer: d
Problem: the cost of 20 articles is equal to selling price of 10 . find the gain or loss percent ?
Options: a ) 50 % , b ) 100 % , c ) 25 % , d ) 15 % , e ) 60 %
Rationale: c . p . of each article be $ 1 c . p . of 10 articles = 10 gain % = 10 / 10 * 100 = 100 % answer is b
Answer: b
Problem: a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 6500 rs , what is the value of buzness ?
Options: a ) 150000 , b ) 16000 , c ) 15000 , d ) 190000 , e ) 13000
Rationale: "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 6500 - > x = 13000 answer : e"
Answer: e
Problem: johnny makes $ 7.35 per hour at his work . if he works 6 hours , how much money will he earn ?
Options: a ) $ 30 , b ) $ 54 , c ) $ 48.32 , d ) $ 44.10 , e ) $ 9.60
Rationale: 4.75 * 6 = 28.50 . answer is c .
Answer: c
Problem: find the 25 % of rs . 200 .
Options: a ) rs . 50 , b ) rs . 70 , c ) rs . 100 , d ) rs . 80 , e ) rs . 60
Rationale: explanation : 25 % of 200 = > 25 / 100 * 200 = rs . 50 answer : a
Answer: a
Problem: what is the least common multiple of 15 , 16 , and 24 ?
Options: a ) 60 , b ) 120 , c ) 240 , d ) 360 , e ) 720
Rationale: "let us first write the numbers in the form of prime factors : 15 = 3 * 5 16 = 2 ^ 4 24 = 2 * 17 ^ 1 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 240 option c"
Answer: c
Problem: how many integers from 101 to 800 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "first digit possibilities - 1 through 7 = 7 8 is not possible here because it would result in a number greater than 8 ( i . e 808 , 818 . . ) second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 7 * 10 = 70 answer is c ."
Answer: c
Problem: a bowl of fruit contains 14 apples and 25 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 19
Rationale: "number of apples = 14 number of oranges = 25 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 25 - x ) = 39 - x 14 / ( 39 - x ) = 7 / 10 = > 20 = 39 - x = > x = 19 answer e"
Answer: e
Problem: on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent r of thatbeforejuly 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before r = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % . b
Answer: b
Problem: 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 140 kg then find the average weight of all the 7 rounds ?
Options: a ) 98.5 kgs , b ) 80 kgs , c ) 76.5 kgs , d ) 67.5 kgs , e ) 58.2 kgs
Rationale: "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 140 / 7 = 80 kgs answer : b"
Answer: b
Problem: the ratio of the volumes of two cubes is 8 : 27 what is the ratio of their total surface areas ?
Options: a ) 2 : 4 , b ) 3 : 6 , c ) 4 : 12 , d ) 4 : 9 , e ) 1 : 3
Rationale: "ratio of the sides = â ³ â ˆ š 8 : â ³ â ˆ š 27 = 2 : 3 ratio of surface areas = 4 : 9 answer : d"
Answer: d
Problem: what is the greatest of 3 consecutive integers whose sum is 21 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 5
Rationale: "the sum of three consecutive integers can be written as n + ( n + 1 ) + ( n + 2 ) = 3 n + 3 if the sum is 24 , we need to solve the equation 3 n + 3 = 21 ; = > 3 n = 18 ; = > n = 6 the greatest of the three numbers is therefore 6 + 2 = 8 answer : c"
Answer: c
Problem: the measure of the side of a square is multiplied by 6 . if x represents the perimeter of the original square , what is the value of the new perimeter ?
Options: a ) 3 x , b ) 4 x , c ) 6 x , d ) 12 x , e ) 27 x
Rationale: "original perimeter = x hence original side = x / 4 new side = 6 x / 4 new perimeter = 4 * 6 x / 4 = 6 x correct option : c"
Answer: c
Problem: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 24000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 5 : 2
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 24000 × 9 = 45 × 12 : 24 × 9 = 15 × 12 : 8 × 9 = 5 : 2 answer is e ."
Answer: e
Problem: if a and b get profits of rs . 4,000 and rs . 2,000 respectively at the end of year then ratio of their investments are
Options: a ) 4 : 1 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 1
Rationale: "ratio = 4000 / 2000 = 2 : 1 answer : e"
Answer: e
Problem: a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 45 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 21,360 , e ) $ 29,160
Rationale: "for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.45 * 12000 = 12000 - 5400 x = 6600 earning becomes 9360 + 3 x = 9360 + 3 * 6600 = 29160 ans : e"
Answer: e
Problem: speed of a boat in standing water is 8 kmph and the speed of the stream is 2 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
Options: a ) 48 hours , b ) 51 hours , c ) 36 hours , d ) 56 hours , e ) none
Rationale: "sol . speed upstream = 6 kmph ; speed downstream = 10 kmph . ∴ total time taken = [ 210 / 6 + 210 / 10 ] hours = 56 hours . answer d"
Answer: d
Problem: find the annual income derived by investing $ 6800 in 20 % stock at 136 .
Options: a ) 550 , b ) 1000 , c ) 2500 , d ) 300 , e ) 4000
Rationale: "by investing $ 136 , income obtained = $ 20 . by investing $ 6800 , income obtained = $ [ ( 20 / 136 ) * 6800 ] = $ 1000 . answer b ."
Answer: b
Problem: if x = - 12 / 5 and y = - 6 / 7 , what is the value of the expression - 2 x – y ^ 2 ?
Options: a ) 741 / 357 , b ) 456 / 789 , c ) 636 / 735 , d ) 564 / 263 , e ) - 636 / 735
Rationale: "x = - 12 / 15 and y = - 6 / 7 = = > - 2 ( - 12 / 15 ) - ( - 6 / 7 ) ^ 2 = 24 / 15 - 36 / 49 = 636 / 735 ans : c"
Answer: c
Problem: a man can row his boat with the stream at 16 km / h and against the stream in 6 km / h . the man ' s rate is ?
Options: a ) 5 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 9 kmph
Rationale: "explanation : ds = 16 us = 6 s = ? s = ( 16 - 6 ) / 2 = 5 kmph answer : a"
Answer: a
Problem: if the compound interest on a certain sum of money for 4 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 880 , b ) rs . 890 , c ) rs . 1200 , d ) rs . 900 , e ) none
Rationale: "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 4 yrs = ( 3000 x 10 x 4 ) / 100 = 1200 / - answer : c ."
Answer: c
Problem: when n is divided by 27 , the remainder is 4 . what is the remainder when n + 16 is divided by 7 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "assume n = 23 remainder ( n / 27 ) = 4 n + 16 = 39 remainder ( 39 / 7 ) = 4 option c"
Answer: c
Problem: jar a has 16 % more marbles than jar b . what percent of marbles from jar a need to be moved into jar b so that both jars have equal marbles ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 13 %
Rationale: an easy way to solve this question is by number plugging . assume there are 100 marbles in jar b then in jar a there will be 116 marbles . now , for both jars to have equal marbles we should move 8 marbles from a to b , which is 8 / 116 = ~ 7 % of a . answer : b .
Answer: b
Problem: a and b started a business investing rs . 21,000 and rs . 28,000 respectively . out of a total profit of rs . 14,000 , b ’ s share is :
Options: a ) 7600 , b ) 7700 , c ) 7800 , d ) 7900 , e ) 8000
Rationale: "ratio of their shares = 21000 : 28000 = 3 : 4 . b ’ s share = rs . 14000 * 4 / 7 = rs . 8000 answer : e"
Answer: e
Problem: a merchant marks goods up by 75 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 5 % . what % discount did the merchant offer ?
Options: a ) 20 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "let p be the original price of the goods and let x be the rate after the markup . ( 1.75 p ) * x = 1.05 p x = 1.05 / 1.75 = 0.6 which is a discount of 40 % . the answer is d ."
Answer: d
Problem: find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 17 per cubic meter ?
Options: a ) 2998 , b ) 2799 , c ) 2890 , d ) 1683 , e ) 2780
Rationale: "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 17 = 1683 answer : d"
Answer: d
Problem: 1370 , 1320 , 1070 , x , - 6430
Options: a ) - 180 , b ) 6530 , c ) 6630 , d ) 6730 , e ) 6830
Rationale: "1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a ."
Answer: a
Problem: if ( 27 / 4 ) x - 18 = 3 x + 27 what is the value of x ?
Options: a ) 12 , b ) - 12 , c ) 1 / 12 , d ) - 1 / 12 , e ) 3
Rationale: ( 27 / 4 ) x - 18 = 3 x + 27 = > 27 x - 72 = 12 x + 108 = > 15 x = 180 = > x = 12 answer : a
Answer: a
Problem: if the average marks of 3 classes of 55 , 60 and 45 students respectively is 50 , 55 , 60 , then find the average marksof all the students is
Options: a ) 53 , b ) 53.5 , c ) 54.68 , d ) 55.6 , e ) 67.2
Rationale: required average = 55 x 50 + 60 x 55 + 45 x 60 55 + 60 + 45 = 2750 + 3300 + 2700 160 = 8750 160 = 54.68 c
Answer: c
Problem: the batting average of a particular batsman is 63 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 208 , c ) 210 , d ) 223 , e ) 248
Rationale: explanation : total runs scored by the batsman = 63 * 46 = 2898 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2898 – 2552 = 346 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 346 2 x = 496 x = 248 runs answer e
Answer: e
Problem: a lady builds 10 cm length , 13 cm width , and 5 cm height box using 5 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 107 , b ) 108 , c ) 130 , d ) 150 , e ) 145
Rationale: "number of cubes required = volume of box / volume of cube = 10 * 13 * 5 / 5 = 130 cubes answer : c"
Answer: c
Problem: a train 275 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 8 , b ) 6 , c ) 5 , d ) 15 , e ) 1
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 275 * 3 / 55 = 15 sec . answer : d"
Answer: d
Problem: when 2 + 3 = 65 , 3 + 4 = 125 , 4 + 5 = 205 , then 5 + 6 = ?
Options: a ) 285 , b ) 305 , c ) 315 , d ) 350 , e ) 245
Rationale: "2 + 3 = > 2 ã — 3 = 6 = > 6 ã — 10 + 5 = 65 3 + 4 = > 3 ã — 4 = 12 = > 12 ã — 10 + 5 = 125 4 + 5 = > 4 ã — 5 = 20 = > 20 ã — 10 + 5 = 205 then 5 + 6 = > 5 ã — 6 = 30 = > 30 ã — 10 + 5 = 305 answer : b"
Answer: b
Problem: a certain experimental mathematics program was tried out in 2 classes in each of 22 elementary schools and involved 31 teachers . each of the classes had 1 teacher and each of the teachers taught at least 1 , but not more than 3 , of the classes . if the number of teachers who taught 3 classes is n , then the least and greatest possible values of n , respectively , are
Options: a ) 0 and 13 , b ) 0 and 14 , c ) 1 and 10 , d ) 1 and 6 , e ) 2 and 8
Rationale: "one may notice that greatest possible values differ in each answer choice in contrast to the least values , which repeat . to find out the greatest value you should count the total classes ( 22 * 2 = 44 ) , then subtract the total # of teachers since we know from the question that each teacher taught at least one class ( 44 - 31 = 13 ) . thus we get a number of the available extra - classes for teachers , and all that we need is just to count how many teachers could take 2 more classes , which is 13 / 2 = 6.5 . so the greatest possible value of the # of teachers who had 3 classes is 6 . only answer d has this option ."
Answer: d
Problem: a is twice as good a work man as b and together they finish a piece of work in 24 days . the number of days taken by a alone to finish the work is :
Options: a ) 28 days . , b ) 16 days . , c ) 12 days . , d ) 24 days . , e ) 36 days .
Rationale: "solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 2 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 24 divide 1 / 14 in the ratio 2 : 1 . ∴ a ’ s 1 day ’ s work = ( 1 / 24 x 2 / 3 ) = 1 / 36 hence , a alone can finish the work in 36 days . answer e"
Answer: e
Problem: what will be the difference between simple and compound interest at 12 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) 94.19 , b ) 94.12 , c ) 93.5 , d ) 64.1 , e ) 64.11
Rationale: "s . i . = ( 1000 * 12 * 4 ) / 100 = rs . 480 c . i . = [ 1000 * ( 1 + 12 / 100 ) 4 - 1000 ] = rs . 573.5 difference = ( 573.5 - 480 ) = rs . 93.5 answer : c"
Answer: c
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 290 m long ?
Options: a ) 40 sec , b ) 52 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 290 = 650 m required time = 650 * 2 / 25 = 52 sec answer : b"
Answer: b
Problem: q ' = 3 q - 3 , what is the value of ( 7 ' ) ' ?
Options: a ) 6 , b ) 106 , c ) 206 , d ) 306 , e ) 406
Rationale: "( 7 ' ) ' = ( 3 * 7 - 3 ) ' = 18 ' = 18 * 18 - 18 = 306 answer d"
Answer: d
Problem: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.50 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 2 : 0 , b ) 2 : 3 , c ) 2 : 1 , d ) 8 : 9 , e ) 2 : 8
Rationale: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 80 : 90 = 8 : 9 answer : d"
Answer: d
Problem: a grocer has a sale of rs . 5400 , rs . 9000 , rs . 6300 , rs . 7200 and rs . 4500 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5600 ?
Options: a ) s . 1200 , b ) s . 5400 , c ) s . 5400 , d ) s . 4999 , e ) s . 5000
Rationale: "total sale for 5 months = rs . ( 5400 + 9000 + 6300 + 7200 + 4500 ) = rs . 32400 . required sale = rs . [ ( 5600 x 6 ) - 32400 ] = rs . ( 33600 - 32400 ) = rs . 1200 . option a"
Answer: a
Problem: marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 12000 and the marginal cost is $ 200 , and the total cost is $ 16000 , what is the value of n ?
Options: a ) 20 , b ) 50 , c ) 60 , d ) 80 , e ) 100
Rationale: total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 12,000 + n * $ 200 - - > n = 20 . answer : a .
Answer: a
Problem: $ 392 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?
Options: a ) $ 212 , b ) $ 216 , c ) $ 220 , d ) $ 224 , e ) $ 228
Rationale: "let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 392 x = 56 4 x = 224 the answer is d ."
Answer: d
Problem: the cyclist walking at a constant rate of 15 miles per hour is passed by a car traveling in the same direction along the same path at 60 miles per hour . the car stops to wait for the cyclist for 6 minutes after passing her , while the cyclist continues to go at her constant rate , how many minutes must the car wait until the cyclist catches up ?
Options: a ) 9 , b ) 10 , c ) 12 , d ) 15 , e ) 18
Rationale: for the 6 minutes the car continues to overtake the cyclist , she is going at 45 miles per hour faster than the cyclist . once the car stops , the cyclist is going at 15 miles per hour while the car is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 45 / 15 * 6 or 18 minutes answer is ( e )
Answer: e
Problem: the value for d = ( 0.889 × 55 ) / 9.97 to the nearest tenth is
Options: a ) 0.5 , b ) 4.63 , c ) 4.9 , d ) 7.7 , e ) 49.1
Rationale: if we read the q , we can easily home on to the answer , , the numerator is clearly between 40 and 50 . . denomiator is close to 10 . . so d = ( 0.889 × 55 ) / 9.97 is between 4 and 5 . . it may tempt us to solve it since ther are two values between 4 and 5 . . but the catch is innearest tenth 4.63 can be called nearest to hundreth and no tenth , so can be eliminated . . 4.9 is our answer . . . c
Answer: c
Problem: find the least number which when divided by 37 and 7 leaves a remainder of 2 in each case .
Options: a ) 259 , b ) 261 , c ) 263 , d ) 265 , e ) 267
Rationale: the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 37 , 7 ) + 2 = 261 . answer : b
Answer: b
Problem: a cubical tank is filled with water to a level of 1 foot . if the water in the tank occupies 16 cubic feet , to what fraction of its capacity is the tank filled with water ?
Options: a ) 1 / 2
b ) 1 / 3
c ) 1 / 4
d ) 1 / 5
e ) 1 / 6
Rationale: the volume of water in the tank is h * l * b = 16 cubic feet . since h = 1 , then l * b = 16 and l = b = 4 . since the tank is cubical , the capacity of the tank is 4 * 4 * 4 = 64 . the ratio of the water in the tank to the capacity is 16 / 64 = 1 / 4 the answer is c .
Answer: c
Problem: by approximately what percent is x greater than 2 / 5 if ( 3 / 5 ) ( x ) = 1 ?
Options: a ) 723 % , b ) 156 % , c ) 316 % , d ) 37 % , e ) 29 %
Rationale: "what percent is x greater than 2 / 5 if ( 3 / 5 ) ( x ) = 1 ? = > x = 5 / 3 % change = [ ( 5 / 3 - 2 / 5 ) / ( 2 / 5 ) ] * 100 = 316.5 % = 316 % approx ans , c"
Answer: c
Problem: a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 60 % more recliners . what is the percentage increase of the gross ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 28 % , e ) 50 %
Rationale: "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 60 % more ie . , 160 recliners hence her sales tields 160 * 80 = $ 12800 increase in sales = 12800 - 10000 = $ 2800 so % increase = 2800 * 100 / 10000 = 28 % d is the answer"
Answer: d
Problem: 10 play kabadi , 25 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 25 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 25 + 5 = 30 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 30 - 5 = 35 answer : b"
Answer: b
Problem: on dividing a number by 5 , we get 5 as quotient and 0 as remainder . on dividing the same number by 11 , what will be the remainder ?
Options: a ) 5 , b ) 2 , c ) 7 , d ) 9 , e ) 3
Rationale: "number = 5 * 5 + 0 = 25 11 ) 25 ( 2 22 - - - - - - - - 3 required number = 0 . answer : e"
Answer: e
Problem: if the area of a square with sides of length 8 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 18
Rationale: "let length of rectangle = l 8 ^ 2 = l * 4 = > l = 64 / 4 = 16 answer d"
Answer: d
Problem: the average salary of 15 people in the shipping department at a certain firm is $ 21,000 . the salary of 5 of the employees is $ 25,000 each and the salary of 4 of the employees is $ 16,000 each . what is the average salary of the remaining employees ?
Options: a ) $ 19,250 , b ) $ 18,500 , c ) $ 21,000 , d ) $ 15,850 , e ) $ 12,300
Rationale: "total salary . . . 15 * 21 k = 315 k 5 emp @ 25 k = 125 k 4 emp @ 16 k = 64 k remaing 6 emp sal = 315 k - 125 k - 64 k = 126 k average = 126 k / 6 = 21000 ans : c"
Answer: c
Problem: walking at the rate of 3 kmph a man cover certain distance in 6 hr 40 min . running at a speed of 18 kmph the man will cover the same distance in .
Options: a ) 40 min , b ) 25 min , c ) 54 min , d ) 65 min , e ) 58 min
Rationale: "distance = speed * time 3 * 20 / 3 = 20 km new speed = 18 kmph therefore time = 20 / 18 = 10 / 9 = 54 min answer : c ."
Answer: c
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of thesportformulation contains 5 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 15
b ) 30
c ) 45
d ) 75
e ) 90
Rationale: standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 5 . so , x = 325 / 4 ounces . water = ( 60 / 65 ) * ( 325 / 4 ) = 60 * 3 / 4 = 75 ounces . ans d
Answer: d