regisss/math_qa huggingface dataset:
Problem: the value of 3.6 x 0.48 x 2.50 / 0.12 x 0.09 x 0.5 is
Options: a ) 80 , b ) 800 , c ) 8000 , d ) 80000 , e ) none of these
Rationale: "solution therefore = 3.6 x 0.48 x 2.50 / 0.12 x 0.09 x 0.5 = 36 x 48 x 250 / 12 x 9 x 5 = 800 answer b"
Answer: b
Problem: two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 30 hr . if all pipes are opened simultaneously , then the cistern will be filled in
Options: a ) 6.67 hr , b ) 8 hr , c ) 8.5 hr , d ) 10 hr , e ) none of these
Rationale: "solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 30 = 3 / 20 hence , tank will be filled in 20 / 3 = 6.67 hour option ( a )"
Answer: a
Problem: if 1 / 8 of a pencil is black 1 / 2 of the remaining is white and the remaining 7 / 2 is blue find the total length of the pencil ?
Options: a ) 7.33 cm , b ) 6.33 cm , c ) 5.33 cm , d ) 9.33 cm , e ) 8.33 cm
Rationale: ( 1 / 8 ) p + ( 1 / 2 ) p + ( 7 / 2 ) = p on solving the above for p we get 9.333 now checking for the answer : 9.333 / 8 = 1.166 cm 9.333 / 2 = 4.665 cm now 1.166 + 4.665 + ( 7 / 2 ) = 9.33 cm answer : d
Answer: d
Problem: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 42 degrees . find the temperature on friday ?
Options: a ) 34 , b ) 55 , c ) 66 , d ) 81 , e ) 21
Rationale: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 42 tu + w + th = 192 - 42 = 150 f = 184 – 150 = 34 . answer : a"
Answer: a
Problem: a certain taxi company charges $ 2.10 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?
Options: a ) 15.6 , b ) 16.0 , c ) 17.7 , d ) 18.7 , e ) 19.1
Rationale: "a certain taxi company charges $ 2.10 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.10 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.1 + $ 15.6 = $ 17.7 . answer : c ."
Answer: c
Problem: two cyclist start from the same places in opposite directions . one is going towards north at 30 kmph and the other is going towards south 40 kmph . what time will they take to be 50 km apart ?
Options: a ) 1.32 hr , b ) 0.714 hrs , c ) 3.231 hrs , d ) 0.515 hrs , e ) 6.214 hrs
Rationale: "to be ( 30 + 40 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 70 * 50 = 0.714 hrs answer is b"
Answer: b
Problem: in x - y plane , there is a right triangle abc ( ∠ b = 90 o ) . if the length of ac is 25 and the slope of line segment ac is 4 / 3 , what is the length of ab ?
Options: a ) 12 , b ) 18 , c ) 24 , d ) 20 , e ) 40
Rationale: "slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 25 ^ 2 16 x ^ 2 + 9 x ^ 2 = 625 25 x ^ 2 = 625 x ^ 2 = 25 x = 5 therefore ab = 5 * 4 = 20 answer : d"
Answer: d
Problem: the average of 5 consecutive odd numbers a , b , c , d and e is 13 . what percent of b is c ?
Options: a ) 98.2 , b ) 102.8 , c ) 108.2 , d ) 118.2 , e ) 122.8
Rationale: explanation : in such a case the middle number ( c ) is the average ∴ c = 13 and b = 11 required percentage = 13 / 11 x 100 = 118.2 answer : option d
Answer: d
Problem: a palindrome is a number that reads the same forward and backward , such as 343 . how many odd , 8 - digit numbers are palindromes ?
Options: a ) 4000 , b ) 4500 , c ) 5055 , d ) 5000 , e ) 2500
Rationale: "first recognize you only need to consider the first four digits ( because the second four are just the first four flipped ) there are 9000 possibilities for the first four digits of a 8 digit number , 1000 - 9999 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 9000 = 5000 answer : d"
Answer: d
Problem: a person borrows rs . 7000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .
Options: a ) 100 rs , b ) 150 rs , c ) 140 rs , d ) 180 rs , e ) 200 rs
Rationale: "gain in 2 years = [ ( 7000 * 6 * 2 ) / 100 ] - [ ( 7000 * 4 * 2 ) / 100 ] 840 - 560 = 280 gain in 1 year = ( 280 / 2 ) = 140 rs answer : c"
Answer: c
Problem: two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 240 marks in the second test and failed by 57 marks in that test . find the pass mark in the first test ?
Options: a ) 768 , b ) 243 , c ) 246 , d ) 264 , e ) 224
Rationale: "let the maximum mark in each test be m . the candidate failed by 57 marks in the second test . pass mark in the second test = 240 + 57 = 297 45 / 100 m = 297 pass mark in the first test = 40 / 100 m = 40 / 45 * 297 = 264 . answer : d"
Answer: d
Problem: if the side of the regular hexagon above is 2 , what is the circumference of the inscribed circle ?
Options: a ) 2 ∏ √ 3
b ) 3 ∏
c ) 4 ∏ / √ 3
d ) 2 ∏ / √ 3
e ) ∏ √ 3
Rationale: now ac will be 1 because circle is touching the midpoints of the circle . then we get kite acbo . we have ac = 1 and cb = 1 , now we need to find bo which is radius from triplets we get 30 : 60 : 90 = 1 : √ 3 : 2 now cbo is right angled triangle , then we get bo as √ 3 . r = √ 3 . . . circumference is 2 ∏ r is 2 ∏ √ 3 . answer : option a .
Answer: a
Problem: what is the difference between the local value of 1 and 2 in the number 2124 ?
Options: a ) 70 , b ) 75 , c ) 20 , d ) 80 , e ) 60
Rationale: explanation : 100 â € “ 20 = 80 answer : d
Answer: d
Problem: in 10 years , a will be twice as old as b was 10 years ago . if a is now 7 years older than b the present age of b is
Options: a ) 37 , b ) 38 , c ) 39 , d ) 40 , e ) 41
Rationale: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 7 = > 2 b - b - 7 = 30 b = 37 so the present age of b is 37 years answer : a"
Answer: a
Problem: the ratio of the present age of sandy to that of molly is 9 : 2 . eight years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
Options: a ) 18 , b ) 21 , c ) 24 , d ) 27 , e ) 30
Rationale: "let the present age of sandy be 9 x years and that of molly be 2 x years . ( 9 x + 8 ) / ( 2 x + 8 ) = 5 / 2 8 x = 24 x = 3 six years ago , sandy ' s age was 9 ( 3 ) - 6 = 21 the answer is b ."
Answer: b
Problem: rebecca ' s annual income is $ 15 , and jimmy ' s annual income is $ 18 . by how much must rebecca ' s annual income increase so that it constitutes 50 % of rebecca and jimmy ' s combined income ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 3 , e ) 10
Rationale: "total rebecca = x + 15 ; total = x + 20 + 18 x + 15 / x + 33 = 50 / 100 therefore x = 3 d"
Answer: d
Problem: you buy a piece of land with an area of â ˆ š 1600 , how long is one side of the land plot ?
Options: a ) 28 , b ) 40 , c ) 30 , d ) 31 , e ) 32
Rationale: "try filling the numbers into the answer y x y = find the closest to 900 . answer b"
Answer: b
Problem: a can do a work in 15 days b in 14 days and c in 16 days . if they work on it together then in how many days required to complete the work ?
Options: a ) 3360 / 210 , b ) 3360 / 21 , c ) 3360 / 674 , d ) 3360 / 240 , e ) 3360 / 224
Rationale: person ( a ) ( b ) ( c ) ( a + b + c ) time - ( 15 ) ( 14 ) ( 16 ) rate - ( 224 ) ( 240 ) ( 210 ) ( 674 ) work - ( 3360 ) ( 3360 ) ( 3360 ) ( 3360 ) therefore a + b + c requires ( 3360 / 674 ) days to complete entire work = 3360 / 674 answer is c
Answer: c
Problem: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 9 meters , and the interior of tank b has a height of 9 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 75 % , b ) 90 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: "the radius of tank a is 9 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 81 / ( 4 * pi ^ 2 ) = 405 / ( 2 * pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 9 * pi * 100 / ( 4 * pi ^ 2 ) = 450 / ( 2 * pi ) tank a / tank b = 405 / 450 = 9 / 10 = 90 % the answer is b ."
Answer: b
Problem: what is the smallest positive integer x such that 66 - x is the cube of a positive integer
Options: a ) 5 , b ) 7 , c ) 47 , d ) 9 , e ) 2
Rationale: "given 66 - x is a perfect cube so we will take 64 = 4 * 4 * 4 66 - x = 64 x = 66 - 64 = 2 correct option is e"
Answer: e
Problem: a cistern can be filled by a tap in 6 hours while it can be emptied by another tap in 12 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 5.2 hrs , b ) 2.9 hrs , c ) 12 hrs , d ) 7.2 hrs , e ) 1.4 hrs
Rationale: "net part filled in 1 hour = ( 1 / 6 - 1 / 12 ) = 1 / 12 the cistern will be filled in 12 / 1 hrs i . e . , 12 hrs . answer : c"
Answer: c
Problem: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 40 percent ryegrass , what percent of the weight of this mixture is x ?
Options: a ) 100 % , b ) 33.33 % , c ) 40 % , d ) 50 % , e ) 66.66 %
Rationale: "- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 40 % 0.4 x + ( m - x ) 0.25 = 0.4 m 0.15 x = 0.15 m x = 1 m x = 100 % of m a"
Answer: a
Problem: a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 125 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 125 total = 125 + 125 = 250 answer ( e )
Answer: e
Problem: the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if y 12 = 110 , what is the value of y ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 15 , e ) 18
Rationale: ab = ( a - 1 ) ( b - 1 ) y 12 = ( y - 1 ) ( 12 - 1 ) = 110 - - > y - 1 = 10 - - > y = 11 answer : a
Answer: a
Problem: each month a retailer sells 100 identical items . on each item he makes a profit of $ 60 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?
Options: a ) 191 , b ) 213 , c ) 221 , d ) 223 , e ) 226
Rationale: "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 60 sell price = $ 600 + $ 60 thus , the sell price is $ 660 for each item . selling all 100 items gives the retailer . . . 100 ( $ 60 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 660 ) = $ 33 discount $ 627 = $ 600 + $ 27 now , the retailer makes a profit of just $ 27 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 27 ( x ) = $ 2,000 x = 2,000 / 27 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"
Answer: d
Problem: a and b go around a circular track of length 200 m on a cycle at speeds of 36 kmph and 72 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 198 sec , c ) 178 sec , d ) 20 sec , e ) 276 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 200 / ( 36 * 5 / 18 ) , 200 / ( 72 * 5 / 18 ) } = lcm ( 20 , 10 ) = 20 sec . answer : d"
Answer: d
Problem: if x and y are both odd prime numbers and x < y , how many distinct positive r integer factors does 2 xy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: since 2 xy prime r factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .
Answer: d
Problem: a man can row 8 kmph in still water . when the river is running at 3 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.75 , b ) 5.7 , c ) 5.76 , d ) 5.74 , e ) 6.8
Rationale: "m = 8 s = 3 ds = 11 us = 5 x / 11 + x / 5 = 1 x = 3.4 d = 3.4 * 2 = 6.8 answer : e"
Answer: e
Problem: the length of a train and that of a platform are equal . if with a speed of 36 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 752 , b ) 799 , c ) 300 , d ) 750 , e ) 712
Rationale: "speed = [ 36 * 5 / 18 ] m / sec = 10 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 10 ã ¨ x = 10 * 60 / 2 = 300 answer : c"
Answer: c
Problem: the overall age of x and y is 19 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 15 , c ) 12 , d ) 19 , e ) 20
Rationale: "d 19 ( x + y ) â € “ ( y + z ) = 19 x â € “ z = 19"
Answer: d
Problem: for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 16 , then v =
Options: a ) 30 , b ) 33 , c ) 36 , d ) 39 , e ) 42
Rationale: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 16 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 36 the answer is c ."
Answer: c
Problem: find the perimeter and area of the rectangle of length 11 cm and breadth 9 cm .
Options: a ) 71 cm 2 , b ) 99 cm 2 , c ) 141 cm 2 , d ) 171 cm 2 , e ) 221 cm 2
Rationale: "length = 11 cm , breadth = 9 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 11 + 9 ) cm = 2 × 20 cm = 40 cm we know that the area of rectangle = length × breadth = ( 11 × 9 ) cm 22 = 99 cm 2 answer : b"
Answer: b
Problem: a group of men decided to do a work in 55 days , but 15 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ?
Options: a ) 180 , b ) 150 , c ) 140 , d ) 100 , e ) 25
Rationale: "original number of men = 15 * 60 / ( 60 - 55 ) = 180 answer is a"
Answer: a
Problem: two trains are moving in the same direction at 108 kmph and 54 kmph . the faster train crosses a man in the slower train in 24 seconds . find the length of the faster train ?
Options: a ) 320 , b ) 330 , c ) 340 , d ) 350 , e ) 360
Rationale: "relative speed = ( 108 - 54 ) * 5 / 18 = 3 * 5 = 15 mps . distance covered in 27 sec = 24 * 15 = 360 m . the length of the faster train = 360 m . answer : e"
Answer: e
Problem: a student travels from his house to school at 10 km / hr and reaches school 2 hours late . the next day he travels 15 km / hr and reaches school 1 hour early . what is the distance between his house and the school ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "let x be the distance from his house to the school . x / 10 = x / 15 + 3 6 x = 4 x + 180 2 x = 180 x = 90 km the answer is d ."
Answer: d
Problem: a train 250 m long , running with a speed of 50 km / hr will pass a tree in ?
Options: a ) 18 sec , b ) 20 sec , c ) 25 sec , d ) 30 sec , e ) 1 min
Rationale: "speed = 50 * 5 / 18 = 125 / 9 m / sec time taken = 250 * 9 / 125 = 18 sec answer : a"
Answer: a
Problem: the length of minute hand of a clock is 5.4 cm . what is the area covered by this in 20 minutes
Options: a ) 15.27 , b ) 16.27 , c ) 17.27 , d ) 30.54 , e ) 30.27
Rationale: "area of circle is pi * r ^ 2 but in 20 minutes area covered is ( 20 / 60 ) * 360 = 120 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.4 ^ 2 ) * ( 120 / 360 ) = 30.54 cm ^ 2 answer : d"
Answer: d
Problem: country x imposes a two - tiered tax on imported cars : the first tier imposes a tax of 25 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 15 % . if ron imported a $ 30000 imported car and ended up paying $ 5500 in taxes , what is the first tier ' s price level ?
Options: a ) $ 10000 , b ) $ 11000 , c ) $ 12000 , d ) $ 10500 , e ) $ 11500
Rationale: let t be the tier price , p be total price = 30000 per the given conditions : 0.25 t + 0.15 ( p - t ) = 5500 0.25 t + 0.15 * 30000 - 0.15 t = 5500 0.10 t + 4500 = 5500 0.10 t = 5500 - 4500 = 1000 t = 1000 / 0.10 = 10000 answer a
Answer: a
Problem: in the faculty of reverse - engineering , 230 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 618 . , d ) 649 . , e ) 666 .
Rationale: "answer is d : 649 solution : total number of students studying both are 423 + 230 - 134 = 519 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 519 , so 100 % is approx . 649 ."
Answer: d
Problem: the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 48 . what is a possible value for the mean of the distribution ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 55 , e ) 50
Rationale: "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 48 : { mean } - 3 * { sd } > 48 ; { mean } - 6 > 48 ; { mean } > 54 . answer : d ."
Answer: d
Problem: a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 9 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?
Options: a ) 3 , b ) 9 , c ) 15 , d ) 21 , e ) 30
Rationale: "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 9 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 9 ) = 0.08 t - - > 60 + 6 ( t - 9 ) = 8 t - - > t = 3 . answer : a ."
Answer: a
Problem: zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 9 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 9 questions did zachary answer correctly ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "i got two equations : 3 x - 2 y = 25 x + y = 9 3 x - 2 ( 9 - x ) = 25 3 x - 18 + 2 x = 25 5 x = 43 x = 8.6 or between 8 and 9 . ( ans c )"
Answer: c
Problem: if the average of 5 positive integers is 60 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
Options: a ) 50 , b ) 52 , c ) 49 , d ) 68 , e ) 74
Rationale: "sum of 5 integer ( a , b , c , d , e ) = 5 * 60 = 300 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 300 i . e . 5 a = 290 i . e . a = 58 i . e . largest e = 58 + 10 = 68 answer : option d"
Answer: d
Problem: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 160 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 140
Rationale: "set up equation : x = total number of workers 160 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 160 = 16 / 30 x x = 300 300 - 160 = 140 answer e"
Answer: e
Problem: the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 180,000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
Rationale: "percentage increase = increase in price / original price * 100 = ( 180000 - 120000 ) / 120000 * 100 = 50 % answer : b"
Answer: b
Problem: sum of 53 odd numbers is ?
Options: a ) 2709 , b ) 2809 , c ) 2909 , d ) 3009 , e ) 3109
Rationale: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 53 odd numbers = 53 ^ 2 = 2809 answer : b"
Answer: b
Problem: find the value of 5 + 2 â € ¢ ( 8 â € “ 3 )
Options: a ) 25 , b ) 13 , c ) 17 , d ) 24 , e ) 15
Rationale: 5 + 2 â € ¢ ( 8 â € “ 3 ) = 5 + 2 ( 5 ) = 5 + 2 * 5 = 5 + 10 = 15 correct answer e
Answer: e
Problem: the mass of 1 cubic meter of a substance is 500 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 0.8 , b ) 1.25 , c ) 2.0 , d ) 2.5 , e ) 80.0
Rationale: "density is mass divided by volume . so density of the given substance will be mass / volume = 500 kg / 1 m ^ 3 = 800 kg / m ^ 3 or 1 g / 1.5 cm ^ 3 = 0.5 g / cm ^ 3 . next , ask yourself if 500,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 500,000 = 10 / 5 = 2.0 cubic centimeters . answer is c"
Answer: c
Problem: what least number should be added to 1057 , so that the sum is completely divisible by 23
Options: a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5
Rationale: "explanation : ( 1057 / 23 ) gives remainder 22 22 + 1 = 23 , so we need to add 1 answer : option b"
Answer: b
Problem: he ratio between the sale price and the cost price of an article is 5 : 6 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 6 , b ) 1 : 8 , c ) 1 : 6 , d ) 2 : 1 , e ) 2 : 5
Rationale: "let c . p . = rs . 6 x and s . p . = rs . 5 x . then , gain = rs . x required ratio = x : 6 x = 1 : 6 . answer : c"
Answer: c
Problem: . in digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 3323 , b ) 1000 , c ) 2877 , d ) 2992 , e ) 7111
Rationale: 20 * 10 * 5 = 1000 answer : b
Answer: b
Problem: when 1 / 20 % of 8,000 is subtracted from 1 / 10 of 8,000 , the difference is
Options: a ) 50 , b ) 200 , c ) 380 , d ) 798 , e ) 400
Rationale: 1 / 20 % of 8000 = 4 1 / 10 of 8000 = 800 800 - 2 = 798 ans : d
Answer: d
Problem: 35 % of the employees of a company are men . 60 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?
Options: a ) 4 % , b ) 10 % , c ) 96 % , d ) 90.12 % , e ) 70.77 %
Rationale: no of employees = 100 ( say ) men = 35 women = 65 men speaking french = 0.6 * 35 = 21 employees speaking french = 0.4 * 100 = 40 therefore women speaking french = 40 - 21 = 19 and women not speaking french = 65 - 19 = 46 % of women speaking french = 46 / 65 * 100 = 70.77 % answer e
Answer: e
Problem: how many integers k greater than 100 and less than 700 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "not sure if this is the shortest . . but this is how i did this there are 5 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . 506 | 607 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 5 sets with 10 such number in each set will give 5 x 10 = 50 integers . a"
Answer: a
Problem: a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 45 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "a - b = 120 miles b - c = 60 miles avg speed = 45 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 45 = 180 / 4 t t = 60 b - c = 60 mph answer e"
Answer: e
Problem: which greatest possible length can be used to measure exactly 15 meter 20 cm , 12 meter 20 cm and 14 meter 20 cm
Options: a ) 20 cm , b ) 25 cm , c ) 24 cm , d ) 55 cm , e ) 30 cm
Rationale: "explanation : convert first all terms into cm . i . e . 1520 cm , 1220 cm , 1420 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 20 . option a"
Answer: a
Problem: dick and jane each saved $ 5,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 10,000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "1990 dick saved = $ 5500 jane saved = $ 4500 ( jane saved $ 500 less than she did the prior year ) jane saved approximately $ 500 / 5000 $ ( 10 % ) less in 1990 answer : a"
Answer: a
Problem: robert ate 7 chocolates , nickel ate 5 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2
Rationale: 7 - 5 = 2 . answer is e
Answer: e
Problem: a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 600 feet . what is its area , in square feet ?
Options: a ) 172,800
b ) 19,600
c ) 20,000
d ) 20,400
e ) 20,800
Rationale: you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 600 , you can deduce the following a = 360 b = 480 360 x 480 = 172,800 a is the answer .
Answer: a
Problem: on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor
Options: a ) 12 , b ) 14 , c ) 18 , d ) 22 , e ) 24
Rationale: "d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 a )"
Answer: a
Problem: find compound interest on $ 10000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 3886.25 , b ) 3286.25 , c ) 3186.25 , d ) 3386.25 , e ) 3586.25
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 10000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 10000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 13886.25 . : . c . i . = rs . ( 13886.25 - 10000 ) = $ 3886.25 answer a ."
Answer: a
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.28 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.40 , b ) $ 3.00 , c ) $ 3.20 , d ) $ 3.60 , e ) $ 4.80
Rationale: "total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 1.28 therefore , x = $ 4.80 . answer e"
Answer: e
Problem: what is the range of all the roots of | x ^ 2 - 4 | = x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 4 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 4 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 4 or x = 1 i guess range is 4 - 1 = 3 b"
Answer: b
Problem: sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 60 ps per meter is ?
Options: a ) 287 , b ) 369 , c ) 150 , d ) 279 , e ) 361
Rationale: "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.60 = rs . 150 answer : c"
Answer: c
Problem: the cost price of a radio is rs . 1680 and it was sold for rs . 1450 , find the loss % ?
Options: a ) 18 , b ) 13 , c ) 15 , d ) 18 , e ) 41
Rationale: "1680 - - - - 230 100 - - - - ? = > 13 % answer : b"
Answer: b
Problem: when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 7 . when n is divided by ( p + 3 ) , the quotient is 15 and the remainder is 1 . what is the value of n ?
Options: a ) 151 , b ) 331 , c ) 511 , d ) 691 , e ) 205
Rationale: "n / p = 18 7 / p = 18 p + 7 n / ( p + 2 ) = 15 1 / ( p + 3 ) = 15 p + 45 + 1 solving these two equations we get p = 11 n = 205 answer is e ."
Answer: e
Problem: if a person walks at 25 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
Options: a ) 50 km , b ) 56 km , c ) 13.3 km , d ) 70 km , e ) 80 km
Rationale: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 25 25 x = 10 x + 200 15 x = 200 x = 13.3 km . answer : c"
Answer: c
Problem: a big container is 30 % full with water . if 45 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 100 liters
Rationale: "a big container is 30 % full with water and after 45 liters of water is added , the container becomes 75 % full . hence these 45 liters account for 45 % of the container , which means that the capacity of it is 45 / 0.45 = 100 liters . or : if the capacity of the container is x liters then : 0.3 x + 45 = 0.75 x - - > x = 100 liters . answer : e ."
Answer: e
Problem: 32 % of 1500 is
Options: a ) 480 , b ) 440 , c ) 370 , d ) 415 , e ) 435
Rationale: 1 % of 1500 is = 15 32 % of 1500 is = 32 * 15 = 480 answer : a
Answer: a
Problem: find the smallest number that should be multiplied with 54000 to make it a perfect cube .
Options: a ) 4
b ) 5
c ) 6
d ) 3
e ) 7
Rationale: 54000 = 2 ^ 1 * 3 ^ 3 * 10 ^ 3 to make it ps * 2 ^ 2 or 4 answer : a
Answer: a
Problem: a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 500000 ?
Options: a ) 160 , b ) 200 , c ) 240 , d ) 300 , e ) 480
Rationale: the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b .
Answer: b
Problem: the average of 7 numbers is 25 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) a ) 110 , b ) b ) 122 , c ) c ) 120 , d ) d ) 125 , e ) e ) 145
Rationale: "explanation : average of new numbers = 25 * 5 = 125 answer : option d"
Answer: d
Problem: a 90 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 25 , b ) 20 , c ) 47 , d ) 36 , e ) 30
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 90 = 25 answer : a"
Answer: a
Problem: there are cats got together and decided to kill the mice of 999964 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
Options: a ) 941,1009 , b ) 991,1001 , c ) 991,1009 , d ) 791,1009 , e ) 994,1006
Rationale: "999964 can be written as 1000000 â € “ 36 = 10002 â € “ 62 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 6 ) * ( 1000 - 6 ) = ( 1006 ) * ( 994 ) given that number of cats is less than number if mice . so number of cats is 994 and number of mice were 1006 answer e"
Answer: e
Problem: what is the remainder when you divide 2 ^ 200 - 1 by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: answer is c . this is very similar to the 32 ^ 32 ^ 32 - 1 divided by 7 question .
Answer: c
Problem: a courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is :
Options: a ) 16000 , b ) 18000 , c ) 20000 , d ) 22000 , e ) none of these
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 2500 × 1600 / 20 × 10 ) = 20000 option c"
Answer: c
Problem: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1008 ?
Options: a ) 900 , b ) 2217 , c ) 2889 , d ) 2777 , e ) 2991
Rationale: "1008 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 900 answer : a"
Answer: a
Problem: if a sum of money doubles itself in 20 years at simple interest , the ratepercent per annum is
Options: a ) 12 , b ) 12.5 , c ) 13 , d ) 5 , e ) 14
Rationale: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 20 ) = 5 option d"
Answer: d
Problem: what is the greatest integer m for which the number 50 ! / 10 ^ m is an integer ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 11 , e ) 12
Rationale: "as for 50 ! / 10 ^ m , the greatest value of m will be obtained by finding the maximum number of 5 s in 50 ! the quick process for that ( discussed in the link above ) is 50 / 5 = 10 10 / 5 = 2 total number of 5 s is 12 . so maximum value of m will also be 12 . answer ( e )"
Answer: e
Problem: at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 7.50 per hour , how much less than a manager does a chef earn each hour ?
Options: a ) $ 1.40 , b ) $ 3 , c ) $ 3.40 , d ) $ 4.40 , e ) $ 5.40
Rationale: "manager wages per hour = $ 7.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 7.50 ) = = > $ 3.75 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 3.75 = ( 20 * ( $ 3.75 ) ) / 100 - - > ( $ 75 ) / 100 - - > $ 0.75 therefore , chef wages per hour = $ 3.75 + $ 0.75 = = > $ 4.5 difference of wages between manager and chef = $ 7.50 - $ 4.5 = = > $ 3 answer : b"
Answer: b
Problem: a person incurs a loss of 5 % be selling a watch for rs . 1140 . at what price should the watch be sold to earn 5 % profit
Options: a ) rs . 1200 , b ) rs . 1230 , c ) rs . 1260 , d ) rs . 1290 , e ) none of these
Rationale: "explanation : let the new s . p . be x , then . ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) = > ( 95 / 1140 = 105 / x ) = > x = 1260 option c"
Answer: c
Problem: a train is 400 meter long is running at a speed of 60 km / hour . in what time will it pass a signal post ?
Options: a ) 28 seconds , b ) 30 seconds , c ) 40 seconds , d ) 24 seconds , e ) 18 seconds
Rationale: speed = 60 km / hr = 60 * ( 5 / 18 ) m / sec = 150 / 9 m / sec total distance = 400 meter time = distance / speed = 400 * ( 9 / 150 ) = 24 seconds answer : d
Answer: d
Problem: the average of first 10 natural numbers is ?
Options: a ) 5.6 , b ) 5.5 , c ) 5.1 , d ) 5.8 , e ) 5.2
Rationale: "sum of 10 natural no . = 110 / 2 = 55 average = 55 / 10 = 5.5 answer : b"
Answer: b
Problem: if a / b = 4 / 5 , then ( 5 a - 3 b ) / ( 5 a + 3 b ) = ?
Options: a ) 4 , b ) 2 / 3 , c ) 3 , d ) 1 , e ) 1 / 7
Rationale: "answer dividing numerator as well as denominator by b , we get given exp . = ( 5 a - 3 b ) / ( 5 a + 3 b ) = ( 5 a / b - 3 ) / ( 5 a / b + 3 ) since a / b = 4 / 5 this implies that = [ ( 5 * 4 ) / 5 - 3 ] / [ ( 5 * 4 ) / 5 + 3 ) ] = ( 4 - 3 ) / ( 4 + 3 ) = 1 / 7 option : e"
Answer: e
Problem: how long does a train 105 m long running at the speed of 68 km / hr takes to cross a bridge 90 m length ?
Options: a ) 13.9 sec , b ) 10.7 sec , c ) 17.9 sec , d ) 61.9 sec , e ) 47.98 sec
Rationale: "speed = 68 * 5 / 18 = 19 m / sec total distance covered = 105 + 90 = 205 m . required time = 205 / 19 = 10.7 sec . answer : b"
Answer: b
Problem: there are 6 people in the elevator . their average weight is 152 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
Options: a ) 145 , b ) 168 , c ) 189 , d ) 190 , e ) 200
Rationale: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 152 ) = 1057 - 912 = 145 . answer a"
Answer: a
Problem: ms . lopez deposits $ 150 in an account that pays 20 % interest , compounded semiannually . how much money will there be in the account at the end of one year ?
Options: a ) $ 118.00 , b ) $ 120.00 , c ) $ 181.15 , d ) $ 122.00 , e ) $ 140.00
Rationale: "using formula - a = p ( 1 + r / n ) ^ nt given p = 150 n = 2 t = 1 r = 0.2 substituting value in formula a = 150 ( 1 + 0.2 / 2 ) ^ 2 a = 181.15 $ = c"
Answer: c
Problem: a , b , c can complete a piece of work in 25 , 5,10 days . working together , they complete the same work in how many days ?
Options: a ) 2 , b ) 4 / 5 , c ) 50 / 17 , d ) 10 , e ) 24 / 7
Rationale: "a + b + c 1 day work = 1 / 25 + 1 / 5 + 1 / 10 = 17 / 50 a , b , c together will complete the job in 50 / 17 days answer is c"
Answer: c
Problem: how much is 70 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 22 , b ) 67 , c ) 88 , d ) 12 , e ) 8
Rationale: "( 70 / 100 ) * 40 – ( 4 / 5 ) * 25 = 8 answer : e"
Answer: e
Problem: one man adds 3 liters of water to 12 liters of milk and another 4 liters of water to 10 liters of milk . what is the ratio of the strengths of milk in 2 mixtures ?
Options: a ) 11 : 21 , b ) 15 : 33 , c ) 28 : 25 , d ) 3 : 2 , e ) 31 : 33
Rationale: "strength of milk in the mixture = quantity of milk / total quantity of mixture strength of milk in the 1 st mixture = 12 / 15 strength of the milk 2 nd mixture = 10 / 14 the ratio of their strengths = 12 / 15 : 10 / 14 = 28 : 25 answer is c"
Answer: c
Problem: 27 is a perfect cube . when x is added to the prime factor of 27 , the result is a prime number . what is x ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 8 , e ) 11
Rationale: 27 is 3 * 3 * 3 then a 3 + 1 = 4 b 3 + 3 = 6 c 3 + 5 = 8 d 3 + 8 = 11 e 3 + 11 = 14 here d is the only addition that gives a prime number .
Answer: d
Problem: a part - time employee ’ s hourly wage was increased by 10 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
Options: a ) 9 % , b ) 15 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 10 % wage increase , the employee makes $ 1.10 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.10 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.10 to get : new # of hours = 100 / 1.10 ≈ 90 hours so , the number of hours decreases from 100 hours to ( approximately ) 90 hours . this represents a 10 % decrease ( approximately ) . answer choice a is the closest answer ."
Answer: a
Problem: the price of stock decreased by 5 % last year and rose by 10 % this year . what is the net percentage change in the price of the stock ?
Options: a ) 0.2 % , b ) 0.8 % , c ) 1.2 % , d ) 1.6 % , e ) 4.5 %
Rationale: "( 100 % - 5 % ) * ( 100 % + 10 % ) = 0.95 * 1.10 = 1.045 = 104.5 % . the net percentage change in the price of the stock is ( + ) 4.5 % the answer is e"
Answer: e
Problem: the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 7 seconds than it was moving after 5 seconds ?
Options: a ) 4 , b ) 28 , c ) 15 , d ) 48 , e ) 63
Rationale: "given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 5 ) = 5 ^ 2 + 2 * 5 = 35 z ( 7 ) = 7 ^ 2 + 2 * 7 = 63 therefore z ( 7 ) - z ( 3 ) = 63 - 35 = 28 km / hr option b"
Answer: b
Problem: a soccer team played 280 games and won 65 percent of them . how many games did it win ?
Options: a ) 182 , b ) 100 , c ) 104 , d ) 150 , e ) 124
Rationale: "65 % of 280 = x 0.65 * 280 = x 182 = x answer : a"
Answer: a
Problem: the difference between two numbers is 2395 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is
Options: a ) 120 , b ) 239 , c ) 476 , d ) 523 , e ) 526
Rationale: let the smaller number be x . then , larger number = ( 2395 + x ) therefore 2395 + x = ( 6 x + 15 ) ‹ = › 5 x = 2380 ‹ = › x = 476 . answer : c
Answer: c
Problem: right triangle xyzs the base of the prism in the figure above . if xy = xz = â ˆ š 9 and the height of the prism is 6 , what is the volume of the prism ?
Options: a ) 3
b ) 27
c ) 13
d ) 12
e ) 15
Rationale: volume of prism = area of base * height = 1 / 2 * ( square root of 9 ) * ( square root of 9 ) * 6 = 27 answer : b
Answer: b
Problem: on dividing 22 by a number , the quotient is 7 and the remainder is 1 . find the divisor .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 7
Rationale: "d = ( d - r ) / q = ( 22 - 1 ) / 7 = 21 / 7 = 3 c"
Answer: c
Problem: the smallest number which when diminished by 5 , is divisible by 12 , 16 , 18 , 21 and 28 is
Options: a ) 1008 , b ) 1013 , c ) 1022 , d ) 1032 , e ) 1043
Rationale: "required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 5 = 1008 + 5 = 1013 answer : b"
Answer: b
Problem: the ratio between x and y is 7 / 5 ; x is multiplied by y and y is multiplied by x , what is the ratio between the new values of x and y ?
Options: a ) 7 / 5 , b ) 5 / 7 , c ) 1 , d ) 49 / 25 , e ) it can not be determined
Rationale: ratio = 7 k / 5 k = 7 / 5 , 14 / 10 , etc . x is multiplied by y and y is multiplied by x - - > ( 7 k * 9 k ) / ( 9 k * 7 k ) = 1 answer : c
Answer: c
Problem: when x is multiplied by 3 , the result is 14 more than the result of subtracting x from 26 . what is the value of x ?
Options: a ) 10 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: the equation that can be formed is : 3 x - 14 = 26 - x or , 4 x = 40 or , x = 10 . a answer .
Answer: a
Problem: raman , lakshmi and muthu enter into partnership . raman invests some money at the beginning , lakshmi invests double the amount after 6 months , and muthu invests thrice the amount after 8 months . if the annual gain be rs . 36000 . lakshmi ' s share is ?
Options: a ) 12000 , b ) 14000 , c ) 8000 , d ) 5000 , e ) 3000
Rationale: x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 36000 = 12000 answer : a
Answer: a
Problem: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 10 per square m ?
Options: a ) s . 9500 , b ) s . 50000 , c ) s . 57000 , d ) s . 60000 , e ) s . 62000
Rationale: length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 10 * 950 = rs . 9500 a
Answer: a
Problem: how many multiples of 4 are less than 6540 , and also multiples of 7 ?
Options: a ) 234 , b ) 208 , c ) 340 , d ) 237 , e ) 267
Rationale: "lcm of 4 & 7 = 28 tried dividing 6540 by 28 got quotient 233.5 ' so a is answer"
Answer: a
Problem: 31 of the scientists that attended a certain workshop were wolf prize laureates , and 18 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 50 of the scientists attended that workshop , how many of them were nobel prize laureates ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 24 , d ) d ) 29 , e ) d ) 36
Rationale: "lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 13 . . so total who won n = 11 + 18 = 29 . . d"
Answer: d
Problem: if 4 men can colour 48 m long cloth in 2 days , then 2 men can colour 36 m long cloth in
Options: a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
Rationale: "the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 2 = 3 day . c"
Answer: c
Problem: how many integers between 324,700 and 458,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,339
Rationale: "there is one number in hundred with 1 in th tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 324,700 and 458,600 is 458,600 - 324,700 = 133,900 - one number per each hundred gives 133,900 / 100 = 1,339 numbers . answer : e"
Answer: e
Problem: a library has an average of 540 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 300 , b ) 276 , c ) 290 , d ) 285 , e ) none
Rationale: "since the month begins with sunday , to there will be five sundays in the month average required = ( 540 x 5 + 240 x 25 ) / 30 ) = 290 answer : option c"
Answer: c
Problem: on the number line , the number p is twice as many units from - 2 as - 2 is from 5 . if p is less than – 2 , what is the value of p ?
Options: a ) – 16 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
Rationale: "distance between - 2 and 5 = 7 since number p is twice as many units from - 2 as - 2 is from 5 , therefore p can be - 16 since , p is less than - 2 , the value of p = - 16 answer a"
Answer: a
Problem: when sold at a 70 % discount , a sweater nets the merchant a 40 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 78.58 %
Rationale: "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 70 % of 100 = 30 . . profit = 40 % . . therefore the wholesale purchase cost = x . . . . 1.4 x = 30 or x = 21.42 . . . marked price was 100 so . . . so answer is 78.58 % . . e"
Answer: e
Problem: on a certain farm the ratio of horses to cows is 4 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 13 : 7 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 30 , b ) 60 , c ) 75 , d ) 90 , e ) 105
Rationale: "originally , there were 4 k horses and k cows . 7 ( 4 k - 15 ) = 13 ( k + 15 ) 28 k - 13 k = 195 + 105 15 k = 300 k = 20 the difference between horses and cows is ( 4 k - 15 ) - ( k + 15 ) = 3 k - 30 = 30 the answer is a ."
Answer: a