regisss/math_qa huggingface dataset:
Problem: a $ 500 investment and a $ 1,500 investment have a combined yearly return of 10 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 9 % , b ) 10 % , c ) 105 / 8 % , d ) 11 % , e ) 12 %
Rationale: the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 10 ) = ( 500 â ˆ — 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 11 % ( option d ) answer : d
Answer: d
Problem: the number of positive integer solutions for the equation x + y + z + t = 18 is
Options: a ) 640 , b ) 780 , c ) 380 , d ) 540 , e ) 680
Rationale: "the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 18 - 1 c 4 - 1 = 17 c 3 = 680 answer : e"
Answer: e
Problem: the average age of a group of n people is 15 years old . one more person aged 37 joins the group and the new average is 17 years old . what is the value of n ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "15 n + 37 = 17 ( n + 1 ) 2 n = 20 n = 10 the answer is a ."
Answer: a
Problem: the ratio between the speeds of two trains is 7 : 8 . if the second train runs 400 km in 4 hours , what is the the speed of the first train ?
Options: a ) 87.0 , b ) 87.5 , c ) 87.2 , d ) 87.1 , e ) 87.4
Rationale: speed and time are inversely proportional ( when distance is constant ) ⇒ speed ∝ 1 time ( when distance is constant ) here distance is constant and hence speed and time are inversely proportionalspeed ∝ 1 time ⇒ speed 1 speed 2 = time 2 time 1 ⇒ 78 = 4 time 1 ⇒ time 1 = 4 × 87 hr ⇒ speed of the first train = distancetime 1 = 400 ( 4 × 87 ) = 100 × 78 = 12.5 × 7 = 87.5 km / hr answer : b
Answer: b
Problem: what is the unit digit of ( 8 ! * 4 ! / 8 ! * 3 ! ) ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "( 8 ! * 4 ! / 8 ! * 3 ! ) = ( 4 ! / 3 ! ) = 24 / 6 = 4 units digit of the above product will be equal to 4 answer e"
Answer: e
Problem: area of square with side x is equal to the area of a triangle with base x . the altitude of the triangle is
Options: a ) x / 2
b ) x
c ) 2 x
d ) 4 x
e ) 3 x
Rationale: x ^ 2 = 1 / 2 ã ƒ â € ” x ã ƒ â € ” h or h = 2 x ^ 2 / x = 2 x answer : c
Answer: c
Problem: a baseball card decreased in value 60 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 64 %
Rationale: let the initial value of baseball card = 100 after first year , value of baseball card = ( 1 - 60 / 100 ) * 100 = 40 after second year , value of baseball card = ( 1 - 10 / 100 ) * 40 = 36 total percent decrease of the card ' s value over the two years = ( 100 - 36 ) / 100 * 100 % = 64 % answer e
Answer: e
Problem: there are 10 books on a shelf , of which 4 are paperbacks and 6 are hardbacks . how many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback ?
Options: a ) 75 , b ) 120 , c ) 210 , d ) 246 , e ) 252
Rationale: "paperbacks - 4 , hardbacks - 6 5 books in total and at least 1 from each . total combinations for 5 books = ( 1 pb , 4 hb ) + ( 4 pb , 1 hb ) + ( 3 pb , 2 hb ) + ( 2 pb , 3 hb ) 1 pb , 4 hb = 4 c 1 * 6 c 4 = 60 4 pb , 1 hb = 4 c 4 * 6 c 1 = 6 3 pb , 2 hb = 4 c 3 * 6 c 2 = 60 2 pb , 3 hb = 4 c 2 * 6 c 3 = 120 total combinations of 5 books = 60 + 6 + 60 + 120 = > 246 ans d ."
Answer: d
Problem: a walk 20 m towards north east . b walk towards east 8 m and then 12 m south . now calculate distance between a and b ?
Options: a ) 30 m , b ) 20 m , c ) 35 m , d ) 40 m , e ) 38 m
Rationale: its coming 30.4 m since 1 st triangle we get 18.31 and extra 12 so 18.31 + 12 = 30.31 = 30 m answer : a
Answer: a
Problem: if the difference between compound interest ( interest compounded yearly ) and simple interest on a sum for 3 years at 20 % p . a . is rs . 132 , then the sum is
Options: a ) rs . 3500 , b ) rs . 1500 , c ) rs . 2500 , d ) rs . 3000 , e ) none
Rationale: "c . i - s . i = 132 c . i = a - p a = p ( 1 + ( r / 100 ) ) ^ n a = x ( 1 + ( 20 / 100 ) ) ^ 3 a = x ( 6 / 5 ) ^ 3 a = 216 / 125 ( x ) c . i = ( 91 / 125 ) x s . i = ( pnr ) / 100 = ( x * 3 * 20 ) / 100 = ( 6 / 10 ) x diff = 132 diff = ( 91 / 25 ) x - ( 6 / 10 ) x = ( 182 x - 150 x ) / 250 = 32 x / 250 32 x / 250 = 132 x = ( 132 * 250 ) / 32 x = 1031.25 answer : e"
Answer: e
Problem: the mass of 1 cubic meter of a substance is 700 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 ) 1.42 , c ) 8.0 , d ) 12.5 , e ) 80.0
Rationale: "density is mass divided by volume . so density of the given substance will be mass / volume = 700 kg / 1 m ^ 3 = 700 kg / m ^ 3 or 1 g / 1.42 cm ^ 3 = 0.7 g / cm ^ 3 . next , ask yourself if 700,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 700,000 = 10 / 8 = 1.42 cubic centimeters . answer is b"
Answer: b
Problem: a plot abcd is as shown in figure , where af = 30 m , ce = 40 m , ed = 50 m , ae = 120 m . find the area of the plot abcd ?
Options: a ) 7207
b ) 7206
c ) 7203
d ) 7200
e ) 7201
Rationale: area of plot abcd = area of ade + area of afb + area of bcef = 1 / 2 * 50 * 120 + 1 / 2 * 40 * 30 + 40 * 90 = 3000 + 600 + 3600 = 7200 sq . m answer : d
Answer: d
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 126 km / hr
Options: a ) 8.5 seconds , b ) 2.86 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
Rationale: "first convert speed into m / sec speed = 126 * ( 5 / 18 ) = 35 m / sec time = distance / speed = 100 / 35 = 2.86 seconds answer : b"
Answer: b
Problem: two bullet train s 140 m and 170 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 12.8 sec . , c ) 11.16 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: "relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 170 ) m = 310 m . required time = 310 x 9 / 250 = 11.16 sec . answer c"
Answer: c
Problem: a rectangular garden is 12 m by 5 m , what is its area ?
Options: a ) 12 square meters
b ) 5 square meters
c ) 44 square meters
d ) 60 square meters
e ) 22 square meters
Rationale: area of a rectangle : a = w × h d ) 60 square meters
Answer: d
Problem: indu gave bindu rs . 3125 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) s . 10 , b ) s . 2 , c ) s . 5 , d ) s . 3 , e ) s . 4
Rationale: "3125 = d ( 100 / 4 ) 2 d = 5 answer : c"
Answer: c
Problem: if the ratio of a to b is 7 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 15
Rationale: "a : b = 7 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 7 : 15 answer e"
Answer: e
Problem: the average of first 18 even numbers is ?
Options: a ) 19 , b ) 18 , c ) 16 , d ) 11 , e ) 17
Rationale: "sum of 18 even numbers = 18 * 19 = 342 average = 342 / 18 = 19 answer : a"
Answer: a
Problem: a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 238 less than the sum lent . what was the sum lent ?
Options: a ) 228 , b ) 350 , c ) 289 , d ) 500 , e ) 821
Rationale: "p - 238 = ( p * 4 * 8 ) / 100 p = 350 answer : b"
Answer: b
Problem: for every integer n ≥ 3 , the function g ( n ) is defined as the product of all the odd integers from 1 to n , inclusive . what is the value of g ( 99 ) – g ( 97 ) ?
Options: a ) 98 , b ) 100 , c ) 0 , d ) 99 , e ) 97
Rationale: g ( 99 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 g ( 97 ) = 1 * 3 * 5 * 7 * 9 * . . . * 97 g ( 99 ) - g ( 97 ) = 1 * 3 * 5 * 7 * 9 * . . . * 99 - 1 * 3 * 5 * 7 * 9 * . . . * 97 = 1 * 3 * 5 * 7 * 9 * . . . * 97 * ( 99 - 1 ) = 1 * 3 * 5 * 7 * 9 * . . . * 97 * 98 hence : a .
Answer: a
Problem: in the first 5 overs of a cricket game , the run rate was only 2.1 . what should be the rate in the remaining 30 overs to reach the target of 200 runs ?
Options: a ) 6.25 , b ) 6.28 , c ) 6.31 , d ) 6.19 , e ) 6.21
Rationale: "required run rate = [ 200 - ( 2.1 * 5 ) ] / 30 = 189.50 / 30 = 6.31 answer : c"
Answer: c
Problem: what is the sum of all even numbers from 1 to 901 ?
Options: a ) 122821 , b ) 202950 , c ) 281199 , d ) 122850 , e ) 128111
Rationale: "explanation : 900 / 2 = 450 450 * 451 = 202950 answer : b"
Answer: b
Problem: the lcm and hcf of two numbers are 100 and 10 respectively . find the larger of the two numbers if their sum is 110 .
Options: a ) 100 , b ) 12 , c ) 35 , d ) 466 , e ) 56
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 100 * 10 = 1000 so the answer which we are looking for has to be a factor of 1000 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 1000 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Problem: a couple decides to have 4 children . if they succeed in having 4 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 3 girls and 1 boy ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 1 / 2
Rationale: "sample space = 2 ^ 4 = 16 . favourable events = { bbgg } , { bgbg } , { bggb } , { ggbb } , { gbgb } , { gbbg } . { bggg } , { gbbb ) probability = 8 / 16 = 1 / 2 . ans ( e ) ."
Answer: e
Problem: what will be the compound interest on a sum of rs . 40,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s : 10123.19 , b ) s : 10123.29 , c ) s : 10123.20 , d ) s : 10123.28 , e ) s : 16197.12
Rationale: "amount = [ 40000 * ( 1 + 12 / 100 ) 3 ] = 40000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 56197.12 c . i . = ( 56197.12 - 40000 ) = rs : 16197.12 answer : e"
Answer: e
Problem: a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 370 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 190 , c ) 120 , d ) 130 , e ) 220
Rationale: orchestra seats - a balcony seats - b a + b = 370 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 370 = 3320 - 2960 = 360 i . e . a = 90 and b = 370 - 90 = 280 more seats in balcony than orchestra = b - a = 280 - 90 = 190 answer : option b
Answer: b
Problem: if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 81 , how much does one shirt cost ?
Options: a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 21 , e ) $ 16.80
Rationale: "3 j + 2 s = 69 2 j + 3 s = 81 - - - - - - - - - - - - - - - - 5 j + 5 s = 150 - - - - ( divide by 5 ) - - - > j + s = 30 3 j + 2 s = j + 2 ( j + s ) = j + 60 = 69 - - - > j = 9 3 * 9 + 2 s = 69 27 + 2 s = 69 2 s = 42 s = 21 answer : d"
Answer: d
Problem: a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . how many feet does the squirrel travels if the post is 27 feet tall and 3 feet in circumference ?
Options: a ) 10 feet , b ) 12 feet , c ) 27 feet , d ) 15 feet , e ) 18 feet
Rationale: "total circuit = 27 / 3 = 9 total feet squirrel travels = 9 * 3 = 27 feet answer : c"
Answer: c
Problem: how many zeroes are there at the end of the number n , if n = 60 ! + 120 ! ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: the number of zeroes at the end of 60 ! will be less than the number of zeroes at the end of 120 ! hence it is sufficient to calculate the number of zeroes at the end of 60 ! the number of zeroes = [ 60 / 5 ] + [ 60 / 25 ] + [ 60 / 125 ] = 12 + 2 + 0 = 14 the answer is b .
Answer: b
Problem: if x is a sum of all even integers on the interval 13 . . . 61 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 13 , c ) 26 , d ) 24 , e ) 1014
Rationale: "x = 14 + 16 + . . . + 60 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 60 ) / 2 * 24 = 37 * 24 . gcd of 24 and 37 * 22 is 24 . answer : d ."
Answer: d
Problem: a train leaves delhi at 11 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 40 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 360 , b ) 288 , c ) 600 , d ) 888 , e ) 121
Rationale: "d = 30 * 3 = 90 rs = 40 – 30 = 10 t = 90 / 10 = 9 d = 40 * 9 = 360 km answer : a"
Answer: a
Problem: if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exactly twice in 2 consecutive flips ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.375 , d ) 0.5 , e ) 0.666
Rationale: "total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 = 4 ways for 2 h tt , thus probability is = p ( tt ) = 1 / 4 = . 25 answer : b"
Answer: b
Problem: how many multiples of 8 are less than 7600 , and also multiples of 19 ?
Options: a ) 104 , b ) 100 , c ) 50 , d ) 89 , e ) 90
Rationale: "lcm of 8 & 19 = 152 tried dividing 7600 by 152 got quotient 50 ' so c is answer"
Answer: c
Problem: in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 5,7 ) , ( 12,7 ) , ( 2,3 ) , ( 9,3 ) ?
Options: a ) 21 , b ) 28 . , c ) 35 . , d ) 49 . , e ) 52 .
Rationale: "area of parallelogram = b * h . base = distance in x coordinates between ( 2,3 ) and ( 9,3 ) = 7 height = difference in y coordinates between ( 5,7 ) and ( 2,3 ) = 3 . area = 7 * 3 = 21 . answer : a"
Answer: a
Problem: on dividing 265 by a number , the quotient is 12 and the remainder is 1 . find the divisor .
Options: a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
Rationale: "d = ( d - r ) / q = ( 265 - 1 ) / 12 = 264 / 12 = 22 e )"
Answer: e
Problem: of the 12,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
Options: a ) 14.3 % , b ) 13.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
Rationale: "the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 13.67 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . b"
Answer: b
Problem: given two sets a = { 11 , 44 , 55 } and b = { 01 } , if one number is chosen from each set at random , what is the probability that the sum of both numbers is an even number
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 7 , d ) 1 / 2 , e ) 3
Rationale: one way to look at it : the number from set a can be anything . the number selected from set b will determine whether the sum is odd or even . for example , if a 4 is selected from set a , we need a 0 from set b to get an even sum . if a 5 is selected from set a , we need a 1 from set b to get an even sum . and so on . so , p ( sum is even ) = p ( select any number from set aandselect the number from set b that makes the sum even ) = p ( select any number from set a ) xp ( select the number from set b that makes the sum even ) = 1 x 1 / 2 = 1 / 2 = d
Answer: d
Problem: what is the least value of x , so that 2 x 4472 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 9 , d ) 3 , e ) 2
Rationale: "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 4 + 4 + 7 + 2 = 19 + x least value of x may be ' 8 ' , so that the total 19 + 8 = 27 is divisible by 9 . answer : option b"
Answer: b
Problem: a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 230 per month . what is his monthly salary ?
Options: a ) 5000 , b ) 5750 , c ) 2878 , d ) 2990 , e ) 2771
Rationale: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 â € “ 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 230 = > 5750 answer : b"
Answer: b
Problem: one hour after adrienne started walking the 60 miles from x to y , william started walking from x to y as well . adrienne walks 3 miles per hour and william walks 1 mile per hour faster than adrienne . how far from x will william be when he catches up to adrienne ?
Options: a ) 8 miles , b ) 9 miles , c ) 10 miles , d ) 11 miles , e ) 12 miles
Rationale: first , determine how far adrienne has walked in the one hour . she has walked three miles which means she is three miles ahead of william when he sets off . william walks at four miles / hour which means that every hour , william will get one mile closer to adrienne . if he gets one mile closer every hour , it will take him three hours to catch up to her which means he travels 3 hours * 4 miles / hour = 12 miles and she travels 4 hours * 3 miles / hour = 12 miles . he will be 12 miles from x when he catches up to her . a slightly different way to solve . . . we do n ' t know how long they will walk before they catch up to one another but we do know that a walks for one hour more than j . j = t and a = t + 1 . we are looking for the distance at which they meet up which means the distance will be the same . d = r * t so , r * t ( william ) = r * t ( adrienne ) r * ( t ) = r * ( t + 1 ) 4 t = 3 t + 3 t = 3 d = r * t d = 4 * 3 d = 12 d ) 12 miles
Answer: d
Problem: a shipment of 250 smartphones contains 76 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?
Options: a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3
Rationale: "probability of chosing one defective phone from a lot of 250 which ontains 76 defective phones is = ( 76 / 250 ) probability of chosing one defective phone from a lot of 249 ( we already picked one ) which ontains 75 ( we already picked one ) defective phones is = ( 75 / 249 ) combined probability of series of events = product of the probabilities = ( 76 / 250 ) * ( 75 / 249 ) 76 / 250 is close to ( 7 / 23 ) and ( 75 / 249 ) = ( 25 / 83 ) so answer is ( 7 / 23 ) * ( 25 / 83 ) = ( 1 / 11 ) so , answer will be c"
Answer: c
Problem: if 48 machine can finish a job in 80 days , then how many more machines would be needed to finish the job in one - fifth less time ?
Options: a ) a . 4 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
Rationale: "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 48 machines ( identical ones , i assume ) work simultaneously for 80 days , they will do a total of 48 * 80 machine - days of work . so the job requires 48 * 80 days of machine work in total . we instead want the job done in 1 / 5 less time , so in 64 days . so we ' ll need 48 * 80 / 64 = 60 machines , or 12 additional machines . d"
Answer: d
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 ) 24000
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 2500 × 160020 × 10 ) = 20000 answer : option c"
Answer: c
Problem: a train 108 m long is moving at a speed of 50 km / hr . it crosses a train 112 m long coming from opposite direction in 6 seconds . what is the speed of the second train ?
Options: a ) 82 kmph , b ) 76 kmph , c ) 44 kmph , d ) 58 kmph , e ) 56 kmph
Rationale: explanation : total distance = 108 + 112 = 220 m time = 6 s relative speed = distance / time = 220 / 6 m / s = 110 / 3 m / s = ( 110 / 3 ) × ( 18 / 5 ) km / hr = 132 km / hr = > 50 + speed of second train = 132 km / hr = > speed of second train = 132 - 50 = 82 km / hr answer : option a
Answer: a
Problem: john found that the average of 15 numbers is 40 . if 14 is added to each number then the mean of number is ?
Options: a ) 54 , b ) 45 , c ) 65 , d ) 78 , e ) 64
Rationale: ( x + x 1 + . . . x 14 ) / 15 = 40 54 option a
Answer: a
Problem: the perimeter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 23.57 , b ) 23.54 , c ) 23.5 , d ) 24.55 , e ) 25.14
Rationale: "let the side of the square be a cm . perimeter of the rectangle = 2 ( 18 + 14 ) = 64 cm perimeter of the square = 64 cm i . e . 4 a = 64 a = 16 diameter of the semicircle = 16 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 16 ) = 1 / 2 ( 22 / 7 ) ( 16 ) = 25.14 cm to two decimal places answer : e"
Answer: e
Problem: when 6 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?
Options: a ) 32 , b ) 180 , c ) 60 , d ) 27 , e ) 11
Rationale: "explanation : let the number be 26 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 6 = a / 30 = > a = 180 answer : b"
Answer: b
Problem: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 31 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 15.5 minutes , b ) 31 minutes , c ) 35 minutes , d ) 62 minutes , e ) 93 minutes
Rationale: "danny ' s time is 31 minutes . the time to reach halfway is 15.5 minutes . steve ' s time is 62 minutes . the time to reach halfway is 31 minutes . the time difference is 31 - 15.5 = 15.5 minutes the answer is a ."
Answer: a
Problem: in a group of 140 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?
Options: a ) 0.35 , b ) 0.55 , c ) 0.65 , d ) 0.75 , e ) 0.85
Rationale: "number of people whose age is less than 20 is given by 140 - 90 = 50 probability p that a person selected at random from the group is less than 20 is given by 50 / 140 = 0.35 correct answer a"
Answer: a
Problem: if radius of a circle is reduced by 10 % , then how much % of its area will be reduced ?
Options: a ) 10 %
b ) 19 %
c ) 20 %
d ) 36 %
e ) 30 %
Rationale: let initial radius = a then , area = π a ^ 2 . new radius = 90 % of a = 9 a / 10 . new area = π * 81 a ^ 2 / 100 = 81 / 100 π a ^ 2 reduce in area = [ π a ^ 2 - 81 / 100 π a ^ 2 ] = 19 / 100 π a ^ 2 % reduce = [ ( 19 * π a ^ 2 / 100 ) * ( 1 * 100 / π a ^ 2 ) ] % = 19 % answer b
Answer: b
Problem: a rope of which a calf is tied is increased from 12 m to 21 m , how much additional grassy ground shall it graze ?
Options: a ) 933.4 , b ) 1219 , c ) 1210 , d ) 1212 , e ) 1312
Rationale: "π ( 212 – 122 ) = 933.4 answer : a"
Answer: a
Problem: in a school with 640 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
Options: a ) 160 , b ) 200 , c ) 250 , d ) 350 , e ) none
Rationale: sol . let the number of grils be x . then , number of boys = ( 640 - x ) . then , ( 11 3 / 4 × 640 ) ⇔ 11 x + 12 ( 640 - x ) ⇔ x = 7680 - 7520 ⇔ 160 . answer a
Answer: a
Problem: if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 33 , what is the value of x ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 32 , e ) 37
Rationale: "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 33 x = 31 correct option : b"
Answer: b
Problem: two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 4 days ?
Options: a ) 2 / 5 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 9 , e ) 2 / 9
Rationale: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 4 days = 4 ( 1 / 18 ) = 2 / 9 . answer e"
Answer: e
Problem: 30 pens and 75 pencils were purchased for 690 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 18 , d ) 13 , e ) 14
Rationale: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 690 – 150 ) = 540 ∴ average price of a pen = 540 ⁄ 60 = 18 answer c"
Answer: c
Problem: if the price of a tv is first decreased by 20 % and then increased by 45 % , then the net change in the price will be :
Options: a ) 4 % increase , b ) 10 % increase , c ) 10 % decrease , d ) 16 % increase , e ) none of these
Rationale: "explanation : solution : let the original price be rs . 100 . new final price = 145 % of ( 80 % of 100 ) = rs . 145 / 100 * 80 / 100 * 100 = rs . 116 . . ' . increase = 16 % answer : d"
Answer: d
Problem: two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team e . if team a ' s average speed was 5 mph greater than team e ' s , what was team e ' s average mph ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team e ' s speed was s . then team e ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team e . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team e is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct .
Answer: d
Problem: what is the square root of 4,624 ?
Options: a ) a ) 18 , b ) b ) 9 , c ) c ) 68 , d ) d ) 62 , e ) e ) 81
Rationale: "a square root of a number is a number times itself equals the original number . ex ) the square root of 81 is 9 because 9 times itself ( 9 ) equals the original number ( 81 ) . 68 * 68 = 4,624 4624 divided by x = 68 x = 68 ( c ) 68"
Answer: c
Problem: a and b can do a piece of work in 40 days and 50 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?
Options: a ) 28 days , b ) 60 days , c ) 20 days , d ) 30 days , e ) 40 days
Rationale: "explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 40 + 1 / 50 ] = 10 [ 5 + 4 / 200 ] = 9 / 20 a complete remaining work in 9 / 20 * 40 = 18 total work = 10 + 18 = 28 days answer : option a"
Answer: a
Problem: sahil purchased a machine at rs 13000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
Options: a ) rs . 22000 , b ) rs . 24500 , c ) rs . 26500 , d ) rs . 28500 , e ) none of these
Rationale: explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 13000 + 5000 + 1000 = 19000 150 % of 19000 = 150 / 100 * 19000 = 28500 option d
Answer: d
Problem: the area of a square field is a square feet and the perimeter is p feet . if 6 a = 6 ( 2 p + 9 ) , what is the perimeter of the field , in feet ? ( here a = a ^ 2 )
Options: a ) 28
b ) 36
c ) 40
d ) 56
e ) 84
Rationale: you can also solve this via using the given numbers in the answer choices ! of course you need to be aware of the basic properties as outlined by the other posts above ( a = x ^ 2 and p = 4 x ) starting with d you will notice that x = 14 is way too big for your area ( 14 ^ 2 ) and will not satisfy : 6 a = 6 ( 2 p + 9 ) or a = 2 p + 9 - - > eliminate d and e now pick b ( its either too big , then its a , or too small then you know its c or it is b itsself ) and picking b indeed solves the problem ! ( 36 / 4 - - > 9 ; a = 9 ^ 2 = 81 and 81 = 2 x 36 + 9 )
Answer: b
Problem: how many numbers from 10 to 43 are exactly divisible by 3 ?
Options: a ) 13 , b ) 11 , c ) 16 , d ) 17 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 . 11 numbers . 10 / 3 = 3 and 43 / 3 = 14 = = > 14 - 3 = 11 . therefore 11 digits b )"
Answer: b
Problem: working together , printer a and printer b would finish the task in 30 minutes . printer a alone would finish the task in 50 minutes . how many pages does the task contain if printer b prints 3 pages a minute more than printer a ?
Options: a ) 200 , b ) 400 , c ) 600 , d ) 800 , e ) 900
Rationale: "30 * a + 30 * b = x pages in 30 mins printer a will print = 30 / 50 * x pages = 3 / 5 * x pages thus in 30 mins printer printer b will print x - 3 / 5 * x = 2 / 5 * x pages also it is given that printer b prints 3 more pages per min that printer a . in 30 mins printer b will print 90 more pages than printer a thus 3 / 5 * x - 2 / 5 * x = 90 = > x = 400 pages answer : b"
Answer: b
Problem: train speed 36 kph . dist travelled in 3 minutes in meters
Options: a ) 1600 , b ) 1700 , c ) 1800 , d ) 1900 , e ) 2000
Rationale: 36 kmph = 10 m / sec d = 10 * 180 = 1800 meters answer : c
Answer: c
Problem: 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 65 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
Options: a ) 1 , b ) 25 , c ) 35 , d ) 45 , e ) 75
Rationale: "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 65 % = 117 responded as satisfied , so remaining satisfied are 120 - 117 = 3 so 3 is what percentage of 300 - 1 % so the answer should be a"
Answer: a
Problem: in a company of 148 employees , 92 are females . a total of 78 employees have advanced degrees and the rest have a college degree only . if 31 employees are males with college degree only , how many employees are females with advanced degrees ?
Options: a ) 50 , b ) 51 , c ) 52 , d ) 53 , e ) 54
Rationale: "the number of males is 148 - 92 = 56 . the number of males with advanced degrees is 56 - 31 = 25 . the number of females with advanced degrees is 78 - 25 = 53 . the answer is d ."
Answer: d
Problem: a cycle is bought for rs . 900 and sold for rs . 1260 , find the gain percent ?
Options: a ) 39 % , b ) 20 % , c ) 40 % , d ) 74 % , e ) 83 %
Rationale: "900 - - - - 360 100 - - - - ? = > 40 % answer : c"
Answer: c
Problem: a van takes 6 hours to cover a distance of 288 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 32 kmph , d ) 80 kmph , e ) 90 kmph
Rationale: time = 6 distence = 288 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 288 / 9 = 32 kmph c
Answer: c
Problem: a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 30 sec . what is the length of the goods train ?
Options: a ) 299 , b ) 277 , c ) 350 , d ) 270 , e ) 281
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 30 sec . let the length of the train be x meters . then , ( x + 250 ) / 30 = 20 x = 350 m . answer : c"
Answer: c
Problem: the ratio of the adjacent angles of a parallelogram is 8 : 10 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 168 ° , b ) 228 ° , c ) 156 ° , d ) 224 ° , e ) 164 °
Rationale: "the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 8 x + 10 x = 180 ° or , 18 x = 180 ° or , x = 10 ° hence the angles of the parallelogram are 80 ° and 100 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 80 ° + 84 ° = 164 ° answer : e"
Answer: e
Problem: if the price of a certain computer increased 30 percent from d dollars to 364 dollars , then 2 d =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 560
Rationale: before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 364 ( given ) i . e . d = 364 / 1.3 = $ 280 i . e . 2 d = 2 * 280 = 560 answer : option e
Answer: e
Problem: find the value of 72518 x 9999 = m ?
Options: a ) 456578972 , b ) 436567874 , c ) 653658791 , d ) 725117481 , e ) 725107482
Rationale: "72518 x 9999 = 72518 x ( 10000 - 1 ) = 72518 x 10000 - 72518 x 1 = 725180000 - 72518 = 725107482 e"
Answer: e
Problem: ratio of two numbers x and y is 2 : 5 . if x is increased by 50 % and y is increased by 8 then the new ratio becomes 3 : 10 . what is the ratio 3 y : ( x + 6 )
Options: a ) 15 : 8 , b ) 8 : 15 , c ) 2 : 5 , d ) 5 : 2 , e ) 13 : 6
Rationale: "let : x = 2 n y = 5 n 3 n / ( 5 n + 5 ) = 3 / 10 30 n = 3 * ( 5 n + 5 ) n = 1 so , x = 2 ; y = 5 3 y / ( x + 6 ) = 15 / 8 answer = a"
Answer: a
Problem: the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnut purchased if you paid $ 19 ?
Options: a ) 24 , b ) 25 , c ) 35 , d ) 36 , e ) 37
Rationale: "a is the number of dozen of doughnuts at a price of $ 6 / dozen 1 + 6 a = 19 a = 3 the total number of doughnuts purchased - - > 1 + 3 * 12 = 37 answer : e"
Answer: e
Problem: factory x ' s bulbs work for over 4000 hours in 59 % of cases , whereas factory y ' s bulbs work for over 4000 hours in 65 % of cases . it is known that factory x supplies 60 % of the total bulbs available . what is the chance that a purchased bulb will work for longer than 4000 hours ?
Options: a ) 66.4 % , b ) 61.4 % , c ) 77.4 % , d ) 65 % , e ) 53.9 %
Rationale: "for x , 60 % of 59 % will work . for y , 40 % of 65 % will work . * 40 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.60 ( 0.59 ) = . 354 0.40 ( 0.65 ) = 0.26 the combined probability then is 35.4 + 26.00 = 61.4 % ans b"
Answer: b
Problem: walking 6 / 7 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 28 m , b ) 20 m , c ) 22 m , d ) 23 m , e ) 24 m
Rationale: speed ratio = 1 : 6 / 7 = 7 : 6 time ratio = 6 : 4 1 - - - - - - - - 6 4 - - - - - - - - - ? = > 24 m answer : e
Answer: e
Problem: if 6 a = 7 b = 20 , then 84 ab =
Options: a ) 50 , b ) 100 , c ) 625 , d ) 800 , e ) 1250
Rationale: "6 a * 7 b = 20 * 20 = 400 42 ab = 400 i . e . 84 ab = 800 answer : option d"
Answer: d
Problem: a 180 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 109 , b ) 108 , c ) 109 , d ) 106 , e ) 101
Rationale: "s = 180 / 6 * 18 / 5 = 108 kmph answerb"
Answer: b
Problem: a is twice efficient as b and together they do the same work in as much time as c and d together . if c and d can complete the work in 20 and 30 daysrespectively , working alone , then in how many days a can complete the work individually :
Options: a ) 12 days , b ) 18 days , c ) 24 days , d ) 30 days , e ) none of these
Rationale: explanation : a + b = c + d | | | | ratio of efficiency 10 x + 5 x 9 x + 6 x | ________| | _________| 15 x 15 x therefore , ratio of efficiency of a : c = 10 : 9 therefore , ratio of days taken by a : c = 9 : 10 therefore , number of days taken by a = 18 days answer : b
Answer: b
Problem: a $ 500 investment and a $ 1,500 investment have a combined yearly return of 19 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 9 % , b ) 10 % , c ) 23 % , d ) 21 % , e ) 22 %
Rationale: "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 19 ) = ( 500 â ˆ — 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 23 % ( option c ) answer : c"
Answer: c
Problem: it is well known that a triangle ’ s area is √ ( p ( p - a ) ( p - b ) ( p - c ) ) , when p = ( a + b + c ) / 2 , such that a , b , c are the lengths of sides of the triangle . if the triangle has 300 , 300 , and 300 as the side ’ s lengths , what is the triangle ’ s area ?
Options: a ) 34,200 , b ) 36,200 , c ) 38,200 , d ) 42,200 , e ) 38,971
Rationale: it is well known that a triangle ’ s area is √ ( p ( p - a ) ( p - b ) ( p - c ) ) , when p = ( a + b + c ) / 2 , - > p = ( 300 + 300 + 300 ) / 2 = 450 , area = √ ( 450 ( 450 - 300 ) ( 450 - 300 ) ( 450 - 300 ) ) = 38,971 . therefore , the answer is e .
Answer: e
Problem: in the fifth grade at parkway elementary school there are 450 students . 320 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 81 . , d ) 95 . , e ) 108 .
Rationale: "total students = 450 boys = 320 , girls = 130 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 130 - 35 = 95 . correct option : d"
Answer: d
Problem: excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 32 kmph . of how many minutes does the train stop per hour ?
Options: a ) a ) 40 , b ) b ) 30 , c ) c ) 20 , d ) d ) 10 , e ) e ) 5
Rationale: "explanation : t = 16 / 48 * 60 = 20 answer : option c"
Answer: c
Problem: at a kennel with 80 dogs , 45 of the dogs wear tags and 40 wear flea collars . if 6 of the dogs wear both , then how many of the dogs wear neither a collar nor tags ?
Options: a ) 1 , b ) 6 , c ) 34 , d ) 79 , e ) 85
Rationale: dogs wear neither a collar nor tags = 80 - ( 45 + 40 - 6 ) dogs wear neither a collar nor tags = 80 - 79 dogs wear neither a collar nor tags = 80 - 79 hence , answer will be 1 answer : a
Answer: a
Problem: the ratio 9 : 5 expressed as a percent equals
Options: a ) 12.5 % , b ) 40 % , c ) 180 % , d ) 125 % , e ) none
Rationale: "solution 9 : 5 = 9 / 5 = ( 9 / 5 x 100 ) % . = 180 % . answer c"
Answer: c
Problem: the sum of all two digit numbers divisible by 7 is
Options: a ) 910 , b ) 510 , c ) 728 , d ) 628 , e ) 810
Rationale: "required numbers are 14 , 21,28 . . . . . 98 this is an a . p . in which a = 14 , d = 7 and l = 98 . let the number of terms in it be n . then t = 98 so a + ( n - 1 ) d = 98 . 14 + ( n - 1 ) * 7 = 98 , 14 + 7 n - 7 = 98 7 + 7 n = 98 7 n = 98 - 7 n = 91 / 7 then n = 13 . required sum = n / 2 ( a + l ) = 13 / 2 ( 14 + 98 ) = 728 answer is c ."
Answer: c
Problem: a number when divided by a certain divisor left remainder 241 , when twice the number was divided by the same divisor , the remainder was 115 . find the divisor ?
Options: a ) 370 , b ) 365 , c ) 380 , d ) 367 , e ) 460
Rationale: "easy solution : n = dq 1 + 241 2 n = 2 dq 1 + 482 - ( 1 ) 2 n = dq 2 + 115 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 367 d * some integer = 367 checking all options only ( d ) syncs with it . answer d"
Answer: d
Problem: find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 65 = x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: e ) 5
Answer: e
Problem: the edges of three metal cubes are 1 cm , 2 cm , and 4 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ?
Options: a ) 3.8 , b ) 4.2 , c ) 4.6 , d ) 5.0 , e ) 5.4
Rationale: "the total volume is 1 ^ 3 + 2 ^ 3 + 4 ^ 3 = 73 the edge of the new cube is the cube root of 73 which is about 4.2 cm . the answer is b ."
Answer: b
Problem: every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` dog ' ' ?
Options: a ) 72 , b ) 75 , c ) 78 , d ) 81 , e ) 84
Rationale: "` ` dog ' ' = ( 4 + 15 + 7 ) * 3 = 78 . the answer is c ."
Answer: c
Problem: the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 21 . what is the last numbers ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "a + b + c = 18 b + c + d = 15 a + d = 21 a – d = 3 a + d = 21 2 d = 18 d = 9 answer : e"
Answer: e
Problem: 15 ants can move 600 sugar cubes of 10 grams each to their home in 5 hours . then how many sugar cubes of 5 grams each , will 20 ants move in 3 hours ?
Options: a ) 360
b ) 480
c ) 720
d ) 960
e ) 1000
Rationale: d 15 ants move 600 / 5 = 120 sugar cubes of 10 grams in 1 hour . 5 grams sugar cubes will take less time to move . thus if weight of the sugar cube is 5 grams , 15 ants will move 120 x 10 / 5 = 240 sugar cubes in 1 hour . more ants , more sugar cubes they can move . 20 ants will move 240 x 20 / 15 = 320 sugar cubes in 1 hour thus in 3 hours , 20 ants will move 320 x 3 = 960 sugar cubes of 5 grams .
Answer: d
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 6 years at 10 % per annum is rs . 80 of money ?
Options: a ) 1000 , b ) 1200 , c ) 4800 , d ) 3600 , e ) 8400
Rationale: "p = 80 ( 100 / 10 ) 6 = > p = 1500 answer : c"
Answer: c
Problem: a grocery store bought some mangoes at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 4 for a dollar and the other at a rate of 6 for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?
Options: a ) 1 : 4 , b ) 1 : 5 , c ) 2 : 3 , d ) 3 : 2 , e ) 2 : 5
Rationale: "the cost price of a mango = 1 / 5 dollars . the selling price of a mango from the first stack = 1 / 4 dollars - - > the profit from one mango = 1 / 4 - 1 / 5 = 1 / 20 dollars . the selling price of a mango from the second stack = 1 / 6 dollars - - > the loss from one mango = 1 / 5 - 1 / 6 = 1 / 30 dollars . the profit from one mango from the first stack is 4 times the loss from one mango from the second stack . the ratio is 1 / 20 * 30 / 1 = 3 : 2 d"
Answer: d
Problem: what is the positive difference between the sum of the squares of the first 6 positive integers and the sum of the prime numbers between the first square and fourth square ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 50
Rationale: forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + 5 ^ 2 + 6 ^ 2 = 91 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 91 is 50 . so the answer is ( e ) .
Answer: e
Problem: john makes $ 60 a week from his job . he earns a raise and now makes $ 80 a week . what is the % increase ?
Options: a ) 16 % , b ) 33.33 % , c ) 17 % , d ) 17.61 % , e ) 17.56 %
Rationale: "increase = ( 20 / 60 ) * 100 = ( 2 / 6 ) * 100 = 33.33 % . b"
Answer: b
Problem: find the area of a parallelogram with base 28 cm and height 32 cm .
Options: a ) 200 , b ) 384 , c ) 345 , d ) 244 , e ) 896
Rationale: "area of a parallelogram = base * height = 28 * 32 = 896 cm 2 answer : option e"
Answer: e
Problem: a can complete a work in 18 days and b can do the same work in 10 days . if a after doing 3 days , leaves the work , find in how many days b will do the remaining work ?
Options: a ) 2 days , b ) 8 days , c ) 6 days , d ) 7 days , e ) 10 days
Rationale: "the required answer = ( 18 - 3 ) * 5 / 18 = 150 / 18 = 8 days answer is b"
Answer: b