regisss/math_qa huggingface dataset:
Problem: if 10 gallons of grape juice are added to 40 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 28 % , d ) 34 % , e ) 50 %
Rationale: "mixture contains 4 gallons of grape juice out of 40 gallons after addition : 14 gallons of grape juice out of 50 gallons = = > 28 % answer c"
Answer: c
Problem: 18 men can complete a piece of work in 30 days . in how many days can 15 men complete that piece of work ?
Options: a ) 23 days , b ) 36 days , c ) 22 days , d ) 29 days , e ) 20 days
Rationale: "b 36 days 18 * 30 = 15 * x = > x = 36 days"
Answer: b
Problem: if the sales tax be reduced from 4 ( 1 / 4 ) % to 1 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 4500 ?
Options: a ) rs . 156.66 , b ) rs . 150.23 , c ) rs . 123.75 , d ) rs . 135.06 , e ) none of these
Rationale: explanation : required difference = ( 4 ( 1 / 4 ) of rs . 4500 ) - ( 1 ( 1 / 2 ) of rs . 4500 ) = ( 17 / 4 – 3 / 2 ) % of rs . 4500 = ( 11 / 4 ) x ( 1 / 100 ) x 4500 = rs . 123.75 answer c
Answer: c
Problem: two , trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) 9 : 14
Rationale: let the slower train have speed of 1 unit and faster train a speed of r units of speed . let t = time to when the trains meet . rt 1 t howrah | - - - - - - - - - - - - - - - - - - - - - - - | - - - - - - - - - - | patna meet they meet rt units from howrah and 1 t units from patna for the second part of the journey the fast train at speed r has 1 t unit of distance and 9 hours to do it so 1 t / r = 9 slow train has rt units of distance at speed of 1 unit and 16 hours to do it . rt / 1 = 16 so rt / 1 16 - - - - - = - - - - giving r ^ 2 = 16 / 9 1 t / r 9 r = 4 / 3 answer : b
Answer: b
Problem: in a colony of 70 resident s , the ratio of the number of men and women is 4 : 3 . among the women , the ratio of the educated to the uneducated is 1 : 4 . if the ratio of the number of education to uneducated persons is 8 : 27 , then find the ratio of the number of educated and uneducated men in the colony ?
Options: a ) 1 : 9 , b ) 1 : 6 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 ratio 3
Rationale: number of men in the colony = 4 / 7 ( 70 ) = 40 number of women in the colony = 3 / 7 ( 70 ) = 30 number of educated women in the colony = 1 / 5 ( 30 ) = 6 number of uneducated women in the colony = 4 / 5 ( 30 ) = 24 number of educated persons in the colony = 8 / 35 ( 70 ) = 16 as 6 females are educated , remaining 10 educated persons must be men . number of uneducated men in the colony = 40 - 10 = 30 number of educated men and uneducated men are in the ratio 10 : 30 = > 1 : 3 answer : e
Answer: e
Problem: what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 300 inclusive ?
Options: a ) 155 , b ) 195 , c ) 200 , d ) 205 , e ) 210
Rationale: "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 300 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 30 ( 10 ) = 300 so we know that there are 30 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 300 = 310 20 + 290 = 310 30 + 280 = 310 etc . since there are 30 total terms , this pattern will create 15 ' pairs ' of 310 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 15 ) ( 310 ) / ( 30 ) = 155 answer : a"
Answer: a
Problem: if 0.75 : x : : 5 : 8 , then x is equal to
Options: a ) 1.12 , b ) 1.25 , c ) 1.20 , d ) 1.3 , e ) none
Rationale: "sol . ( x × 5 ) = ( 0.75 × 8 ) ⇒ x = 6 / 5 = 1.20 . answer c"
Answer: c
Problem: the reciprocal of the hcf and lcm of two are 1 / 13 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 156 , e ) 169
Rationale: reciprocal of the hcf and lcm of two are 1 / 13 and 1 / 312 so , hcf = 13 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 13 * 312 / 24 = 169 answer : e
Answer: e
Problem: the ratio of two no . addition and subtraction be 4 : 3 . the what is the ratio of numbers ?
Options: a ) 3 : 2 , b ) 4 : 3 , c ) 5 : 1 , d ) 6 : 5 , e ) 7 : 1
Rationale: ( x + y ) / ( x - y ) = 4 / 3 dividing numerator and denominator by y ( x / y ) + 1 / ( x / y ) - 1 = 4 / 3 let x / y be z z + 1 / z - 1 = 4 / 3 3 z + 3 = 4 z - 4 z = 7 x / y = 7 answer e
Answer: e
Problem: among 300 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 30 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 30 , b ) 90 , c ) 120 , d ) 172 , e ) 188
Rationale: "i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 90 using your analysis : we see that the total number of students who study either maths or sociology = 132 + 168 - 90 = 210 so , in the image we know that the number of students in the zone with the black boundary = 210 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 300 , we can write : 210 + b + w = 300 or , b + w = 300 - 210 = 90 that is , b = 90 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 90 b"
Answer: b
Problem: 6 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.16666 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 6 / 36 = . 16666 answer ( b )"
Answer: b
Problem: a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 9,800 sedans in anytown , how many motorcycles are there ?
Options: a ) 2800 , b ) 2100 , c ) 3600 , d ) 4200 , e ) 5200
Rationale: "let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 9800 = > 7 x = 9800 = > x = 1400 total number of motorcycles = 2 x = 2 * 1400 = 2800 answer a"
Answer: a
Problem: in a can , there is a mixture of milk and water in the ratio 1 : 5 . if it is filled with an additional 2 litres of milk the can would be full and ratio of milk and water would become 2.00001 : 5.00001 . find the capacity of the can ?
Options: a ) 14 , b ) 44 , c ) 48 , d ) 50 , e ) 56
Rationale: let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 1 / 6 ( t - 2 ) after adding milk , quantity of milk in the mixture = 2 / 7 t . 2 t / 7 - 2 = 1 / 6 ( t - 2 ) 5 t = 84 - 14 = > t = 14 . answer : a
Answer: a
Problem: the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 55 kms . what was the total distance travelled in 12 hours ?
Options: a ) 252 kms , b ) 152 kms , c ) 552 kms , d ) 792 kms , e ) 152 kms
Rationale: "explanation : total distance travelled in 12 hours = ( 55 + 57 + 59 + . . . . . upto 12 terms ) this is an a . p with first term , a = 55 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 55 + { 12 - 1 ) x 2 ] = 6 ( 132 ) = 792 kms . answer : d"
Answer: d
Problem: 45 x ? = 35 % of 900
Options: a ) 16.2 , b ) 7 , c ) 5 , d ) 500 , e ) none
Rationale: "answer let 45 x a = ( 35 x 900 ) / 100 ∴ a = ( 35 x 9 ) / 45 = 7 correct option : b"
Answer: b
Problem: the ratio of radius of a circle and the side of a square is 2 : 13 . find the ratio of their areas :
Options: a ) 2 : 1
b ) 4 : 7
c ) 8 : 77
d ) 4 : 169
e ) none
Rationale: radius / side = 2 / 13 â ‡ ’ area of circle / area of square = 4 / 169 answer : d
Answer: d
Problem: if the average of 54 , 55 , 57 , 58 , 59 , 62 , 62 , 63 , 65 and x is 60 , what is the value of x ?
Options: a ) 60 , b ) 62 , c ) 64 , d ) 65 , e ) 66
Rationale: "sum of the deviations of the numbers in the set from the mean is always zero 54 , 55 , 57 , 58 , 59 , 62 , 62 , 63 , 65 mean is 60 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 60 + 5 = 65 d"
Answer: d
Problem: a ranch has both horses and ponies . exactly 5 / 6 of the ponies have horseshoes , and exactly 2 / 3 of the ponies with horseshoes are from iceland . if there are 4 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
Options: a ) 18 , b ) 21 , c ) 38 , d ) 40 , e ) 57
Rationale: "5 / 6 * p have horseshoes , so p is a multiple of 6 . 2 / 3 * 5 / 6 * p = 5 / 9 * p are icelandic ponies with horseshoes , so p is a multiple of 9 . the minimum value of p is 18 . then h = p + 4 = 22 . the minimum number of horses and ponies is 40 . the answer is d ."
Answer: d
Problem: 20 , 22 , 26 , 34 , 41 , 46 , 56 , 67 , __ ?
Options: a ) 72 , b ) 80 , c ) 88 , d ) 68 , e ) 78
Rationale: "next no . = previous + ( sum of digits ) 20 + ( 2 + 0 ) = 22 22 + ( 2 + 2 ) = 26 26 + ( 2 + 6 ) = 34 - - - - - - - - 56 + ( 5 + 6 ) = 67 67 + ( 6 + 7 ) = 80 answer : b"
Answer: b
Problem: the sale price sarees listed for rs . 278 after successive discount is 18 % and 19 % is ?
Options: a ) 321 , b ) 276 , c ) 342 , d ) 265 , e ) 198
Rationale: "explanation : 278 * ( 88 / 100 ) * ( 81 / 100 ) = 198 answer : e"
Answer: e
Problem: in a group of 90 students , 36 are taking history , and 30 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?
Options: a ) 9 , b ) 19 , c ) 23 , d ) 27 , e ) 29
Rationale: "number of students taking history = h = 36 number of students taking statistics = s = 30 total number of students = t = 90 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 90 - 59 = 31 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 90 = 36 + 30 + 31 - x or x = 7 now , number of students taking only history will be h - x or 36 - 7 = 29 answer : - e"
Answer: e
Problem: what least number must be subtracted from 427398 so that remaining no . is divisible by 14
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "explanation : on dividing 427398 by 14 we get the remainder 6 , so 6 should be subtracted answer : option c"
Answer: c
Problem: if the average ( arithmetic mean ) of a and b is 20 , and c – a = 30 , what is the average of b and c ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 35 , e ) 45
Rationale: "a + b / 2 = 20 = > a + b = 40 a = c - 30 . . . sub this value c - 30 + b = 40 = > c + b = 70 = > c + b / 2 = 35 answer : d"
Answer: d
Problem: three unbiased coins are tossed . what is the probability of getting 1 heads and 1 tail ?
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8
Rationale: "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 3 heads then e = { tht , hth } p ( e ) = n ( e ) / n ( s ) = 2 / 8 = 1 / 4 answer is b"
Answer: b
Problem: the average monthly salary of laborers and supervisors in a factory is rs . 1250 per month ; where as the average monthly salary of 6 supervisors is rs . 2450 . if the average monthly salary of the laborers is rs . 950 find the number of laborers ?
Options: a ) 87 , b ) 42 , c ) 78 , d ) 76 , e ) 26
Rationale: 5 x 6 x 2 x 50 25 100 250 x + 150 x + 200 x = 4200 600 x = 4200 x = 7 = > 6 x = 42 answer : b
Answer: b
Problem: the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 40 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 35 % , e ) 79 %
Rationale: "take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 40 % then output equals 154 to restore new holidy demand output to original 100 . final - initial / final * 100 = 54 / 154 * 100 = 35 % approxiamately . option d is correct ."
Answer: d
Problem: balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 424 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did . how many balls made up the triangle ?
Options: a ) 1176 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560
Rationale: as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 424 ) ( x - 8 ) ^ 2 = t + 424 - - - - - ( b ) now the hardest part of the question will be to solve these 2 equations and this looks like time consuming but the easy way will be plug and play . also , we ' ve to find a value of t ( from 5 optiosn given below ) which can make a square of a a number . one we know this , it will be a cake walk . we can see that option a fits this criteria in eq ( b ) . add - 1176 + 424 = 1600 = 40 ^ 2 = ( x - 8 ) ^ 2 hence , x = 48 . cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 48 * 49 / 2 = 1176 hence , answer is a .
Answer: a
Problem: a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.50 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 4.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "cashews / peanuts = ( mean price - peanuts price ) / ( cashew price - mean price ) = ( 2.5 - 1.5 ) / ( 4 - 2.5 ) = 2 / 3 cashew = ( 2 / 5 ) * 100 = 40 kg answer is a ."
Answer: a
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 44 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48
Rationale: "annie earned 40 x + 4 ( 2 x ) = 48 x let h be the number of hours that harry worked . harry earned 30 x + 1.5 x ( h - 30 ) = 48 x ( 1.5 x ) ( h ) = 63 x h = 42 hours the answer is b ."
Answer: b
Problem: two pipes a and b can fill a cistern in 9 and 18 minutes respectively , and a third pipe c can empty it in 24 minutes . how long will it take to fill the cistern if all the three are opened at the same time ?
Options: a ) 6 min , b ) 7 min , c ) 8 min , d ) 10 min , e ) 17 min
Rationale: "1 / 9 + 1 / 18 - 1 / 24 = 1 / 8 8 / 1 = 8 answer : c"
Answer: c
Problem: laura took out a charge account at the general store and agreed to pay 5 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 2.10 , b ) $ 36.75 , c ) $ 37.16 , d ) $ 38.10 , e ) $ 38.80
Rationale: "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 5 % interest = ( 5 / 100 ) * 35 = 1.75 $ total amount that laura owes a year later = 35 + 1.75 = 36.75 $ answer b"
Answer: b
Problem: a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: "first $ 20 million : royalties / sales ratio = 3 / 20 = 36 / 240 next $ 108 million : royalties / sales ratio = 9 / 108 = 1 / 12 = 20 / 240 answer : c"
Answer: c
Problem: what is the sum of the integers from - 194 to 195 inclusive ?
Options: a ) 0 , b ) 5 , c ) 195 , d ) 875 , e ) 965
Rationale: "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = 194 + 195 / 2 = 0.5 number of items ( n ) = b - a + 1 = 195 - ( - 194 ) + 1 = 195 + 195 = 390 . sum = average * n = 0.5 * 390 = 195 . answer is c"
Answer: c
Problem: if x and y are integers such that | y + 3 | ≤ 3 and 2 y – 3 x + 6 = 0 , what is the least possible value q of the product xy ?
Options: a ) - 12 , b ) - 3 , c ) 0 , d ) 2 , e ) none of the above
Rationale: "how to deal with inequalities involving absolute values ? first example shows us the so callednumber case in this case we have | y + 3 | ≤ 3 which is generalized | something | ≤ some number . first we solve as if there were no absolute value brackets : y + 3 ≤ 3 y ≤ 0 so y is 0 or negative second scenario - remove the absolute value brackets . put a negative sign around the other side of the inequality , andflip the sign : y + 3 > = - 3 y > = - 6 therefore we have a possible range for y : - 6 = < y < = 0 ok , so far so good , we ' re half way through . what about x ? here ' s the formula : 2 y – 3 x + 6 = 0 , rewrite it as 2 y + 6 = 3 x . you can say that 2 y + 6 is a multiple of 3 ( = 3 x ) . so all values which must be integer must also satisfy this constraint . i ' m just saying that , so it ' s easier to evaluate all the possible numbers ( - 6 , - 3 , 0 ) . if you plug in y = 0 , x will be 2 and xy = 0 as the lowest possible value q . hence , answer choice c is the one to go ."
Answer: c
Problem: the average of first seven prime numbers which are between 30 and 70 is
Options: a ) 35.4 , b ) 42 , c ) 44.4 , d ) 57 , e ) 67
Rationale: "explanation : first seven prime numbers which are between 30 and 70 = 31 , 37 , 41 , 43 , 47 , 53 , 59 average = ( 31 + 37 + 41 + 43 + 47 + 53 + 59 ) / 7 = 44.4 answer : c"
Answer: c
Problem: a batsman makes a score of 90 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?
Options: a ) 25 , b ) 31 , c ) 27 , d ) 29 , e ) 42
Rationale: "let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 90 = total runs scored in 17 innings = > 16 ( x - 3 ) + 90 = 17 x = > 16 x - 48 + 90 = 17 x = > x = 42 answer is e ."
Answer: e
Problem: if x / y = 3 / z , then 4 x ^ 2 =
Options: a ) y / z , b ) xy , c ) y ² / z ² , d ) 36 y ² / z ² , e ) 15 y ² / z ²
Rationale: "this question is most easily solved by isolating y in the equation and substituting into the expression 4 x ² : x / y = 3 / z x = 3 y / z if we substitute 3 y / z into the expression for x , we get : 4 ( 3 y / z ) ² = 4 ( 9 y ² / z ² ) = 36 y ² / z ² . the correct answer is choice ( d ) ."
Answer: d
Problem: the captain of a cricket team of 11 members is 25 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 24 years
Rationale: "explanation : let the average age of the whole team by x years . 11 x â € “ ( 25 + 28 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 44 2 x = 44 x = 22 . so , average age of the team is 22 years . answer c"
Answer: c
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.90 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.6
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.9 = 3 * x - - > x = $ 0.6 . answer : e ."
Answer: e
Problem: if a person walks at 25 km / hr instead of 10 km / hr , he would have walked 31 km more . the actual distance traveled by him is ?
Options: a ) 30 , b ) 25 , c ) 20.67 , d ) 12.33 , e ) 19.48
Rationale: "let the actual distance traveled is ' x ' km then by given conditions , we have x / 10 = ( x + 31 ) / 25 25 x = 10 x + 310 x = 20.67 km ans - c"
Answer: c
Problem: the speed of a boat in still water is 8 kmph . if it can travel 1 km upstream in 1 hr , what time it would take to travel the same distance downstream ?
Options: a ) 14 minutes , b ) 4 minutes , c ) 24 minutes , d ) 28 minutes , e ) 23 minutes
Rationale: "speed of the boat in still water = 8 km / hr speed upstream = 1 ⁄ 1 = 1 km / hr speed of the stream = 8 - 1 = 7 km / hr speed downstream = ( 8 + 7 ) = 15 km / hr answer is b time taken to travel 1 km downstream = 1 / 15 hr = ( 1 × 60 ) / 15 = 4 minutes"
Answer: b
Problem: # p is defined as 2 p - 20 for any number p . what is p , if # ( # ( # p ) ) = 12 ?
Options: a ) – 108 , b ) 19 , c ) 10 , d ) 16 , e ) 18
Rationale: # p = 2 p - 20 - - - > # ( # p ) = 2 ( 2 p - 20 ) - 20 = 4 p - 60 and thus # ( 4 p - 60 ) = 2 ( 4 p - 60 ) - 20 = 8 p - 140 = 12 - - - > 8 p = 152 - - - > p = 19 , b is the correct answer .
Answer: b
Problem: if 90 percent of 600 is 50 percent of x , then x = ?
Options: a ) 100 , b ) 1000 , c ) 1080 , d ) 1020 , e ) 1200
Rationale: "0.9 * 600 = 0.5 * x x = 9 / 5 * 600 = 1080"
Answer: c
Problem: a number increased by 20 % gives 1080 . the number is ?
Options: a ) 800 , b ) 700 , c ) 500 , d ) 900 , e ) 600
Rationale: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 20 % = 120 % 120 % - - - - - - - > 1080 ( 120 ã — 9 = 1080 ) 100 % - - - - - - - > 900 ( 100 ã — 9 = 900 ) option ' d '"
Answer: d
Problem: a train 500 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 87 kmph , b ) 97 kmph , c ) 72 kmph , d ) 90 kmph , e ) 19 kmph
Rationale: "length = speed * time speed = l / t s = 500 / 20 s = 25 m / sec speed = 25 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 90 kmph answer : d"
Answer: d
Problem: if 5 < x < 12 and y = x + 3 , what is the greatest possible integer value of x + y ?
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "x + y = x + x + 3 = 2 x + 3 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 11.5 then x + y = 11.5 + 14.5 = 26 . the answer is d ."
Answer: d
Problem: on dividing a number by 357 , we get 42 as remainder . on dividing the same number by 17 , what will be the remainder ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 7 , e ) 2
Rationale: "let x be the number and y be the quotient . then , x = 357 * y + 42 = ( 17 * 21 * y ) + ( 17 * 2 ) + 8 = 17 * ( 21 y + 2 ) + 8 . required number = 8 . answer is c"
Answer: c
Problem: evaluate : 20 - 16 ÷ 4 × 3 =
Options: a ) 16 , b ) 10 , c ) 4 , d ) 8 , e ) 6
Rationale: "according to order of operations , 16 ÷ 4 × 3 ( division and multiplication ) is done first from left to right 16 ÷ 4 × 3 = 4 × 3 = 12 hence 20 - 16 ÷ 4 × 3 = 20 - 12 = 8 correct answer d ) 8"
Answer: d
Problem: a train 1020 m long running at 102 kmph crosses a platform in 50 sec . what is the length of the platform ?
Options: a ) 287 , b ) 298 , c ) 396 , d ) 726 , e ) 267
Rationale: "d = 102 * 5 / 18 = 50 = 1416 â € “ 1020 = 396 answer : c"
Answer: c
Problem: a seller of used cars has 15 cars to sell and each of his clients selected 3 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "ifno caris selected more than once then the number of clients = 15 / 3 = 5 but since every car is being selected three times so no . of clients must be thrice as well = 5 * 3 = 15 answer : option e"
Answer: e
Problem: if a rectangular room measures 11 meters by 6 meters by 4 meters , what is the volume of the room in cubic centimeters ? ( 1 meter = 100 centimeters )
Options: a ) 24,000 , b ) 240,000 , c ) 2 , 400,000 , d ) 24 , 000,000 , e ) 264 , 000,000
Rationale: "e . 264 , 000,000 11 * 100 * 6 * 100 * 4 * 100 = 264 , 000,000"
Answer: e
Problem: a rock is dropped into a well and the distance traveled is 16 t 2 feet , where t is the time . if the water splash is heard 3 seconds after the rock was dropped , and that the speed of sound is 1100 ft / sec , approximate the height of the well
Options: a ) 134.8 feet , b ) 136.2 feet , c ) 132.7 feet , d ) 132.2 feet , e ) 115.3 feet
Rationale: let t 1 be the time it takes the rock to reach the bottom of the well . if h is the height of the well , we can write h = 16 t 1 2 let t 2 be the time it takes sound wave to reach the top of the well . we can write h = 1100 t 2 the relationship between t 1 and t 2 is t 1 + t 2 = 3 eliminate h and combine the equations h = 16 t 1 2 and h = 1100 t 2 to obtain 16 t 1 2 = 1100 t 2 we now substitute t 2 by 3 - t 1 in the above equation 16 t 1 2 = 1100 ( 3 - t 1 ) the above is a quadratic equation that may be written as 16 t 1 2 + 1100 t 1 - 3300 = 0 the above equations has two solutions and only one of them is positive and is given by t 1 = 2.88 seconds ( 2 decimal places ) we now calculate the height h of the well h = 16 t 1 2 = 16 ( 2.88 ) 2 = 132.7 feet answer c
Answer: c
Problem: a man can row his boat with the stream at 18 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 3 kmph , c ) 8 kmph , d ) 7 kmph , e ) 5 kmph
Rationale: "ds = 18 us = 4 s = ? s = ( 18 - 4 ) / 2 = 7 kmph answer : d"
Answer: d
Problem: how is 2 % expressed as a decimal fraction ?
Options: a ) 0.2 , b ) 0.02 , c ) 0.002 , d ) 0.0002 , e ) 2
Rationale: 2 / 100 = 0.02 answer : b
Answer: b
Problem: for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers v are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a"
Answer: a
Problem: 25.25 / 3000 is equal to :
Options: a ) 0.008416667 , b ) 0.110773333 , c ) 0.12526234 , d ) 0.01072333 , e ) 0.12725002
Rationale: "25.25 / 3000 = 2525 / 300000 = 0.008416667 answer : a"
Answer: a
Problem: a man can row downstream at 28 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 2 , 9 , b ) 4 , 9 , c ) 8 , 9 , d ) 19 , 9 , e ) 7 , 9
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 28 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 38 = > x = 19 , y = 9 . answer : d"
Answer: d
Problem: two bullet trains of equal lengths take 8 seconds and 15 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 13 sec . , b ) 10.4 sec . , c ) 12 sec . , d ) 17 sec . , e ) 19 sec .
Rationale: speed of the first bullet train = 120 / 8 m / sec = 15 m / sec . speed of the second bullet train = 120 / 15 m / sec = 8 m / sec . relative speed = ( 15 + 8 ) = 23 m / sec . required time = ( 120 + 120 ) / 23 sec = 10.4 sec . b
Answer: b
Problem: how many even number in the range between 10 to 170 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 31 , d ) 33 , e ) 54
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 170 using ap formula , we can say 170 = 10 + ( n - 1 ) * 2 or n = 81 . for 6 , 12,18 , . . . 168 using ap formula , we can say 168 = 12 + ( n - 1 ) * 6 or n = 27 . hence , only divisible by 2 but not 3 = 81 - 27 = 54 . hence , answer e"
Answer: e
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ?
Options: a ) 80 feet , b ) 70 feet , c ) 60 feet , d ) 50 feet , e ) 20 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 600 = > breadth = 30 feet area to be fenced = 2 b + l = 2 * 30 + 20 = 80 feet answer : option a"
Answer: a
Problem: when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.16 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 50 , d ) 25 , e ) 12
Rationale: "by the definition of a remainder , the remainder here is equal to 8 / y . the remainder in decimal form is given as . 16 therefore , 8 / y = . 16 solve for y and get 50 . c"
Answer: c
Problem: the mean of 30 values was 140 . it was detected on rechecking that one value 145 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 140.33 , c ) 152 , d ) 148 , e ) none of the above
Rationale: "corrected mean = 140 × 30 − 135 + 145 / 30 = 4200 − 135 + 145 / 30 = 4210 / 30 = 140.33 answer b"
Answer: b
Problem: two trains 110 meters and 180 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.2 , b ) 7.85 , c ) 6.85 , d ) 5.85 , e ) 6.15
Rationale: "t = ( 110 + 180 ) / ( 80 + 65 ) * 18 / 5 t = 7.20 answer : a"
Answer: a
Problem: the perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 28 cm 2 , b ) 27 cm 2 , c ) 29 cm 2 , d ) 25 cm 2 , e ) 35 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 20 / 2 = 25 cm 2 answer : d"
Answer: d
Problem: you buy a piece of land with an area of √ 900 , how long is one side of the land plot ?
Options: a ) 28
b ) 29
c ) 30
d ) 31
e ) 32
Rationale: try filling the numbers into the answer y x y = find the closest to 900 . answer c
Answer: c
Problem: a large box contains 21 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 250 , b ) 350 , c ) 450 , d ) 550 , e ) 525
Rationale: "the number of chocolate bars is equal to 21 * 25 = 525 correct answer e"
Answer: e
Problem: a typist uses a sheet measuring 20 cm by 30 cm lenghtwise . if a margin of 2 cm is left on each side and a 3 cm margin on the top and bottom , then what is the percentage of page used by the typist ?
Options: a ) 62 % , b ) 63 % , c ) 64 % , d ) 65 % , e ) 66 %
Rationale: area of the sheet = ( 20 * 30 ) cm 2 = 600 cm 2 area used for typing = ( [ 20 - 4 ] * [ 30 - 6 ] ) cm 2 = 384 cm 2 therefore required percentage = ( 384 / 600 ) * 100 = 64 % answer c
Answer: c
Problem: an association of mathematics teachers has 1,260 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 62 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 25.83 %
Rationale: "total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 62 percent of the votes cast number of votes for winning candidate = ( 62 / 100 ) * 525 = 325.5 percent of total membership that voted for winning candidate = ( 325.5 / 1260 ) * 100 = 25.83 % answer e"
Answer: e
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 161 ?
Options: a ) 2670 , b ) 2980 , c ) 3550 , d ) 4030 , e ) 4540
Rationale: "100 + 102 + . . . + 160 = 100 * 31 + ( 2 + 4 + . . . + 60 ) = 100 * 31 + 2 * ( 1 + 2 + . . . + 30 ) = 100 * 31 + 2 ( 30 ) ( 31 ) / 2 = 100 * 31 + 30 * 31 = 130 ( 31 ) = 4030 the answer is d ."
Answer: d
Problem: a clock shows the time as 11 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 25 minutes , e ) 40 minutes
Rationale: "there are 7 hours in between 11 a . m . to 6 p . m . 7 * 5 = 35 minutes . answer : c"
Answer: c
Problem: a man is 26 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 22 years , c ) 24 years , d ) 20 years , e ) 19 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 26 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 26 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 24 answer : c"
Answer: c
Problem: a and b can do a piece of work in 6 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?
Options: a ) 15.5 days , b ) 19.5 days , c ) 17.5 days , d ) 16.5 days , e ) 30 days
Rationale: "c = 1 / 5 – 1 / 6 = 1 / 30 = > 30 days answer : e"
Answer: e
Problem: an aeroplane covers a certain distance at a speed of 120 kmph in 5 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 520 , b ) 620 , c ) 820 , d ) 740 , e ) 720
Rationale: "distance = ( 120 x 5 ) = 600 km . speed = distance / time speed = 600 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 600 x 3 / 5 ) km / hr = 360 km / hr answer a ) 360 km / hr"
Answer: a
Problem: a man swims downstream 18 km and upstream 12 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 8
Rationale: "18 - - - 3 ds = 6 ? - - - - 1 12 - - - - 3 us = 4 ? - - - - 1 m = ? m = ( 6 + 4 ) / 2 = 5 answer : b"
Answer: b
Problem: amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.3 km ?
Options: a ) 600 m , b ) 325 m , c ) 300 m , d ) 400 m , e ) 100 m
Rationale: "b 325 m distance covered by amar = 18 / 4.8 ( 1.3 km ) = 3 / 8 ( 1300 ) = 325 m answer is b"
Answer: b
Problem: a sum of rs . 2678 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1629 , b ) 1648 , c ) 2677 , d ) 2986 , e ) 2679
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2678 - x ) * 3 * 5 ) / 100 24 x / 100 = 40170 / 100 - 15 x / 100 39 x = 40170 = > x = 1030 second sum = 2678 â € “ 1030 = 1648 answer : b"
Answer: b
Problem: the sum of two numbers is 24 and their product is 148 . find the sum of the squares of that numbers .
Options: a ) 250 , b ) 280 , c ) 230 , d ) 290 , e ) 250
Rationale: let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 24 ab = 148 so , 24 ^ 2 = a ^ 2 + b ^ 2 + 2 * 148 576 = a ^ 2 + b ^ 2 + 296 a ^ 2 + b ^ 2 = 280 ans b
Answer: b
Problem: two numbers n and 12 have lcm = 54 and gcf = 8 . find n .
Options: a ) 24 , b ) 34 , c ) 36 , d ) 54 , e ) 64
Rationale: the product of two integers is equal to the product of their lcm and gcf . hence . 12 × n = 54 × 8 n = 54 × 8 / 12 = 36 correct answer c
Answer: c
Problem: the two lines y = x and x = - 6 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length of a cube whose surface area is equal to 6 z ?
Options: a ) 16 , b ) 3 √ 2 , c ) 8 , d ) 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 6 , - 6 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 6 × 6 ) = 18 ; so z = 18 . the next step requires us to find the length of a side of a cube that has a face area equal to 18 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 18 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 18 . clearly s = √ 18 = 3 √ 2 , oranswer choice ( b ) ."
Answer: b
Problem: the average age of 35 students in a class is 16 years . the average age of 21 students is 14 . what is the average age of remaining 14 students ?
Options: a ) 14 years , b ) 17 years , c ) 19 years , d ) 21 years , e ) none
Rationale: "solution sum of the ages of 14 students = ( 16 x 35 ) - ( 14 x 21 ) = 560 - 294 . = 266 . ∴ required average = 266 / 14 = 19 years . answer c"
Answer: c
Problem: in the coordinate plane , one of the vertices of a square is the point ( - 6 , - 4 ) . if the diagonals of that square intersect at point ( 3 , 2 ) , what is the area of that square ?
Options: a ) 100
b ) 169
c ) 324
d ) 196
e ) 225
Rationale: one point ( - 6 - 4 ) , intersection ( 3,2 ) so the distance from the first point - 6 - 3 = - 9 is the midpoint of the square - - > whole side 18 , 18 * 18 = 324 c
Answer: c
Problem: mr . jones gave 40 % of the money he had to his wife . he also gave 20 % of the remaining amount to his 3 sons . half of the amount now left was spent on miscellaneous items and the remaining amount of rs . 12000 was deposited in the bank . how much money did mr . jones have initially ?
Options: a ) 100000 , b ) 12000 , c ) 15000 , d ) 13000 , e ) 65000
Rationale: "let the initial amount with mr . jones be rs . x then , ( 1 / 2 ) [ 100 - ( 3 * 20 ) ] % of x = 12000  ( 1 / 2 ) * ( 40 / 100 ) * ( 60 / 100 ) * x = 12000  x = ( ( 12000 * 25 ) / 3 ) = 100000 answer a"
Answer: a
Problem: if n = 3 * 4 * p where p is a prime number greater than 3 , how many different positive non - prime divisors does n have , excluding 1 and n ?
Options: a ) six , b ) seven , c ) eight , d ) nine , e ) ten
Rationale: n = 3 ∗ 2 ^ 2 ∗ p number of divisors = 2 * 3 * 2 = 12 the 12 divisors includes 1 , n , 3 , 2 and p number of different non prime divisors excluding 1 and n = 12 - 5 = 7 answer : b
Answer: b
Problem: of all the students in a certain dormitory , 1 / 2 are first - year students and the rest are second - year students . if 4 / 5 of the first - year students have not declared a major and if the fraction of second - year students who have declared a major is 1 / 2 times the fraction of first - year students who have declared a major , what fraction of all the students in the dormitory are second - year students who have not declared a major ?
Options: a ) 1 / 15 , b ) 1 / 5 , c ) 9 / 20 , d ) 1 / 3 , e ) 2 / 5
Rationale: "tot students = x 1 st year student = x / 2 - - - - > non majaor = 4 / 5 ( x / 2 ) - - - - - > maj = 1 / 5 ( x / 2 ) 2 nd year student = x / 2 - - - - > maj = 1 / 2 ( 1 / 5 ( x / 2 ) ) = 1 / 20 ( x ) - - - > non major = x / 2 - 1 / 20 ( x ) = 9 / 20 ( x ) hence 9 / 20 c"
Answer: c
Problem: a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 1419 , what is the value of n ?
Options: a ) 86 , b ) 38 , c ) 62 , d ) 122 , e ) 672
Rationale: factorise 1419 . . 3 * 11 * 43 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 43 = 86 . . ans : a
Answer: a
Problem: what is the dividend ? the divisor is 17 , the quotient is 4 and the remainder is 8 .
Options: a ) 76 , b ) 67 , c ) 176 , d ) 671 , e ) 0
Rationale: "divided = divisor * quotient + remainder ? = 17 * 4 + 8 68 + 8 76 ( e . g . answer : a )"
Answer: a
Problem: line m lies in the xy - plane . the y - intercept of line m is - 1 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 8 ) . what is the slope of line m ?
Options: a ) - 3 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: ans : e solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 8 ) . midpoint is ( 4 , - 2 ) as we can see that the y axis of intercept point is ( 0 , - 1 ) means line m is parallel to x axis slope m = 0 ans : e
Answer: e
Problem: the average of first 10 prime numbers is ?
Options: a ) 12.6 , b ) 12.5 , c ) 12.9 , d ) 12.2 , e ) 12.1
Rationale: "sum of 10 prime no . = 129 average = 129 / 10 = 12.9 . answer : c"
Answer: c
Problem: if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 50 , what is the value of f ( 5 ) ?
Options: a ) 104 , b ) 60 , c ) 92 , d ) 50 , e ) 25
Rationale: "f ( x ) = 2 x ^ 2 + y f ( 2 ) = 50 = > 2 * ( 2 ) ^ 2 + y = 50 = > 8 + y = 50 = > y = 42 f ( 5 ) = 2 * ( 5 ) ^ 2 + 42 = 92 answer c"
Answer: c
Problem: a man has an investment of $ 3000 which yields a fixed 305 for every $ 500 invested . if the man takes out $ 12.6 for every $ 500 how long will it take for him to double his investment assuming no compounding of interest .
Options: a ) 4 , b ) 33.8 , c ) 10 , d ) 30 , e ) 37.3
Rationale: annual increase is ( 500 + 30.5 - 12.6 ) * 6 = 3107.4 hence every year there is an increase of 107.4 for his saving to double he needs additional $ 4000 therefore $ 4000 / 107.4 = 37.3 correct option is e ) 37.3
Answer: e
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 47 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48
Rationale: "annie earned 40 x + 7 ( 2 x ) = 54 x let h be the number of hours that harry worked . harry earned 30 x + 1.5 x ( h - 30 ) = 54 x ( 1.5 x ) ( h ) = 69 x h = 46 hours the answer is d ."
Answer: d
Problem: car a runs at the speed of 80 km / hr & reaches its destination in 5 hr . car b runs at the speed of 100 km / h & reaches its destination in 2 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 5 , b ) 11 : 8 , c ) 2 : 1 , d ) 15 : 7 , e ) 16 : 9
Rationale: "sol . distance travelled by car a = 80 × 5 = 400 km distance travelled by car b = 100 × 2 = 200 km ratio = 400 / 200 = 2 : 1 answer : c"
Answer: c
Problem: the area of one square is x ^ 2 + 10 x + 25 and the area of another square is 4 x ^ 2 − 12 x + 9 . if the sum of the perimeters of both squares is 32 , what is the value of x ?
Options: a ) 0 , b ) 2 , c ) 2.5 , d ) 4.67 , e ) 10
Rationale: "spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 5 ) ^ 2 & a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 5 & l 2 = 2 x - 3 p 1 = 4 ( x + 5 ) & p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 32 4 ( x + 5 ) + 4 ( 2 x - 3 ) = 32 . . . . . . . . . . . . . . > x = 2 answer : b"
Answer: b
Problem: sandy had $ 217 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ?
Options: a ) $ 270 , b ) $ 290 , c ) $ 310 , d ) $ 330 , e ) $ 350
Rationale: "let the money sandy took for shopping be x . 0.7 x = 217 x = 310 the answer is c ."
Answer: c
Problem: the cube root of . 000216 is :
Options: a ) 0.6
b ) 0.06
c ) 0.9
d ) 0.2
e ) 0.61
Rationale: answer : b ) . 06
Answer: b
Problem: at a special sale , 12 tickets can be purchased for the price of 4 tickets . if 12 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 12 tickets ?
Options: a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 60 % , e ) 66.6 %
Rationale: "let the price of a ticket be rs . 100 , so 4 tickets cost 400 & 12 tickets cost 1200 12 tickets purchased at price of 4 tickets ie . , for 400 , so amount saved s rs . 800 , % of 5 tickets = ( 800 / 1200 ) * 100 = 66.6 % answer : e"
Answer: e
Problem: a person can swim in still water at 12 km / h . if the speed of water 6 km / h , how many hours will the man take to swim back against the current for 6 km ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 12 s = 6 us = 12 - 6 = 6 d = 36 t = 36 / 6 = 6 answer : d"
Answer: d
Problem: a train 320 m in length crosses a telegraph post in 12 seconds . the speed of the train is ?
Options: a ) 77 kmph , b ) 95 kmph , c ) 94 kmph , d ) 98 kmph , e ) 96 kmph
Rationale: "s = 320 / 12 * 18 / 5 = 96 kmph answer : e"
Answer: e
Problem: 12 + 13 + 14 + . . . 51 + 52 + 53 + 54 = ?
Options: a ) 1419 , b ) 1362 , c ) 1363 , d ) 1364 , e ) 1365
Rationale: "sum = 12 + 13 + 14 + . . . 51 + 52 + 53 + 54 sum of n consecutive positive integers starting from 1 is given as n ( n + 1 ) / 2 sum of first 54 positive integers = 55 * 54 / 2 sum of first 11 positive integers = 11 * 12 / 2 sum = 12 + 13 + 14 + . . . 51 + 52 + 53 + 54 = 55 * 54 / 2 - 11 * 12 / 2 = 1419 answer : a"
Answer: a
Problem: 2 x + y = 13 | y | < = 13 for how many ordered pairs ( x , y ) that are solutions of the system above are x and y both integers ?
Options: a ) 7 , b ) 10 , c ) 12 , d ) 13 , e ) 14
Rationale: hi - the questions says | y | < = 13 so the values of y will range from 0 to 13 . so the values of y will be 0,1 , 2,3 , 4,5 , 6,7 , 8,9 , 10,11 , 12,13 . so 14 ( e ) is the answer . remember sign does n ' t matter for y as y will always be positive .
Answer: e
Problem: mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month . if mary ' s savings by the end of the year from these monthly savings were 7 times the amount she spent per month , what should be the fraction of her salary that she spent each month ?
Options: a ) 1 / 4 , b ) 3 / 4 , c ) 10 / 19 , d ) 11 / 19 , e ) 12 / 19
Rationale: saving = s , expenditure = e , income = i at the end of 12 months ; 12 s = 7 e = 7 ( i - s ) = > 19 s = 7 i = > savings = 7 / 19 i hence expenditure = 1 - ( 7 / 19 ) = 12 / 19 answer ( e )
Answer: e
Problem: what is the total number of integers between 20 and 70 that are divisible by 2 ?
Options: a ) 19 , b ) 25 , c ) 24 , d ) 26 , e ) 20
Rationale: "22 , 24 , 26 , . . . , 56,58 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 70 - 22 ) / ( 2 ) + 1 = 48 / 2 + 1 = 24 + 1 = 25 answer is b"
Answer: b
Problem: 9 men went to a hotel . 8 of them spent 3 each over their meals and the ninth spent 5 more than the average expenditure of all the 9 . the total money spent by all of them was
Options: a ) 26 , b ) 40 , c ) 29.25 , d ) 32.625 , e ) none of the above
Rationale: let the average expenditure of all the ninte be x then , 3 × 8 + x + 5 = 9 x ⇒ x = 3.625 ∴ total money spent = 9 x = 9 × 3.625 = 32.625 answer d
Answer: d