regisss/math_qa huggingface dataset:
Problem: 12008 - 50 ÷ 10.00 = ?
Options: a ) 1195 , b ) 120 , c ) 12000 , d ) 12003 , e ) none
Rationale: "answer given expression = 12008 - 50 ÷ 10.00 = 12008 - 5 = 12003 correct option : d"
Answer: d
Problem: 6 ^ 4 − 4 ^ 4 = ?
Options: a ) 20 , b ) 52 , c ) 104 , d ) 520 , e ) 1040
Rationale: "we can write the above in terms of ( a + b ) ( a - b ) 6 ^ 4 − 4 ^ 4 = ( 6 ^ 2 ) 2 - ( 4 ^ 2 ) 2 = ( 6 ^ 2 − 4 ^ 2 ) * ( 6 ^ 2 + 4 ^ 2 ) = ( 36 − 16 ) * ( 36 + 16 ) = > 20 * 52 = 1040 ans option e ."
Answer: e
Problem: find the value of ( 950 + 220 / 900 ) × 900
Options: a ) 854542 , b ) 856945 , c ) 758965 , d ) 855220 , e ) 826450
Rationale: "( 855000 + 220 ) / 900 * 900 = 855000 + 220 = 855220 answer : d"
Answer: d
Problem: __ 2 a x __ b ____ cc in the multiplication problem above , a , b , and c represent distinct digits . if the sum of a and b is equal to 4.6 , what is the value of c ?
Options: a ) 6 , b ) 5.2 , c ) 4 , d ) 3 , e ) 2
Rationale: if a + b = 4.6 assuming a and b are positive then a * b < 10 ( they could be either 1,2 , 3,4 ) therefore a * b = c 2 * b = c a + b = 4.6 three simple equations - divide the 1 st / 2 nd - - > a = 2 plug it the 3 rd - - > b = 2.6 - - > c = 5.2 ( answer b )
Answer: b
Problem: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 9 % . if ron imported a $ 18,000 imported car and ended up paying $ 1950 in taxes , what is the first tier ' s price level ?
Options: a ) $ 11500 , b ) $ 11000 , c ) $ 12000 , d ) $ 12100 , e ) $ 12500
Rationale: let t be the tier price , p be total price = 18000 per the given conditions : 0.12 t + 0.09 ( p - t ) = 1950 0.12 t + 0.09 * 18000 - 0.09 t = 1950 0.03 t + 1620 = 1950 0.03 t = 1950 - 1620 = 330 t = 330 / 0.03 = 11000 answer b
Answer: b
Problem: if ( 4 - x ) / ( 3 + x ) = x , what is the value of x ^ 2 + 4 x - 4 ?
Options: a ) - 4 , b ) - 1 , c ) 0 , d ) 1 , e ) 4
Rationale: "( 4 - x ) = x * ( 3 + x ) ( 4 - x ) = 3 x + x ^ 2 0 = x ^ 2 + 4 x - 4 the answer is c ."
Answer: c
Problem: in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 2 , - 2 ) , ( 2 , 6 ) , ( 14 , 2 ) , ( 14 , - 5 ) ?
Options: a ) 90 , b ) 95 , c ) 104 , d ) 117 , e ) 182
Rationale: "by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 8 + 7 ) × 12 = 90 . the answer is a ."
Answer: a
Problem: a scuba diver descends at a rate of 40 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 3000 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 70 minutes , b ) 72 minutes , c ) 75 minutes , d ) 76 minutes , e ) 77 minutes
Rationale: "time taken to reach = 3000 / 40 = 75 minutes answer : c"
Answer: c
Problem: a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a boy alone in 18 days , how long will a woman take to complete the work ?
Options: a ) 9 days , b ) 21 days , c ) 24 days , d ) 27 days , e ) 28 days
Rationale: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 18 ( 1 man + 1 boy ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 18 = 2 / 9 therefore , 1 woman ’ s 1 day ’ s work = 1 / 3 – 2 / 9 = 3 - 2 / 9 = 1 / 9 therefore , the woman alone can finish the work in 9 days . answer : option a"
Answer: a
Problem: running at the same constant rate , 6 identical machines can produce a total of 270 pens per minute . at this rate , how many pens could 10 such machines produce in 4 minutes ?
Options: a ) 1500 , b ) 1545.6 , c ) 1640.33 , d ) 1800 , e ) none of these
Rationale: "explanation : let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 | | : : 270 : x time 1 : 4 | = > 6 * 1 * x = 10 * 4 * 270 = > x = ( 10 * 4 * 270 ) / 6 = > x = 1800 answer : d"
Answer: d
Problem: a tank with a volume of 45 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 5 cubic inches / min and the 2 outlet pipes empty it out at the rates of 14 cubic inches / min and 6 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches )
Options: a ) 5184 , b ) 5276 , c ) 5368 , d ) 5460 , e ) 5552
Rationale: "the tank is emptied at this rate : 14 + 6 - 5 = 15 cubic inches / min the tank has a volume of 45 * 12 * 12 * 12 = 77760 cubic inches . the time it takes to empty the tank is 77760 / 15 = 5184 minutes . the answer is a ."
Answer: a
Problem: from the sale of sleeping bags , a retailer made a gross profit of 13 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options: a ) 3.0 , b ) 3.36 , c ) 24.78 , d ) 25.0 , e ) 31.36
Rationale: "cost price * 1.13 = selling price - - > cost price * 1.13 = $ 28 - - > cost price = $ 24.78 . answer : c ."
Answer: c
Problem: a light has a rating of 86 watts , it is replaced with a new light that has 18 % higher wattage . how many watts does the new light have ?
Options: a ) 105 , b ) 95 , c ) 80 , d ) 60 , e ) 101
Rationale: final number = initial number + 18 % ( original number ) = 86 + 18 % ( 86 ) = 86 + 15 = 101 . answer e
Answer: e
Problem: a boat running upstream takes 8 hours 48 minutes to cover a certain distance , while it takes 4 hours to cover the same distance running downstream . what is the ratio between the speed of the boat and speed of the water current respectively ?
Options: a ) 8 / 5 , b ) 8 / 3 , c ) 3 / 5 , d ) 5 / 8 , e ) 5 / 3
Rationale: let the man ' s rate upstream be x kmph and that downstream be y kmph . then , distance covered upstream in 8 hrs 48 min = distance covered downstream in 4 hrs . 44 * x / 5 = 4 * y y = 11 / 5 * x required ratio = ( y + x ) / 2 : ( y - x ) / 2 = 8 / 5 : 3 / 5 = 8 / 3 ans - b
Answer: b
Problem: a worker makes a toy in every 1 h . if he works for 100 h , then how many toys will he make ?
Options: a ) 40 , b ) 54 , c ) 45 , d ) 39 , e ) 100
Rationale: "no . of toys = 100 / 1 = 100 answer : e"
Answer: e
Problem: there are 3000 students in a school and among them 20 % of them attends chess class . 40 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?
Options: a ) 240 , b ) 10 , c ) 100 , d ) 50 , e ) 20
Rationale: "20 % of 3000 gives 600 . so 600 attends chess and 40 % of 600 gives 240 so 240 enrolled for swimming answer : a"
Answer: a
Problem: the present population of a town is 280 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 220 , e ) 308
Rationale: "p = 280 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 280 * ( 1 + 10 / 100 ) = 280 * ( 11 / 10 ) = 308 answer is e"
Answer: e
Problem: mary sold boxes of butter cookies . ann sold 5 times as much as she did . 18 boxes of cookies were sold that day , how many boxes did mary sell ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 10 , e ) 18
Rationale: # of boxes of cookies mary sold = x ann sold 5 times more = 5 x x + 5 x = 18 6 x = 18 x = 18 / 6 = 3 answer : a
Answer: a
Problem: a batsman in his 9 th inning makes a score of 75 and their by increasing his average by 7 . what is his average after the 9 th inning ?
Options: a ) 12 , b ) 19 , c ) 26 , d ) 33 , e ) 40
Rationale: 8 x + 75 = 9 ( x + 7 ) x = 12 + 7 = 19 answer : b
Answer: b
Problem: a man can row at 5 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 3.2 km , b ) 3 km , c ) 2.4 km , d ) 3.6 km , e ) none of these
Rationale: "explanation : speed in still water = 5 kmph speed of the current = 1 kmph speed downstream = ( 5 + 1 ) = 6 kmph speed upstream = ( 5 - 1 ) = 4 kmph let the requited distance be x km total time taken = 1 hour = > x / 6 + x / 4 = 1 = > 2 x + 3 x = 12 = > 5 x = 12 = > x = 2.4 km . answer : option c"
Answer: c
Problem: working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 4 x boxes ?
Options: a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 6 minutes , e ) 8 minutes
Rationale: rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 4 x / 5 x * 10 = 8 min ans : e
Answer: e
Problem: in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 4 rows in all and a total of 134 bricks in the wall , how many bricks does the bottom row contain ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 = 134 4 x - 6 = 134 4 x = 128 x = 32 answer : c"
Answer: c
Problem: if paint costs $ 3.10 per quart , and a quart covers 20 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?
Options: a ) $ 1.60 , b ) $ 16.00 , c ) $ 93.00 , d ) $ 108.00 , e ) $ 196.00
Rationale: "total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 20 = 30 cost will be 30 * 3.1 = $ 93 ans : c"
Answer: c
Problem: a man engaged a servant on the condition that he would pay him rs . 1000 and a uniform after one year service . he served only for 9 months and received uniform and rs . 550 , find the price of the uniform ?
Options: a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 800 , e ) s . 120
Rationale: "9 / 12 = 3 / 4 * 1000 = 750 550 - - - - - - - - - - - - - 200 1 / 4 - - - - - - - - 200 1 - - - - - - - - - ? = > rs . 800 answer : d"
Answer: d
Problem: how many distinct prime numbers are factors of 33150 ?
Options: a ) four , b ) five , c ) six , d ) seven , e ) eight
Rationale: start with the prime factorization : 33150 = 50 * 663 = ( 2 * 5 * 5 ) * 3 * 221 = ( 2 ) * ( 3 ) * ( 5 ^ 2 ) * ( 13 ) * ( 17 ) there are five distinct prime factors , { 2 , 3 , 5 , 13 , and 17 } answer : b .
Answer: b
Problem: a glass was filled with 24 ounces of water , and 0.06 ounce of the water evaporated each day during a 12 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.003 % , b ) 0.03 % , c ) 3 % , d ) 2 % , e ) 30 %
Rationale: "in 12 days 12 * 0.06 = 0.72 ounces of water evaporated , which is 0.72 / 24 â ˆ — 100 = 3 of the original amount of water . answer : c ."
Answer: c
Problem: i chose a number and divide it by 4 . then i subtracted 18 from the result and got 7 . what was the number i chose ?
Options: a ) 600 , b ) 100 , c ) 800 , d ) 900 , e ) none
Rationale: solution : let x be the number i chose , then x / 4 â ˆ ’ 18 = 7 x / 4 = 25 x = 100 answer b
Answer: b
Problem: there are 76 persons . 54 can read hindu , 43 can read times , 37 can read deccan and 15 can read all . if 24 can read hindu and deccan and 27 can read deccan and times then what is the number of persons who read only times and hindu .
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: let ' a ' can be read hindu , let ' b ' can be read times , let ' c ' can be read deccan , from the given data : n ( aubuc ) = 76 , n ( a ) = 54 , n ( b ) = 43 , n ( c ) = 37 , n ( anbnc ) = 15 , n ( anc ) = 24 , n ( bnc ) = 27 , n ( anb ) = ? n ( aubuc ) = n ( a ) + n ( b ) + n ( c ) - n ( anb ) - n ( bnc ) - n ( anc ) + n ( anbnc ) = = > 76 = 54 + 43 + 37 - n ( anb ) - 24 - 27 + 15 = = > n ( anb ) = 54 + 43 + 37 + 15 - 24 - 27 - 76 = = > n ( anb ) = 149 - 127 = = > n ( anb ) = 22 answer : b
Answer: b
Problem: the original price of a suit is $ 100 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?
Options: a ) $ 88 , b ) $ 96 , c ) $ 100 , d ) $ 106 , e ) $ 110
Rationale: "0.8 * ( 1.2 * 100 ) = $ 96 the answer is b ."
Answer: b
Problem: the average runs scored by a batsman in 20 matches is 40 . in the next 30 matches the batsman scored an average of 20 runs . find his average in all the 50 matches ?
Options: a ) 31 , b ) 46 , c ) 28 , d ) 13 , e ) 12
Rationale: "total score of the batsman in 20 matches = 800 . total score of the batsman in the next 30 matches = 600 . total score of the batsman in the 50 matches = 1400 . average score of the batsman = 1400 / 50 = 28 . answer : c"
Answer: c
Problem: the sum of 55 consecutive integers is 5555 . what is the greatest integer in the set ?
Options: a ) 126 , b ) 128 , c ) 130 , d ) 132 , e ) 134
Rationale: "let x be the first integer in the set , then x + 54 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 54 ) = 55 x + 54 * 55 / 2 = 55 ( x + 27 ) then x + 27 = 101 x = 74 the largest integer in the set is 74 + 54 = 128 the answer is b ."
Answer: b
Problem: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 5000 , the number of valid votes that the other candidate got , was :
Options: a ) 1800 , b ) 2700 , c ) 2900 , d ) 2200 , e ) 2300
Rationale: "a number of valid votes = 80 % of 5000 = 4000 . valid votes polled by other candidate = 45 % of 4000 = ( 45 / 100 x 4000 ) = 1800 ."
Answer: a
Problem: how many ounces of a 60 % salt solution must be added to 50 ounces of a 20 percent salt solution so that the resulting mixture is 50 % salt ?
Options: a ) 16.67 , b ) 30 , c ) 50 , d ) 60.33 , e ) 150
Rationale: "let x = ounces of 60 % salt solution to be added . 2 * 50 + . 6 x = . 5 ( 50 + x ) x = 150 answer e"
Answer: e
Problem: for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 8 of whom are females , by how much does the index for the females exceed the index for the males in the group ?
Options: a ) 0.05 , b ) 0.0625 , c ) 0.2 , d ) 0.25 , e ) 0.6
Rationale: index for females = ( 20 - 8 ) / 20 = 3 / 5 = 0.6 index for males = ( 20 - 12 / 20 = 2 / 5 = 0.4 index for females exceeds males by 0.6 - 0.4 = 0.2 answer : c
Answer: c
Problem: chocolate bars are sold in packages of 4 or 9 only . if mark bought 97 chocolate bars exactly , what could be the number of large packs mark bought ?
Options: a ) 3 , b ) 4 , c ) 8 , d ) 9 , e ) 13
Rationale: let number of packs of four = f let number of packs of nine = n 4 f + 9 n = 97 now , we need to test for values of n . since sum 97 is odd and 4 f will always be even , n ca n ' t be even . now , we can test for values e = 2 , 4 and 6 4 * 4 + 9 * 9 = 16 + 81 = 97 answer d
Answer: d
Problem: the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 20 % profit ?
Options: a ) 2000 , b ) 2778 , c ) 2299 , d ) 1920 , e ) 2771
Rationale: "let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 120 % of rs . 1600 = 120 / 100 * 1600 = rs . 1920 . answer : d"
Answer: d
Problem: a student completes a 3 part exam as follows . the student completes sections a in 6 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ?
Options: a ) 7 : 1 , b ) 9 : 2 , c ) 8 : 3 , d ) 5 : 2 , e ) 6 : 1
Rationale: "the time spent on section b and section c is 27 minutes each . the ratio of c to a is 27 : 6 = 9 : 2 the answer is b ."
Answer: b
Problem: find the least number must be subtracted from 531742 so that remaining no . is divisible by 3 ?
Options: a ) 4 , b ) 5 , c ) 1 , d ) 2 , e ) 3
Rationale: "on dividing 531742 by 3 we get the remainder 1 , so 1 should be subtracted c"
Answer: c
Problem: 10 men can cut 10 trees in 2 hours . if 2 men leave the job , how many trees will be cut in 3 hours ?
Options: a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 20
Rationale: 10 men - working 2 hrs - cut 10 trees 1 men - working 1 hr - cuts = 10 / 10 * 2 thus 8 men - working 3 hrs - cut = 10 * 8 * 3 / 10 * 2 = 12 trees answer is a
Answer: a
Problem: a person ' s present age is one - fifth of the age of his mother . after 8 years , he will be one - half of the age of his mother . how old is the mother at present ?
Options: a ) a ) 25 , b ) b ) 44 , c ) c ) 32 , d ) d ) 45 , e ) e ) 40
Rationale: "let the mother ' s present age be x years then the person ' s present age = 2 x / 5 ( 3 x / 5 ) + 8 = 1 / 2 ( x + 8 ) 2 ( 3 x + 40 ) = 5 ( x + 8 ) x = 40 answer is e"
Answer: e
Problem: find the product of the place value and face value of 3 in 5769354
Options: a ) 900 , b ) 9000 , c ) 90 , d ) 9 , e ) 0.9
Rationale: "explanation : place value = local value face value = absolute value the place value of 3 in 5769354 is 3 x 100 = 300 the face value of 3 in 5769354 is nothing but 3 . = > 300 x 3 = 900 answer : option a"
Answer: a
Problem: if x and y are integers such that x ^ 2 = 2 y and xy = 32 , then x – y = ?
Options: a ) - 30 , b ) - 20 , c ) - 5 , d ) - 4 , e ) 20
Rationale: "here x and y are integers . x ^ 2 = 2 y , xy = 32 . substitute ( x ^ 2 ) / 2 = y in xy = > x ^ 3 = 32 * 2 = > x ^ 3 = 64 . here x 3 is positive , x is also positive . x = 4 then y = 8 . x - y = - 4 so option d is correct"
Answer: d
Problem: a shopkeeper loses 15 % , if an article is sold for $ 102 . what should be the selling price of the article to gain 20 % ?
Options: a ) $ 165 , b ) $ 174 , c ) $ 144 , d ) $ 164 , e ) $ 183
Rationale: "c $ 144 given that sp = $ 102 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 102 ) / 85 = 20 * 6 = $ 120 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 120 * 120 ) / 100 = $ 144"
Answer: c
Problem: after decreasing 24 % in the price of an article costs rs . 912 . find the actual cost of an article ?
Options: a ) 226 , b ) 255 , c ) 1200 , d ) 2771 , e ) 332
Rationale: "cp * ( 76 / 100 ) = 912 cp = 12 * 100 = > cp = 1200 answer : c"
Answer: c
Problem: a man sells an article at 10 % gain . had be sold at for rs . 60 / - more he could have gained 20 % what is cost price of article
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 650 , d ) rs . 760 , e ) rs . 800
Rationale: first selling price = 110 % - - - - - > x rupees = sold at for rs . 60 / - = 120 % - - - - - > x + 60 rupees ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 10 % - - - - - - - - > 60 100 % - - - - - - - > rs . 600 / - option ' b '
Answer: b
Problem: a train covers a distance of 10 km in 20 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 50 , b ) 80 , c ) 120 , d ) 100 , e ) 40
Rationale: "speed = ( 10 / 20 * 60 ) km / hr = ( 30 * 5 / 18 ) m / sec = 8.333333 m / sec . length of the train = 8.333333 * 6 = 50 m . answer : a"
Answer: a
Problem: if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 7 ¤ √ 7 =
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 28
Rationale: "x = √ 7 and y also = √ 7 applying the function ( √ 7 + √ 7 ) ^ 2 - ( √ 7 - √ 7 ) ^ 2 = ( 2 √ 7 ) ^ 2 - 0 = 4 x 7 = 28 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 7 and y = √ 7 you get the answer 28 . answer e"
Answer: e
Problem: 6 people can do work in 80 days how much people they required to complete the work in 16 days ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: man and days concept . . . 6 m * 80 d = m * 16 d solve it , total no of people required is 30 ; answer : c
Answer: c
Problem: the average of 10 consecutive integers is 15 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?
Options: a ) 10 , b ) 10.5 , c ) 11 , d ) 11.5 , e ) 12
Rationale: "the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is b ."
Answer: b
Problem: on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 140 km . ram is camped at a location that on the map is 34 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 14.83 , b ) 14.81 , c ) 14.8 , d ) 15.25 , e ) 14.12
Rationale: "explanation : since 312 inch = 140 km so 1 inch = 140 / 312 km so 34 inch = ( 140 ã — 34 ) / 312 = 15.25 km answer : d"
Answer: d
Problem: a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 40 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 44.33 , e ) $ 40.60
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 40 % discount then the original price of it was x * 0.6 = $ 14 - - > x = $ 23,33 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 23,33 + 21 = $ 44,33 . answer : d ."
Answer: d
Problem: a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if the company declares 8 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 960 , d ) rs . 720 , e ) none
Rationale: "solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 8 / 100 x 12000 ) = rs . 960 . answer c"
Answer: c
Problem: a man took loan from a bank at the rate of 12 % p . a . s . i . after 20 years he had to pay rs . 1500 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 625 , b ) 700 , c ) 950 , d ) 825 , e ) 630
Rationale: principal = ( 100 * 1500 ) / ( 12 * 20 ) = rs . 625 answer : a
Answer: a
Problem: david and lewis leave chennai for tirupati simultaneously at 7 a . m in the morning driving in two cars at speeds of 60 mph and 80 mph respectively . as soon as lewis reaches tirupati he returns back to chennai along the same route and meets david on the way back . if the distance between the two cities is 160 miles , how far from chennai did david and lewis meet ?
Options: a ) 100 mlies , b ) 120 miles , c ) 90 miles , d ) 95 miles , e ) 110 miles
Rationale: time taken by lewis to reach tirupati = 160 / 80 = 2 hours in 2 hours , david travels 60 * 2 = 120 miles so distance at which they meet should be greater than 120 miles . only b satisfies . answer is b .
Answer: b
Problem: what is the smallest positive perfect square that is divisible by 12 , 14 , and 42 ?
Options: a ) 900 , b ) 1089 , c ) 1600 , d ) 1764 , e ) 2025
Rationale: "the number needs to be divisible by 2 ^ 2 * 3 , 2 * 7 , and 2 * 3 * 7 . the smallest such perfect square is 2 ^ 2 * 3 ^ 2 * 7 ^ 2 = 1764 the answer is d ."
Answer: d
Problem: rs . 6000 is lent out in two parts . one part is lent at 7 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 5 : 1 , b ) 5 : 7 , c ) 5 : 5 , d ) 5 : 9 , e ) 5 : 3
Rationale: "let the amount lent at 7 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 7 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 450 = > x = 5000 amount lent at 10 % = 1000 required ratio = 5000 : 1000 = 5 : 1 answer : a"
Answer: a
Problem: the product of x and y is a constant . if the value of x is increased by 60 % , by what percentage must the value of y be decreased ?
Options: a ) 30 % , b ) 32 % , c ) 35 % , d ) 37.5 % , e ) 40 %
Rationale: "x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.6 x ( 120 ) i . e . 160 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 160 = 62.5 i . e . y decreases from 100 to 62.5 i . e . decrease of 37.5 % answer : option d"
Answer: d
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 400 , what were her original savings ?
Options: a ) $ 1500 , b ) $ 1600 , c ) $ 1700 , d ) $ 1800 , e ) $ 1900
Rationale: if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 400 . so 1 / 4 of her savings is $ 400 . so her original savings are 4 times $ 400 = $ 1600 correct answer b
Answer: b
Problem: city a to city b , andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph . what was the average speed for the whole trip ?
Options: a ) 56 , b ) 57.5 , c ) 58.9 , d ) 61.4 , e ) 62
Rationale: the total distance is 1 × 50 + 3 × 60 = 2301 × 50 + 3 × 60 = 230 . and the total time is 4 hours . hence , average speed = ( total distancetotal time ) = 2304 = 57.5 b
Answer: b
Problem: laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 15 kmph and prasanna moves southward at a speed of 45 kmph . how far will be prasanna from laxmi after 60 minutes ?
Options: a ) 11 , b ) 50 , c ) 28 , d ) 27 , e ) 60
Rationale: "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 15 kmph x 1 hr = 15 km total southward prasanna ' s distance = 45 kmph x 1 hr = 45 km total distance between prasanna and laxmi is = 15 + 45 = 60 km . answer : e"
Answer: e
Problem: car x began traveling at an average speed of 35 miles per hour . after 84 minutes , car y began traveling at an average speed of 42 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 140 , b ) 175 , c ) 210 , d ) 245 , e ) 270
Rationale: in 84 minutes , car x travels 49 miles . car y gains 7 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is d .
Answer: d
Problem: the cost of producing x tools by a company is given by c ( x ) = 600 x + 5500 ( in $ ) a ) what is the cost of 100 tools ?
Options: a ) 65500 $ , b ) 125800 $ , c ) 125900 $ , d ) 6500 $ , e ) 122500 $
Rationale: solution c ( 100 ) = 600 * 100 + 5500 = 125500 $ answer a
Answer: a
Problem: how many odd numbers between 10 and 1,000 are the squares of integers ?
Options: a ) 12
b ) 13
c ) 14
d ) 15
e ) 16
Rationale: the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 14 numbers . answer : c .
Answer: c
Problem: a man can row 11 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 6.24 km , b ) 6 km , c ) 5.76 km , d ) 5.66 km , e ) 10.87 km
Rationale: "m = 11 s = 1.2 ds = 12.2 us = 9.8 x / 12.2 + x / 9.8 = 1 x = 5.43 d = 5.43 * 2 = 10.87 answer : e"
Answer: e
Problem: if the l . c . m of two numbers is 720 and their product is 38880 , find the h . c . f of the numbers .
Options: a ) 50 , b ) 30 , c ) 125 , d ) 54 , e ) none of these
Rationale: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 38880 / 720 = 54 . answer : d"
Answer: d
Problem: a , b and c have rs . 400 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) a ) 150 , b ) b ) 140 , c ) c ) 130 , d ) d ) 120 , e ) e ) 110
Rationale: "a + b + c = 400 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 400 - - - - - - - - - - - - - - - - c = 150 answer : a"
Answer: a
Problem: an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 12.50 as commission , the cloth sold through him on that day is worth
Options: a ) 333 , b ) 500 , c ) 887 , d ) 299 , e ) 132
Rationale: explanation : let the total sale be rs . x . then , 2.5 % . of x = 12.50 < = > ( 25 / 100 * 1 / 100 * x ) = 125 / 10 < = > x = 500 . answer : b ) 500
Answer: b
Problem: an empty wooden vessel weighs 20 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled .
Options: a ) 3 / 5 , b ) 5 / 9 , c ) 1 / 24 , d ) 9 / 19 , e ) 2 / 5
Rationale: an empty wooden vessel weighs 20 % of its total weight when filled with paint : vessel = 0.2 ( vessel + paint ) ; 20 v = v + p ( so the weight of completely filled vessel is 10 v ) p = 19 v ( so the weight of the paint when the vessels is completely filled is 19 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 20 v ; p ' = 9 v ( so the weight of the paint when the vessels is partially filled is 9 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 9 v / 19 v = 9 / 19 . answer : d .
Answer: d
Problem: a cycle is bought for rs . 900 and sold for rs . 990 , find the gain percent ?
Options: a ) 39 % , b ) 20 % , c ) 23 % , d ) 74 % , e ) 10 %
Rationale: "900 - - - - 90 100 - - - - ? = > 10 % answer : e"
Answer: e
Problem: ( 0.0066 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.006 ) =
Options: a ) 990 , b ) 99.0 , c ) 9.9 , d ) 0.99 , e ) 0.099
Rationale: "( 0.0066 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.006 ) = 0.0060 * 360 / 4 * ( 0.1 ) ( 0.006 ) = 0.066 * 90 / 1 * 0.006 = 66 * 90 / 6 = 11 * 90 = 990 answer : a"
Answer: a
Problem: in the manufacture of a certain product , 9 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.15 % , b ) 0.45 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: "0.09 * 0.05 = 0.0045 = 0.45 % the answer is b ."
Answer: b
Problem: let c be defined as the sum of all prime numbers between 0 and 30 . what is c / 3
Options: a ) 155 , b ) 129 , c ) 61 , d ) 47 , e ) 43
Rationale: "prime numbers between 0 and 30 - 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 sum , c = 129 c / 3 = 43 answer e"
Answer: e
Problem: if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 9600 ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 16
Rationale: required difference = [ 3 ½ % of rs . 9600 ] – [ 3 1 / 3 % of rs . 9600 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 9600 = 1 / 6 % of rs . 9600 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 9600 ] = rs . 16 . answer is e .
Answer: e
Problem: a 6 % stock yields 8 % . the market value of the stock is :
Options: a ) 33 , b ) 75 , c ) 44 , d ) 27 , e ) 91
Rationale: for an income of rs . 8 , investment = rs . 100 . for an income of rs . 6 , investment = rs . 100 x 6 = rs . 75 . 8 market value of rs . 100 stock = rs . 75 . answer : b
Answer: b
Problem: john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 16 , what was the price before the first discount ?
Options: a ) $ 18.44 , b ) $ 28.44 , c ) $ 48.44 , d ) $ 58.44 , e ) $ 38.44
Rationale: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 16 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 16 solve for x x = $ 28.44 correct answer b"
Answer: b
Problem: in an election between the two candidates , the candidates who gets 60 % of votes polled is winned by 280 votes majority . what is the total number of votes polled ?
Options: a ) 1400 , b ) 1600 , c ) 1800 , d ) 2000 , e ) 2100
Rationale: "note : majority ( 20 % ) = difference in votes polled to win ( 60 % ) & defeated candidates ( 40 % ) 20 % = 60 % - 40 % 20 % - - - - - > 280 ( 20 × 14 = 280 ) 100 % - - - - - > 1400 ( 100 × 14 = 1400 ) a )"
Answer: a
Problem: a work can be finished in 16 days by 5 women . the same work can be finished in 8 days by sixteen men . the ratio between the capacity of a man and a woman is
Options: a ) 1 : 3 , b ) 4 : 3 , c ) 2 : 3 , d ) 2 : 1 , e ) 5 : 8
Rationale: "work done by 5 women in 1 day = 1 / 16 work done by 1 woman in 1 day = 1 / ( 16 × 5 ) work done by 16 men in 1 day = 1 / 8 work done by 1 man in 1 day = 1 / ( 8 × 16 ) ratio of the capacity of a man and woman = 1 / ( 8 × 16 ) : 1 / ( 16 × 5 ) = 1 / 8 : 1 / 5 = 1 / 8 : 1 / 5 = 5 : 8 option e"
Answer: e
Problem: the height of a cylinder is 60 cm and the diameter of its base is 5 cm . the total surface area of the cylinder is
Options: a ) 918.14
b ) 981.41
c ) 982.14
d ) 928.41
e ) none of them
Rationale: given h = 60 cm and r = 5 / 2 cm total surface area = 2 π rh + 2 & pir ( power 2 ) = 2 π r ( h + r ) = [ 2 × 22 / 7 × 5 / 2 × ( 60 + 5 / 2 ) ] cm ( power 2 ) = [ 44 / 7 × 5 / 2 × ( ( 120 + 5 ) / 2 ) ] cm ( power 2 ) = 22 / 7 × 5 × 125 / 2 cm ( power 2 ) = ( 55 × 125 ) / 7 cm ( power 2 ) = 6875 / 7 cm ( power 2 ) = 982.14 cm ( power 2 ) answer is c .
Answer: c
Problem: a tank is filled by 3 pipes a , b , c in 7 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 25 hr , b ) 35 hr , c ) 40 hr , d ) 49 hr , e ) 50 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 7 7 / x = 1 / 7 x = 49 hours answer is d"
Answer: d
Problem: there are two positive numbers in the ratio 5 : 8 . if the larger number exceeds the smaller by 27 , then find the smaller number ?
Options: a ) 25 , b ) 66 , c ) 45 , d ) 88 , e ) 44
Rationale: "let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 27 3 x = 27 = > x = 9 = > smaller number = 5 x = 45 . answer : c"
Answer: c
Problem: a worker is paid a regular rate of rs . 20 for completing a survey . the worker completes 100 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 10 % higher than her regular rate . if she completed 70 surveys involving the use of her cellphone , how much did she get that week ?
Options: a ) 2140 , b ) 1140 , c ) 550 , d ) 650 , e ) 750
Rationale: amount earned using her cell phone = 70 * 22 = 1540 earned for remaining surveys = 30 * 20 = 600 total earning = 2140 answer : a
Answer: a
Problem: if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 38 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 700 , b ) $ 800 , c ) $ 900 , d ) $ 1100 , e ) $ 1200
Rationale: "0.1 x = 0.08 ( 2000 - x ) + 38 0.18 x = 198 x = 1100 then the amount invested at 8 % is $ 2000 - $ 1100 = $ 900 the answer is c ."
Answer: c
Problem: if taxi fares were $ 2.00 for the first 1 / 5 mile and $ 0.40 for each 1 / 5 mile there after , then the taxi fare for a 4 - mile ride was
Options: a ) $ 4.60 , b ) $ 9.80 , c ) $ 19.60 , d ) $ 9.60 , e ) $ 29.60
Rationale: "in 4 miles , initial 1 / 5 mile charge is $ 2 rest of the distance = 4 - ( 1 / 5 ) = 19 / 5 rest of the distance charge = 19 ( 0.4 ) = $ 7.6 ( as the charge is 0.4 for every 1 / 5 mile ) = > total charge for 4 miles = 2 + 7.6 = 9.6 answer is d"
Answer: d
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 42 kmph , find the speed of the stream ?
Options: a ) 16 kmph , b ) 18 kmph , c ) 14 kmph , d ) 79 kmph , e ) 27 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 42 / 3 = 14 kmph . answer : c"
Answer: c
Problem: by selling an article at rs . 300 , a profit of 25 % is made . find its cost price ?
Options: a ) s . 486 , b ) s . 455 , c ) s . 240 , d ) s . 480 , e ) s . 489
Rationale: "sp = 300 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 300 * [ 100 / ( 100 + 25 ) ] = 300 * [ 100 / 125 ] = rs . 240 answer : c"
Answer: c
Problem: what will be the compound interest on rs . 25000 a ō er 3 years at the rate of 12 % per annum
Options: a ) rs 10123.20 , b ) rs 10123.30 , c ) rs 10123.40 , d ) rs 10123.50 , e ) none of these
Rationale: "explanation : ( 25000 × ( 1 + 12100 ) 3 ) = > 25000 × 2825 × 2825 × 2825 = > 35123.20 so compound interest will be 35123.20 - 25000 = rs 10123.20 answer : a"
Answer: a
Problem: a batsman scores 26 runs and increases his average from 14 to 15 . find the runs to be made if he wants top increasing the average to 19 in the same match ?
Options: a ) 12 , b ) 18 , c ) 25 , d ) 74 , e ) 88
Rationale: number of runs scored more to increase the ratio by 1 is 26 - 14 = 12 to raise the average by one ( from 14 to 15 ) , he scored 12 more than the existing average . therefore , to raise the average by five ( from 14 to 19 ) , he should score 12 x 5 = 60 more than the existing average . thus he should score 14 + 60 = 74 . answer d
Answer: d
Problem: a and b can do a piece of work in 30 days and 30 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?
Options: a ) 30 days , b ) 35 days , c ) 40 days , d ) 45 days , e ) 50 days
Rationale: "explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 30 + 1 / 30 ] = 10 [ 1 + 1 / 30 ] = 2 / 3 a complete remaining work in 2 / 3 * 30 = 20 total work = 10 + 20 = 30 days answer : option a"
Answer: a
Problem: a total of 520 players participated in a single tennis knock out tournament . what is the total number of matches played in the tournament ? ( knockout means if a player loses , he is out of the tournament ) . no match ends in a tie .
Options: a ) 511 , b ) 519 , c ) 256 , d ) 255 , e ) 1023
Rationale: there are 520 players , only 1 person wins , 519 players lose . in order to lose , you must have lost a game . 519 games . ans - b
Answer: b
Problem: solving a linear equation with several occurrences of the variable , solve for w . simplify answer as much as possible . ( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: ( 7 w + 6 ) / 6 + ( 9 w + 8 ) / 2 = 22 or , [ 7 w + 6 + 3 ( 9 w + 8 ) ] / 6 = 22 or , 7 w + 6 + 27 w + 24 = 132 or , 34 w + 30 = 132 or , 34 w = 132 - 30 or , 34 w = 102 or , w = 102 / 34 therefore , w = 3 answer : c
Answer: c
Problem: given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 7 = f ( 3 x – 6 )
Options: a ) 0 , b ) 2 , c ) 6 , d ) 7 , e ) 13
Rationale: "answer = b = 2 f ( x ) = 3 x – 5 2 * [ f ( x ) ] – 7 = f ( 3 x – 6 ) 2 ( 3 x - 5 ) - 7 = 3 ( 3 x - 6 ) - 5 6 x - 17 = 9 x - 23 x = 2"
Answer: b
Problem: two good train each 750 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 72 sec , e ) none
Rationale: "sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 750 + 750 ) m = 1500 m . required time = ( 1500 x 6 / 125 ) sec = 72 sec . answer d"
Answer: d
Problem: the ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 4800 sq cm . what is the ratio of the width and the area of the rectangle ?
Options: a ) 1 : 72
b ) 1 : 76
c ) 1 : 80
d ) 1 : 84
e ) 1 : 88
Rationale: let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 4800 12 x ^ 2 = 4800 x ^ 2 = 400 x = 20 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 80 the answer is c .
Answer: c
Problem: a work which could be finished in 7 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?
Options: a ) 22 , b ) 20 , c ) 60 , d ) 71 , e ) 11
Rationale: "x - - - - - - - 7 ( x + 10 ) - - - - 6 x * 7 = ( x + 10 ) 6 x = 60 \ answer : c"
Answer: c
Problem: if ( 6 ) ( x ^ 2 ) has 3 different prime factors , at most how many different prime factors does x have ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: x can have at most 3 prime factors , namely the prime factors 2 and 3 , plus one other . if x had more than this number of prime factors , then ( 6 ) ( x ^ 2 ) would have more than 3 prime factors . the answer is c .
Answer: c
Problem: an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 30 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 65.00
Rationale: "without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 38 % , thus he must pay slightly more than $ 62 . answer : e ."
Answer: e
Problem: a car gets 20 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 190 kilometers ?
Options: a ) 3.5 gallons , b ) 9.5 gallons , c ) 8.7 gallons , d ) 4.5 gallons , e ) 9.2 gallons
Rationale: each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 180 kilometers ? 180 ã · 40 = 9.5 ã — 1 gallon = 9.5 gallons correct answer is b ) 9.5 gallons
Answer: b
Problem: what will be the compound interest on a sum of rs . 35,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s : 10123.19 , b ) s : 14172.48 , c ) s : 10123.20 , d ) s : 10123.28 , e ) s : 10123.12
Rationale: "amount = [ 35000 * ( 1 + 12 / 100 ) 3 ] = 35000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 49172.48 c . i . = ( 49172.48 - 35000 ) = rs : 14172.48 answer : b"
Answer: b
Problem: from below option 48 is divisible by which one ?
Options: a ) a ) 3 , b ) b ) 5 , c ) c ) 9 , d ) d ) 7 , e ) e ) 11
Rationale: "48 / 3 = 16 a"
Answer: a
Problem: the list price of an article is rs . 66 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 3.45 % , b ) 4.45 % , c ) 5.45 % , d ) 6.45 % , e ) 7.45 %
Rationale: "66 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 5.45 % answer : c"
Answer: c
Problem: a trader marked the selling price of an article at 60 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 10 % , b ) 10.5 % , c ) 6.8 % , d ) 12.5 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 160 , s . p . = rs . 99 . ∴ discount % = [ 11 / 160 * 100 ] % = 6.8 % answer c"
Answer: c
Problem: a number when divided by 243 gives a remainder 26 , what remainder will be obtained by dividing the same number 14 ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 2 , e ) 3
Rationale: "explanation : 243 + 26 = 269 / 14 = 3 ( remainder ) answer : e"
Answer: e
Problem: a person saved $ 10 in buying an item on sale . if he spent $ 200 for the item , approximately how much percent he saved in the transaction ?
Options: a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 6 %
Rationale: "actual price = 200 + 10 = $ 210 saving = 10 / 210 * 100 = 100 / 21 = 5 % approximately answer is d"
Answer: d
Problem: the average age of 36 students in a group is 14 years . when teacher ' s age is included to it , the average increases by one . find out the teacher ' s age in years ?
Options: a ) 50 , b ) 49 , c ) 53 , d ) 54 , e ) 51
Rationale: "average age of 36 students in a group is 14 sum of the ages of 36 students = 36 × 14 when teacher ' s age is included to it , the average increases by one = > average = 15 sum of the ages of 36 students and the teacher = 37 × 15 hence teachers age = 37 × 15 - 36 × 14 = 37 × 15 - 14 ( 37 - 1 ) = 37 × 15 - 37 × 14 + 14 = 37 ( 15 - 14 ) + 14 = 37 + 14 = 51 answer is e ."
Answer: e
Problem: the amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5 . if they worked a combined total of 128 hours , how many hours did the secretary who worked the longest spend on the project ?
Options: a ) 90 , b ) 70 , c ) 56 , d ) 16 , e ) 14
Rationale: "8 x = 128 = > x = 16 therefore the secretary who worked the longest spent 16 x 5 = 90 hours on the project option ( a )"
Answer: a
Problem: a is 1.5 times as fast as b . a alone can do the work in 20 days . if a and b working together , in how many days will the work be completed ?
Options: a ) 23 , b ) 22 , c ) 12 , d ) 24 , e ) 25
Rationale: a can finish 1 work in 20 days b can finish 1 / 1.5 work in 20 days - since a is 1.5 faster than b this means b can finish 1 work in 20 * 1.5 days = 30 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 20 * 30 / ( 20 + 30 ) = 20 * 30 / 50 = 12 days so answer is c
Answer: c
Problem: if a speaks the truth 65 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.39 , b ) 0.48 , c ) 0.41 , d ) 0.482 , e ) 0.411
Rationale: "explanation : probability that a speaks truth is 65 / 100 = 0.65 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.65 × 0.6 = 0.39 answer : a"
Answer: a