regisss/math_qa huggingface dataset:
Problem: the sum of 4 consecutive numbers is 102 . the greatest among these 3 number is :
Options: a ) 26 , b ) 28 , c ) 29 , d ) 30 , e ) 27
Rationale: let the numbers be x , x + 1 , x + 2 and x + 3 then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 102 4 x = 96 x = 24 greatest number , ( x + 3 ) = 27 answer : e
Answer: e
Problem: the sum of all possible two digit numbers formed from 3 different one digit natural numbers when divided by the sum of the original 3 numbers is equal to ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: let the one digit numbers x , y , z sum of all possible two digit numbers = ( 10 x + y ) + ( 10 x + z ) + ( 10 y + x ) + ( 10 y + z ) + ( 10 z + x ) + ( 10 z + y ) = 22 ( x + y + z ) therefore sum of all possible two digit numbers when divided by sum of one digit numbers gives 22 . answer e
Answer: e
Problem: if a man lost 10 % by selling oranges at the rate of 18 a rupee at how many a rupee must he sell them to gain 32 % ?
Options: a ) 13.25 , b ) 14.36 , c ) 15.85 , d ) 12.27 , e ) 11.25
Rationale: "90 % - - - - 18 132 % - - - - ? 90 / 132 * 18 = 12.27 answer : d"
Answer: d
Problem: mike drives his new corvette from san francisco to las vegas , a journey of 640 miles . he drives the first half of the trip at an average rate of 80 miles per hour , but has to slow down for the second half of his journey . if the second half of the trip takes him 200 percent longer than the first half , what is his average rate z in miles per hour for the entire trip ?
Options: a ) 26.7 , b ) z = 30.0 , c ) z = 40.0 , d ) z = 53.3 , e ) 60.0
Rationale: "veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct ."
Answer: c
Problem: john is going with 10 friends on a trip to sidney for spring break . airfare and hotel costs a total of $ 12100.00 for the group of 11 friends . how much does each person have to pay for their hotel and airfare ?
Options: a ) $ 1010 , b ) $ 1100 , c ) $ 1110 , d ) $ 1101 , e ) $ 1200
Rationale: answer = b the total cost of the trip ( $ 12100.00 ) divided by 11 equals $ 1100.00 .
Answer: b
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what r percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which r is 40 % of 80 hence , d is the answer
Answer: d
Problem: last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.7 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?
Options: a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 4 , e ) 15 / 16
Rationale: x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.7 ( x ) + 0.5 ( 1 - x ) = 0.75 0.2 x = 0.75 - 0.5 x = 0.25 / 0.2 x = 5 / 4 therefore the answer is d : 5 / 4 .
Answer: d
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.50 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 978
b ) 789
c ) 999
d ) 778
e ) 787
Rationale: a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 1.5 = 999 answer : c
Answer: c
Problem: a firm is comprised of partners and associates in a ratio of 2 : 63 . if 50 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ?
Options: a ) 5 , b ) 10 , c ) 12 , d ) 20 , e ) 25
Rationale: the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 10 of the increase in 50 associates . the ratio changed from 20 : 630 to 20 : 680 . thus the number of partners is 20 . the answer is d .
Answer: d
Problem: a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 42 liters of drink a to convert it to drink b ?
Options: a ) 7 , b ) 9 , c ) 12 , d ) 14 , e ) 18
Rationale: in 42 liters of drink a , there are 24 liters of milk and 18 liters of juice . with 24 liters of milk , we need a total of 32 liters of juice to make drink b . we need to add 14 liters of juice . the answer is d .
Answer: d
Problem: the ratio between the number of sheep and the number of horses at the stewar farm is 5 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?
Options: a ) 18 , b ) 28 , c ) 40 , d ) 56 , e ) 58
Rationale: "et no of sheep and horses are 5 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 5 * 8 ) = 40 answer : c"
Answer: c
Problem: working alone , tom finishes cleaning half the house in a third of the time it takes nick to clean the entire house alone . tom alone cleans the entire house in 6 hours . how many hours will it take nick and tom to clean the entire house if they work together ?
Options: a ) 1.5 , b ) 2 , c ) 2.4 , d ) 3 , e ) 3.6
Rationale: answer is 3.6 hours . tom does the complete house in 6 hours while nick does it in 9 hours . 1 / ( 1 / 6 + 1 / 9 ) = 3.6 answer is e
Answer: e
Problem: of the people who responded to a market survey , 360 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 9 to 1 , how many people responded to the survey ?
Options: a ) 80 , b ) 160 , c ) 240 , d ) 360 , e ) 400
Rationale: "ratio = 9 : 1 = > 9 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 360 = > 9 x = 360 = > x = 40 hence total no . of respondents = 360 + 40 = 400 hence e is the answer ."
Answer: e
Problem: 90 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 180 litres , e ) none of these
Rationale: "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 90 = 120 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 120 = 180 litres . answer d"
Answer: d
Problem: machine – a produces 40 % of the total output and machine - b produces 60 % of the total output . an average of 9 units out of a 1000 goods manufactured by machine - a and one unit of 50 units produced by machine - b prove to be defective . what is the probability that a unit chosen at random from the total daily output of the factory is defective ?
Options: a ) a . 0.156 , b ) b . 0.01506 , c ) c . 0.0156 , d ) d . 0.0001566 , e ) e . 0.00001566
Rationale: let total production be 10000 units . . . . a produces 4000 units and 36 units are defective b produces 6000 units and 120 units are defective so , out of total 10,000 units 156 units are defective . . . so the required probability = 156 / 10000 = > 0.0156 answer will be ( c )
Answer: c
Problem: a 470 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ?
Options: a ) 41.1 sec , b ) 64.8 sec , c ) 31.8 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 470 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 990 m time = distance / speed = 990 x 18 / ( 5 x 55 ) = 64.8 sec ans is : b"
Answer: b
Problem: the ratio between the number of sheep and the number of horses at the stewar farm is 7 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ?
Options: a ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 58
Rationale: "et no of sheep and horses are 7 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 7 * 8 ) = 56 answer : d"
Answer: d
Problem: gold is 10 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 9 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 2 , c ) 4 : 1 , d ) 5 : 2 , e ) 4 : 3
Rationale: "g = 10 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 5 wx = x + 1 * 9 w 10 + 5 x = 9 ( x + 1 ) x = 1 / 4 ratio of gold with copper = 1 : 1 / 4 = 4 : 1 answer is c"
Answer: c
Problem: veena ranks 73 rd from the top in a class of 182 . what is her rank from the bottom if 22 students have failed the examination ?
Options: a ) 88 , b ) 108 , c ) 110 , d ) 90 , e ) 93
Rationale: "total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 73 + 1 = 88 answer : a"
Answer: a
Problem: what annual installment will discharge a debt of rs . 1176 due in 3 years at 12 % simple interest ?
Options: a ) 315 , b ) 350 , c ) 325 , d ) 335 , e ) none of them
Rationale: "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1176 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1176 ï ƒ › ( 28 x + 31 x + 25 x ) = ( 1176 * 25 ) x = ( 1176 * 25 ) / 84 = rs . 350 . therefore , each installment = rs . 350 . answer is b ."
Answer: b
Problem: michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 12 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?
Options: a ) 117 % , b ) 120 % , c ) 121 % , d ) 133 % , e ) 140 %
Rationale: "since michelle earns 12 % interest compounded semiannually , then she earns 6 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 6 % * 5 = 30 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 30 % , only answer choice d fits . answer : d"
Answer: d
Problem: if the numerator of a fraction is increased by 50 % and denominator by 20 % , the fraction become 9 / 15 . what was the original fraction ?
Options: a ) 12 / 25 , b ) 13 / 25 , c ) 3 / 5 , d ) 6 / 7 , e ) 7 / 8
Rationale: "explanation : let the fraction be x / y we have 150 x / 120 y = 9 / 15 = x / y = 12 / 25 answer : option a"
Answer: a
Problem: every student of a certain school must take one and only one elective course . in last year , 1 / 2 of the students took p . e . as an elective , 1 / 3 of the students took theatre as an elective , and all of the other students took music . in this year , 1 / 3 of the students who took p . e . and 1 / 4 of the students who took theatre left school , other students did not leave , and no fresh student come in . what fraction of all students took p . e . or music ?
Options: a ) 2 / 3 , b ) 1 / 4 , c ) 7 / 9 , d ) 1 / 5 , e ) 8 / 11
Rationale: lets pick smart numbers . total number of students : 12 p . e . ( 1 / 2 ) : 6 theatre ( 1 / 3 ) : 4 music ( 1 / 6 ) : 2 after leaving school p . e . : 4 theatre : 3 music : 2 new total number of students : 9 p . e . and music : 6 answer 2 / 3 or a
Answer: a
Problem: what is the compound interest paid on a sum of rs . 1500 for the period of 2 years at 10 % per annum .
Options: a ) 230 , b ) 175 , c ) 225 , d ) 315 , e ) none of these
Rationale: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 1500 = 1500 * ( 21 / 100 ) = 315 answer d"
Answer: d
Problem: if sharon ' s weekly salary increased by 20 percent , she would earn $ 600 per week . if instead , her weekly salary were to increase by 15 percent , how much would she earn per week ?
Options: a ) rs . 575 , b ) rs . 600 , c ) rs . 625 , d ) rs . 485 , e ) rs . 590
Rationale: "soln : - ( 600 / 120 ) 115 = 575 in this case long division does not take much time . ( 5 / 1 ) 115 = rs . 575 answer : a"
Answer: a
Problem: jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 3 hours . how long would it take taimour to paint the fence alone ?
Options: a ) 6 hours , b ) 9 hours , c ) 14 hours , d ) 24 hours , e ) 32 hours
Rationale: "i believe the answer is b . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 3 = > 1 / 9 working alone taimour can do the job in 1 = 1 / 9 * hours = > 9 answer b"
Answer: b
Problem: a man is walking at the rate of 9 km / hr crosses a bridge in 15 minutes . the length of the bridge is
Options: a ) 1000 meters , b ) 1050 meters , c ) 2200 meters , d ) 2250 meters , e ) none of these
Rationale: "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . speed = 9 â ˆ — 5 / 18 = 5 / 2 m / sec time = 15 â ˆ — 60 seconds = 900 seconds distance = time â ˆ — speed / distance = 5 / 2 â ˆ — 900 = 2250 meter option d"
Answer: d
Problem: how many multiples of 4 are there between 1 and 99 ?
Options: a ) 20 , b ) 24 , c ) 26 , d ) 25 , e ) 22
Rationale: "4 multiples are 4 , 8,12 , - - - - - - - - - , 92,96 it should be mentioned whether 1 and 99 are inclusive . the answer is ( 96 - 4 ) / 4 + 1 = 24 answer is b"
Answer: b
Problem: patrick purchased 80 pencils and sold them at a loss equal to the selling price of 30 pencils . the cost of 80 pencils is how many times the selling price of 80 pencils ?
Options: a ) 0.75 , b ) 0.8 , c ) 1.375 , d ) 1.4 , e ) 1.85
Rationale: say the cost price of 80 pencils was $ 80 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 80 - 80 p = 30 p - - > p = 8 / 11 . ( cost price ) / ( selling price ) = 1 / ( 8 / 11 ) = 11 / 8 = 1.375 . answer : c .
Answer: c
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 23.5 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 70 % , b ) 60 % , c ) 30 % , d ) 10 % , e ) 20 %
Rationale: "explanation : let c . p . be rs . 100 . then , s . p . = rs . 123.50 let marked price be rs . x . then , 95 / 100 x = 123.50 x = 12350 / 95 = rs . 130 now , s . p . = rs . 130 , c . p . = rs . 100 profit % = 30 % . answer c"
Answer: c
Problem: the hiker walking at a constant rate of 7 miles per hour is passed by a cyclist traveling in the same direction along the same path at 28 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "for the 5 minutes the cyclist continues to overtake the hiker , she is going at 21 miles per hour faster than the hiker . once the cyclist stops , the hiker is going at 7 miles per hour while the cyclist is at rest so the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds . 21 / 7 * 5 or 15 minutes answer is ( b )"
Answer: b
Problem: find the area of a parallelogram with base 18 cm and height 10 cm ?
Options: a ) 281 , b ) 284 , c ) 288 , d ) 255 , e ) 180
Rationale: "area of a parallelogram = base * height = 18 * 10 = 180 cm 2 answer : e"
Answer: e
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 24 cm and breadth 16 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 77.14 cm , b ) 47.14 cm , c ) 84.92 cm , d ) 94.94 cm , e ) 31.42 cm
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 24 + 16 ) = 80 cm parameter of the square = 80 cm i . e . 4 a = 80 a = 20 diameter of the semicircle = 20 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 20 ) = 1 / 2 ( 22 / 7 ) ( 20 ) = 440 / 14 = 31.42 cm to two decimal places answer : e"
Answer: e
Problem: a man gains 20 % by selling an article for a certain price . if the sells it at double the price , the percentage of profit will be ?
Options: a ) 76 % . , b ) 66 % . , c ) 89 % . , d ) 140 % . , e ) 91 % .
Rationale: "let c . p . = rs . x . then , s . p . = rs . ( 12 % of x ) = rs . 6 x / 5 new s . p . = 2 * 6 x / 5 = rs . 12 x / 5 profit = 12 x / 5 - x = rs . 7 x / 5 profit = 7 x / 5 * 1 / x * 100 = 140 % . answer : d"
Answer: d
Problem: mars travels around the sun at a speed of approximately 15 miles per second . the approximate speed is how many miles per hour ?
Options: a ) 48,000 , b ) 51,000 , c ) 54,000 , d ) 57,000 , e ) 60,000
Rationale: 15 * 3600 = 54,000 the answer is c .
Answer: c
Problem: acme ’ s manufacturing costs for sets of horseshoes include a $ 12450 initial outlay , and $ 20.75 per set . they can sell the sets $ 50 . if profit is revenue from sales minus manufacturing costs , and the company producessells 950 sets of horseshoes , what was their profit ?
Options: a ) $ 15300 , b ) $ 14300 , c ) $ 15337.50 , d ) $ 16300 , e ) $ 15800
Rationale: total manufacturing cost = 12,450 + 950 * 20.75 = 32162.5 total selling cost = 950 * 50 = 47500 profit = 47500 - 32162.50 = 15337.50 answer : c
Answer: c
Problem: the average of 9 numbers is 104 . average of the first 5 of them is 99 and that of the last 5 is 100 . find the 5 th number ?
Options: a ) 46 , b ) 59 , c ) 63 , d ) 75 , e ) 88
Rationale: sum of all the 9 numbers = 9 * 104 = 936 sum of the first 5 of them = 5 * 99 = 495 sum of the last 5 of them = 5 * 100 = 500 so , the 5 th number = 495 + 500 - 936 = 59 . answer : b
Answer: b
Problem: the cash realised on selling a 14 % stock is rs . 101.25 , brokerage being 1 / 4 % is
Options: a ) 123 , b ) 106 , c ) 100 , d ) 101 , e ) 240
Rationale: "explanation : cash realised = rs . ( 101.25 - 0.25 ) = rs . 101 . answer : d"
Answer: d
Problem: in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 140 m . then , a wins by :
Options: a ) 60 m , b ) 20 m , c ) 43 m , d ) 20 m , e ) 23 m
Rationale: "to reach the winning post a will have to cover a distance of ( 500 - 140 ) m , i . e . , 360 m . while a covers 3 m , b covers 4 m . while a covers 360 m , b covers 4 x 360 m = 480 m . 3 thus , when a reaches the winning post , b covers 480 m and therefore remains 20 m behind . a wins by 20 m . answer : d"
Answer: d
Problem: tom read a book containing 100 pages by reading the same number of pages each day . if he would have finished the book 10 days earlier by reading 30 pages a day more , how many days did tom spend reading the book ?
Options: a ) 7 , b ) 7.68 , c ) 8 , d ) 9 , e ) 10
Rationale: actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 100 ( we want to find the days , sop = 100 / d ) 2 ) ( p + 30 ) ( d - 10 ) = 100 = > pd - 10 p + 30 d - 300 = 100 as the 1 ) stated u can put 1 ) into 2 ) = > 100 - 10 p + 30 d - 300 = 100 = > 30 d - 10 p = 100 put the bold one into it = > 30 d - 10 ( 100 / d ) = 100 the we get the final equation 30 d ^ 2 - 1000 = 100 d ( divide 16 ) = > d ^ 2 - 5 d - 150 = 0 ( d - 15 ) ( d + 10 ) = 0 so d = 7.68 days . ans : ( b )
Answer: b
Problem: the sum of the squares of three numbers is 241 , while the sum of their products taken two at a time is 100 . their sum is :
Options: a ) 20 , b ) 11 , c ) 21 , d ) 41 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 241 xy + yz + zx = 100 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 241 + ( 2 * 100 ) ( x + y + z ) ^ 2 = 441 so x + y + z = 21 answer : c"
Answer: c
Problem: the speed of a boat in still water is 18 km / hr and the rate of current is 4 km / hr . the distance travelled downstream in 14 minutes is
Options: a ) 1.6 km , b ) 2 km , c ) 5.1 km , d ) 4 km , e ) none of these
Rationale: "explanation : speed downstreams = ( 18 + 4 ) kmph = 22 kmph . distance travelled = ( 22 x 14 / 60 ) km = 5.1 km option c"
Answer: c
Problem: the present worth of rs . 169 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 150.50 , b ) rs . 154.75 , c ) rs . 156.25 , d ) rs . 158 , e ) none
Rationale: "solution present worth = rs . [ 169 / ( 1 + 4 / 100 ) ² ] = rs . ( 169 x 25 / 26 x 25 / 26 ) = rs . 156.25 answer c"
Answer: c
Problem: how many positive integers less than 350 are there such that they are multiples of 17 or multiples of 18 ?
Options: a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40
Rationale: "350 / 17 = 20 ( plus remainder ) so there are 20 multiples of 17 350 / 18 = 19 ( plus remainder ) so there are 19 multiples of 18 we need to subtract 1 because 17 * 18 is a multiple of both so it was counted twice . the total is 20 + 19 - 1 = 38 the answer is c ."
Answer: c
Problem: a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 8 % of bananas were rotten . find the percentage of fruits in good condition .
Options: a ) 87.8 % , b ) 87.9 % , c ) 37.8 % , d ) 87.7 % , e ) 22.8 %
Rationale: "otal number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 8 % of 400 = 8 / 100 × 400 = 3200 / 100 = 32 therefore , total number of rotten fruits = 90 + 32 = 122 therefore number of fruits in good condition = 1000 - 122 = 878 therefore percentage of fruits in good condition = ( 878 / 1000 × 100 ) % = ( 87800 / 1000 ) % = 87.8 % answer : a"
Answer: a
Problem: reema took a loan of rs 1800 with simple interest for as many years as the rate of interest . if she paid rs . 632 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 5.925 % , b ) 5.253 % , c ) 7 % , d ) 6.52 % , e ) 5.200 %
Rationale: "explanation : let rate = r % then time = r years . = > 1800 ∗ r ∗ r / 100 = 632 = > r 2 = 35.11 = > r = 5.925 % option a"
Answer: a
Problem: 12 points lie on a circle . how many cyclic quadrilaterals can be drawn by using these points ?
Options: a ) 334
b ) 377
c ) 495
d ) 766
e ) 261
Rationale: explanation : for any set of 4 points we get a cyclic quadrilateral . number of ways of choosing 4 points out of 12 points is \ inline { \ color { black } 12 c _ 4 { } } = 495 . therefore , we can draw 495 quadrilaterals answer : c ) 495
Answer: c
Problem: there are 15 members in a family . it takes 180 days for a women to complete the work , however man completes in 120 days . they take 17 days to complete the work if men work on alternate days and women work every third day . if all of them started together on the 1 st day , then how many men are there in the family
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "let the number of men be m and so the number of women = 15 - m out of 17 days , men and women work together on 1,4 , 7,10 , 13,16 th days ( total of 6 days ) from the start . men work on alternate days , that is 1 , 3,5 , 7,9 , 11,13 , 15,17 th days ( total of 9 days ) . let the total work be 360 units ( lcm of 180 and 120 ) . 1 man does 360 / 120 = 3 units per day 1 woman does 360 / 180 = 2 units per day based on above facts , total work by men + women in these 17 days = 360 units m * 9 * 3 + ( 15 - m ) * 6 * 2 = 360 , 27 m + 180 - 12 m = 360 , solving m = 12 . num of men = 12 answer : d"
Answer: d
Problem: there is a train and car . the ratio between the speed of a train & a car is 16 : 15 respectively . also , a bus covered a distance of 480 km in 8 hours . the speed of the bus is 3 / 4 th of the speed of the train . how many kilometers will the car cover in 4 hours ?
Options: a ) 200 , b ) 250 , c ) 300 , d ) 350 , e ) 400
Rationale: "the speed of the bus is 480 / 8 = 60 km / hr the speed of the train is ( 60 * 4 ) / 3 = 80 km / hr the speed of the car is 80 / 16 * 15 = 75 km / hr the distance covered by the car in 4 hours is 75 × 4 = 300 km the answer is c ."
Answer: c
Problem: farm tax is levied on the 75 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 0.2083 % , e ) 16.667 %
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 75 ) = 16.667 % the correct answer is ( e ) ."
Answer: e
Problem: what is x if 2 x - y = 14 and y = 2 ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: substitute y by 2 in 2 x - y = 14 2 x - 2 = 14 2 x = 16 if we substitute x by 8 , we have 2 ( 8 ) = 16 . hence x = 8 correct answer b
Answer: b
Problem: the radius of the circle is reduced from 5 cm to 4 cm then the % change of area .
Options: a ) 36 %
b ) 37 %
c ) 35 %
d ) 38 %
e ) 39 %
Rationale: for 5 cm - > pi * r ^ 2 - - > 3.14 * 5 ^ 2 - > 78.539 for 4 cm - > pi * r ^ 2 - - > 3.14 * 4 ^ 2 - > 50.265 % change - > ( 1 - 50.265 / 78.539 ) * 100 = 36 ie 36 % answer : a
Answer: a
Problem: in what time will a train 200 m long cross an electric pole , it its speed be 216 km / hr ?
Options: a ) 2.5 sec , b ) 2.8 sec , c ) 8.5 sec , d ) 3.3 sec , e ) 4.5 sec
Rationale: "speed = 216 * 5 / 18 = 60 m / sec time taken = 200 / 60 = 3.3 sec . answer : d"
Answer: d
Problem: if t = 1 / ( 1 * 2 ) + 1 / ( 2 * 3 ) + 1 / ( 3 * 4 ) + 1 / ( 4 * 5 ) + . . . . . . . . . 1 / [ n ( n + 1 ) ] , for some positive integer n , what is the smallest value of n such that t > 097 ?
Options: a ) 29 , b ) 30 , c ) 31 , d ) 32 , e ) 33
Rationale: we can break the t as : ( n + 1 - n ) / n ( n + 1 ) - - - - for n = 1 to n 1 / n - 1 / n + 1 plug value , 1,2 . . n we will get a pattern 1 - 1 / 2 - - - for 1 1 / 2 - 1 / 3 - - for 2 1 / 3 - 1 / 4 - - for 4 now work with options . . for 31 , t = 1 - 1 / 32 = 30 / 31 = 0.968 for 32 , t = 1 - 1 / 33 = 0,9696 for 33 , t = 1 - 1 / 34 = 33 / 34 - 0.97 so e is correct answer
Answer: e
Problem: jack and jill work at a hospital with 6 other workers . for an internal review , 2 of the 8 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 15 , d ) 1 / 28 , e ) 2 / 3
Rationale: "1 / 8 c 2 = 1 / 28 . answer : d ."
Answer: d
Problem: a pupil ' s marks were wrongly entered as 83 instead of 70 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
Options: a ) 18 , b ) 82 , c ) 26 , d ) 27 , e ) 29
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 83 - 70 ) = > x / 2 = 13 = > x = 26 . answer : c"
Answer: c
Problem: calculate the average of all the numbers between 18 and 57 which are divisible by 7 .
Options: a ) 36.9 , b ) 38.5 , c ) 18.5 , d ) 32.5 , e ) 28.5
Rationale: "explanation : numbers divisible by 7 are 21,28 , 35,42 , 49,56 , average = ( 21 + 28 + 35 + 42 + 49 + 56 , ) / 6 = 231 / 6 = 38.5 answer : b"
Answer: b
Problem: what is the square root of 6,561 ?
Options: a ) 18 , b ) 9 , c ) 45 , d ) 62 , e ) 81
Rationale: "a square root of a number is a number times itself equals the original number . ex ) the square root of 81 is 9 because 9 times itself ( 9 ) equals the original number ( 81 ) . 81 * 81 = 6,561 6561 divided by x = 81 x = 81 ( e ) 81"
Answer: e
Problem: how many positive integers less than 100 are neither multiples of 2 or 5 .
Options: a ) a ) 30 , b ) b ) 31 , c ) c ) 40 , d ) d ) 33 , e ) e ) 34
Rationale: "to answer this q we require to know 1 ) multiples of 2 till 100 = 100 / 2 = 50 2 ) multiples of 5 till 100 = 100 / 5 = 20 add the two 50 + 20 = 70 ; subtract common terms that are multiple of both 2 and 5 . . lcm of 2 and 5 = 10 multiples of 10 till 100 = 100 / 10 = 10 so total multiples of 2 and 5 = 70 - 10 = 6 ans = 100 - 60 = 40 c"
Answer: c
Problem: a trained covered x km at 50 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 22 , b ) 99 , c ) 25 , d ) 66 , e ) 887
Rationale: "total time taken = x / 50 + 2 x / 20 hours = 6 x / 50 = 3 x / 25 hours average speed = 3 x / ( 3 x / 25 ) = 25 kmph answer : c"
Answer: c
Problem: two brothers took the gmat exam , the higher score is x and the lower one is y . if the difference between the two scores is 1 / 3 , what is the value of y / x ?
Options: a ) 3 . , b ) 2 . , c ) 1 / 2 . , d ) 1 / 4 , e ) there is n ' t enough data to answer the question .
Rationale: "answer is d : 1 / 4 x - y = ( x + y ) / 3 solving for y / x = 1 / 4"
Answer: d
Problem: a drink vendor has 60 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?
Options: a ) 135 , b ) 137 , c ) 143 , d ) 310 , e ) 380
Rationale: "the number of liters in each can = hcf of 60 , 144 and 368 = 4 liters . number of cans of maaza = 60 / 4 = 15 number of cans of pepsi = 144 / 4 = 36 number of cans of sprite = 368 / 4 = 92 the total number of cans required = 15 + 36 + 92 = 143 cans . answer : c"
Answer: c
Problem: when 1 / 10 % of 4,000 is subtracted from 1 / 10 of 4,000 , the difference is
Options: a ) 50 , b ) 200 , c ) 396 , d ) 398 , e ) 400
Rationale: "1 / 10 % of 4000 = 4 1 / 10 of 4000 = 400 400 - 4 = 396 ans : c"
Answer: c
Problem: if 15 % of 30 % of 50 % of a number is 99 , then what is the number ?
Options: a ) 4000 , b ) 3050 , c ) 4400 , d ) 4500 , e ) none of these
Rationale: let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 99 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 99 = > a = 10 * 20 * 10 * 2 = 4400 . answer : c
Answer: c
Problem: working together , printer a and printer b would finish the task in 24 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 4 pages a minute more than printer a ?
Options: a ) 600 , b ) 480 , c ) 1000 , d ) 1200 , e ) 1500
Rationale: answer : b .
Answer: b
Problem: if a farmer wants to plough a farm field on time , he must plough 100 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 600 , b ) 490 , c ) 720 , d ) 1400 , e ) 1679
Rationale: "let x be the number of days in the initial plan . therefore , the whole field is 100 â ‹ … x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 100 x = 85 ( x + 2 ) + 40 15 x = 210 x = 14 so the farmer planned to have the work done in 6 days , and the area of the farm field is 100 ( 14 ) = 1400 hectares correct answer d"
Answer: d
Problem: in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 330 baseball fans in the town , each of whom is a fan of exactly one of those 3 teams , how many ny mets fans are there in this town ?
Options: a ) 72 , b ) 88 , c ) 95 , d ) 120 , e ) 135
Rationale: the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 330 = 88 the answer is b .
Answer: b
Problem: a retailer sells 5 shirts . he sells first 2 shirts for $ 30 and $ 20 . if the retailer wishes to sell the 5 shirts for an overall average price of over $ 30 , what must be the minimum average price of the remaining 3 shirts ?
Options: a ) $ 28.50 , b ) $ 30.50 , c ) $ 33.33 , d ) $ 40.50 , e ) $ 50.00
Rationale: first 2 shirts are sold for $ 30 and $ 20 = $ 50 . to get average price of $ 30 , total sale should be 5 * $ 30 = $ 150 so remaining 3 shirts to be sold for $ 150 - $ 50 = $ 100 answer should be 100 / 3 = $ 33.33 that is c
Answer: c
Problem: ratio between rahul and deepak is 4 : 3 , after 10 years rahul age will be 26 years . what is deepak present age .
Options: a ) 12 , b ) 15 , c ) 20 , d ) 22 , e ) 24
Rationale: explanation : present age is 4 x and 3 x , = > 4 x + 10 = 26 = > x = 16 so deepak age is = 3 ( 4 ) = 12 option a
Answer: a
Problem: difference of two numbers is 1760 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2640 , 1000 , b ) 3660 , 4400 , c ) 3000 , 4160 , d ) 2490 , 4150 , e ) 4660 , 3000
Rationale: "let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1760 5 * y / 3 – y = 1760 2 * y / 3 = 1760 y = [ ( 1760 * 3 ) / 2 ] = 2640 . one number = 2640 , second number = 5 * y / 3 = 4400 . answer b ."
Answer: b
Problem: if a clock strikes 12 in 33 seconds , it will strike 6 in how many seconds ?
Options: a ) 33 ⁄ 2 , b ) 15 , c ) 12 , d ) 22 , e ) none of these
Rationale: in order to strike 12 , there are 11 intervals of equal time = 33 ⁄ 11 = 3 seconds each therefore , to strike 6 it has 5 equal intervals , it requires 5 × 3 = 15 sec . answer b
Answer: b
Problem: car a runs at the speed of 50 km / hr & reaches its destination in 8 hr . car b runs at the speed of 25 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 4 : 1 , b ) 11 : 8 , c ) 13 : 7 , d ) 15 : 7 , e ) 16 : 9
Rationale: "sol . distance travelled by car a = 50 × 8 = 400 km distance travelled by car b = 25 × 4 = 100 km ratio = 400 / 100 = 4 : 1 answer : a"
Answer: a
Problem: from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 25 percent . the enrollment on january 1 , 1993 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ?
Options: a ) 36 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "1.25 x = 45 - - > 5 / 4 * x = 45 - - > x = 45 * 4 / 5 = 180 / 5 = 36 . answer : a ."
Answer: a
Problem: if 3 people a , b , c can do a work simultaneously in 6 days . a and b can do work in 10 days . b and c can do work in 15 days . c and a can do the same work in 20 days . in how many days that a can complete the same work alone ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 24 , e ) 19
Rationale: a + b + c = 1 / 6 ( one day work ) a + b = 1 / 10 ; b + c = 1 / 15 ; c + a + 1 / 20 b = 1 / 15 - c ; c = 1 / 20 - a ; - - - - - - - - - ( 2 ) substitute equation 2 in a + b = 1 / 10 a = 1 / 10 - b ; a = 1 / 10 - 1 / 15 + c ; a = 1 / 10 - 1 / 15 + 1 / 20 - a ; 2 a = 1 / 10 - 1 / 15 + 1 / 20 ; a = 1 / 24 ( one day work ) that is the no of days that a can work alone is 24 days the option d is answer
Answer: d
Problem: a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 170 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 30 , b ) 33 , c ) 55 , d ) 77 , e ) 88
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 170 = > . 1 x + 3 / 4 x = 170 = > x = 200 200 - 170 = pure gala = 30 . answer a"
Answer: a
Problem: a man is 46 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 44 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 16 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 46 ) + 2 = 2 ( x + 2 ) x + 48 = 2 x + 4 x = 44 . answer : a"
Answer: a
Problem: pipe a that can fill a tank in an hour and pipe b that can fill the tank in half an hour are opened simultaneously when the tank is empty . pipe b is shut 10 minutes before the tank overflows . when will the tank overflow ?
Options: a ) 37 mins , b ) 35 mins , c ) 40 mins , d ) 32 mins , e ) 36 mins
Rationale: the last 10 minutes only pipe a was open . since it needs 1 hour to fill the tank , then in 10 minutes it fills 1 / 5 th of the tank , thus 5 / 6 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 2 = 3 tanks / hour , therefore to fill 5 / 6 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 5 / 6 ) / 3 = 5 / 18 hours = 27 minutes . total time = 10 + 27 = 37 minutes . answer : a .
Answer: a
Problem: what is the maximum value of vx - yz . if the value of v , x , y , z have to be chosen from the set a where a ( - 3 , - 2 , - 1 , 01 , 23 )
Options: a ) 15 , b ) 66 , c ) 25 , d ) 88 , e ) 17
Rationale: explanation : to maximize the value of vx - yz , we make yz negative and vx as maximum as possible using given value . vx − yz = ( − 3 ) 2 − ( − 3 × 2 ) vx − yz = ( − 3 ) 2 − ( − 3 × 2 ) = 15 answer : a
Answer: a
Problem: x and y are two towns . ganesh covers the distance from x to y at an average speed of 54 km / hr . however , he covers the distance from y to x at an average speed of 36 km / hr . his average speed during the whole journey in km / hr . is :
Options: a ) 34 , b ) 43.2 , c ) 40 , d ) 38 , e ) 29
Rationale: "solution : average speed = 2 xy / x + y = 2 * 54 * 36 / 54 + 36 = 43.2 answer : b"
Answer: b
Problem: p runs 20 % faster than q so p gives q a 50 meter head start . if the race ends in a tie , how far ( in meters ) did p run in the race ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 450
Rationale: let d be the race distance that p ran . let t be the time it took to complete the race . let v be q ' s speed . t = d / 1.2 v = ( d - 50 ) / v d = 1.2 d - 60 0.2 d = 60 d = 300 meters . the answer is b .
Answer: b
Problem: suppose 10 monkeys take 10 minutes to eat 10 bananas . how many monkeys would it take to eat 70 bananas in 70 minutes ?
Options: a ) 9 , b ) 17 , c ) 11 , d ) 10 , e ) 13
Rationale: "one monkey takes 10 min to eat 1 banana , so in 70 mins 1 monkey will eat 7 bananas , so for 70 bananas in 70 min we need 70 / 7 = 10 monkeys answer : d"
Answer: d
Problem: a man walks at a rate of 10 mph . after every ten miles , he rests for 5 minutes . how much time does he take to walk 50 miles ?
Options: a ) 300 , b ) 318 , c ) 320 , d ) 324 , e ) 330
Rationale: to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 5 = 20 minutes . total time = 300 + 20 = 320 minutes . answer : c .
Answer: c
Problem: on a map , 4.5 inches represent 45 miles . how many miles approximately is the distance if you measured 254 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 1000 , b ) 1100 , c ) 1200 , d ) 1250 , e ) 1300
Rationale: "1 inch = 2.54 cm 4.5 inch = 2.54 * 4.5 cm 11.43 cm = 45 miles 254 cms = 45 / 11.43 * 254 = 1000 miles answer : a"
Answer: a
Problem: what is the total number of positive integers that are less than 400 and that have no positive factor in common with 400 other than 1 ?
Options: a ) 100 , b ) 120 , c ) 150 , d ) 160 , e ) 180
Rationale: "since 400 = 2 ^ 4 * 5 ^ 2 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 200 odd numbers from 1 to 400 . we then need to eliminate the 40 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 395 . there are a total of 200 - 40 = 160 such numbers between 1 and 400 . the answer is d ."
Answer: d
Problem: john bought 9.25 m of cloth for $ 416.25 . find the cost price per metre .
Options: a ) 46 , b ) 47 , c ) 45 , d ) 56 , e ) 54
Rationale: "cloth bought by john = 9.25 m cost of 9.25 m = $ 416.25 cost per metre = 416.25 ÷ 9.25 the cost of the cloth per metre = $ 45 answers : c"
Answer: c
Problem: if p is a prime number greater than 3 , find the remainder when p ^ 2 + 12 is divided by 12 .
Options: a ) 6 , b ) 1 , c ) 0 , d ) 8 , e ) 7
Rationale: "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 13 = 36 n ^ 2 + 12 n + 1 + 12 = 36 n ^ 2 + 12 n + 12 + 1 if p = 6 n - 1 , then p ^ 2 + 13 = 36 n ^ 2 - 12 n + 1 + 12 = 36 n ^ 2 - 12 n + 12 + 1 when divided by 12 , it must leave a remainder of 1 . the answer is b ."
Answer: b
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 15 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 432 , b ) 444 , c ) 2881 , d ) 287 , e ) 221
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 15 + 21 = 36 t = 12 d = 36 * 12 = 432 answer : a"
Answer: a
Problem: what is the rate percent when the simple interest on rs . 910 amount to rs . 260 in 4 years ?
Options: a ) 7.14 , b ) 6.14 , c ) 5.14 , d ) 3.14 , e ) 2.14
Rationale: "260 = ( 910 * 4 * r ) / 100 r = 7.14 % answer : a"
Answer: a
Problem: in 1979 approximately 1 / 3 of the 37.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 4 the number that used kennedy airport and 3 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
Options: a ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 3.1 , e ) 1.03
Rationale: "number of passengers using kennedy airport = 37 / 3 = ~ 12.43 passengers using miami airport = 12.43 / 4 = ~ 3.1 passengers using logan airport = 3.1 / 3 = ~ 1.03 so e"
Answer: e
Problem: if $ 792 are divided between worker a and worker b in the ratio 5 : 6 , what is the share that worker b will get ?
Options: a ) 54.54 % , b ) 55.55 % , c ) 56.56 % , d ) 57.57 % , e ) 58.58 %
Rationale: "worker b will get 6 / 11 = 54.54 % the answer is a ."
Answer: a
Problem: evaluate : 1182 - 12 * 3 * 2 = ?
Options: a ) 674 , b ) 574 , c ) 174 , d ) 274 , e ) 374
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 1182 - 12 * 3 * 2 = 1182 - 8 = 174 correct answer c"
Answer: c
Problem: if a ( a - 4 ) = 5 and b ( b - 4 ) = 5 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 4 , c ) 4 , d ) 9 , e ) 48
Rationale: "i . e . if a = - 1 then b = 5 or if a = 5 then b = - 1 but in each case a + b = - 1 + 5 = 4 answer : option c"
Answer: c
Problem: in a software company 4 / 10 of people know c + + , 2 / 4 of them know java , 2 / 8 of them know neither , find the total possibility to know c + + ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: assume 100 persons in a company person knows c + + = 4 / 10 = 100 * 4 / 100 = 20 persons person knows java = 2 / 4 = 100 * 2 / 4 = 50 persons neither = 2 / 8 = 100 * 2 / 8 = 25 persons according to our assumption 100 person = 20 + 50 + 25 = 95 person covered ( 5 remaining ) so , total possibility = 20 person ( c + + ) + 5 ( remaining ) = 25 persons which is 25 / 100 = 1 / 4 answer : a
Answer: a
Problem: the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 10 years . find the average age of the women ?
Options: a ) 87 , b ) 98 , c ) 30 , d ) 28 , e ) 23
Rationale: "20 + 10 + 8 * 2 = 46 / 2 = 23 answer : e"
Answer: e
Problem: the number 0.8 is how much greater than 1 / 2 ?
Options: a ) ½ , b ) 3 / 10 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500
Rationale: "let x be the difference then . 8 - 1 / 2 = x 8 / 10 - 1 / 2 = x x = 3 / 10 ans b"
Answer: b
Problem: two trains running in opposite directions cross a man standing on the platform in 20 seconds and 18 seconds respectively and they cross each other in 19 seconds . the ratio of their speeds is :
Options: a ) 1 : 1 , b ) 3 : 2 , c ) 3 : 8 , d ) 3 : 25 , e ) 3 : 4
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 20 x meters , and length of the second train = 18 y meters . ( 20 x + 15 y ) / ( x + y ) = 19 = = > 20 x + 18 y = 19 x + 19 y = = > x = y = = > x / y = 1 / 1 answer : option a"
Answer: a
Problem: cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 68 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 0.00 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.80
Rationale: 0.85 * { original price } = $ 68 - - > { original price } = $ 80 . { final price } = $ 68 * 1.25 = $ 85 . the difference = $ 85 - $ 85 = $ 5 . answer : d .
Answer: d
Problem: the cost per pound of milk powder and coffee were the same in june . in july , the price of coffee shot up by 200 % and that of milk powder dropped by 60 % . if in july , a mixture containing equal quantities of milk powder and coffee costs $ 5.10 for 3 lbs , how much did a pound of milk powder cost in july ?
Options: a ) $ 4 , b ) $ 0.4 , c ) $ 1 , d ) $ 3 , e ) $ 1.65
Rationale: "lets assume price of coffee in june = 100 x price of tea in june = 100 x price of coffee in july = 300 x ( because of 200 % increase in price ) price of tea in july = 40 x ( because of 60 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of tea in july will be = 450 x + 60 x = 510 x as per question 510 x = 5.10 $ x = 0.01 s so the price of tea in july = 40 x = 40 x 0.01 = 0.4 $ / pound answer b"
Answer: b
Problem: each of the 55 points is placed either inside or on the surface of a perfect sphere . if 60 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ?
Options: a ) 7
b ) 11
c ) 13
d ) 16
e ) 38
Rationale: maximum number of points on the surface is 60 % * 55 = 33 now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 33 points , so at best we can form 16 pairs ( 32 ) . so , answer is ( d )
Answer: d