regisss/math_qa huggingface dataset:
Problem: roses can be purchased individually for $ 7.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?
Options: a ) 156 , b ) 162 , c ) 316 , d ) 324 , e ) 325
Rationale: "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 7.3 = ~ 4 roses for that amount . total = 312 + 4 = 316 . answer : c ."
Answer: c
Problem: what is the equation of a circle of radius 5 units centered at ( 3 , 2 ) ?
Options: a ) x ^ 2 + y ^ 2 + 6 x – 4 y = 23
b ) x ^ 2 + y ^ 2 - 6 x + 4 y = 23
c ) x ^ 2 + y ^ 2 + 6 x + 4 y = 23
d ) x ^ 2 + y ^ 2 - 6 x – 4 y = - 12
e ) x ^ 2 + y ^ 2 - 6 x – 4 y = 12
Rationale: the equation of a circle with center at ( a , b ) and radius r is ( x - a ) ^ 2 + ( y - b ) ^ 2 = r ^ 2 = > answer = ( x - 3 ) ^ 2 + ( y - 2 ) ^ 2 = 5 ^ 2 solving , , we get the equation in answer choice e .
Answer: e
Problem: if the diameter of circle r is 20 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 14 % , e ) 4 %
Rationale: "let diameter of circle r , dr = 20 and diameter of circle s , ds = 100 radius of circle r , rr = 10 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 10 / 50 ) ^ 2 = ( 2 / 10 ) ^ 2 = 4 % answer : e"
Answer: e
Problem: walking with 4 / 5 of my usual speed , i arrive at the bus stop 9 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Rationale: "let t = usual time = distance / usual speed t + 9 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 36 the answer is d ."
Answer: d
Problem: what will be the length of the mini - train , if it crosses a pole in 3 sec while travelling at a speed of 75 kmph ?
Options: a ) 60 m , b ) 65 m , c ) 63.5 m , d ) 64 m , e ) 62.5 m
Rationale: explanation : d = 75 * 5 / 18 * 3 = 62.5 m answer : option e
Answer: e
Problem: if 4 x = 8 y = 12 z , then what is a possible sum of positive integers x , y , and z ?
Options: a ) 52 , b ) 58 , c ) 84 , d ) 122 , e ) 180
Rationale: "4 x = 8 y = 12 z x = 2 y = 3 z 3 ( 2 * 3 ) = 2 ( 3 * 1 ) = 3 ( 1 * 2 ) addition = 18 + 6 + 6 = 30 answer would be multiple of 30 which is 180 answer : e"
Answer: e
Problem: find a two digit number , given that the sum of the digits is 12 and the difference of the digits is 6 . ?
Options: a ) 41 , b ) 46 , c ) 42 , d ) 46 , e ) 47
Rationale: "using elimination method find which of the options fit the description of the number . . . from the option only 41 meets this description sum of digits - - - 4 + 1 = 5 difference of digits - - - 4 - 1 = 3 answer a ."
Answer: a
Problem: it takes joey the postman 1 hours to run a 3 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 6 mile / hour , what is the speed with which joey returns ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 18
Rationale: "let his speed for one half of the journey be 3 miles an hour let the other half be x miles an hour now , avg speed = 6 mile an hour 2 * 3 * x / 3 + x = 6 6 x = 6 x + 18 = > x = 18 e"
Answer: e
Problem: 2056 x 987 = ?
Options: a ) 1936372 , b ) 2029272 , c ) 1896172 , d ) 1923472 , e ) none of them
Rationale: "= 2056 x 987 = 2056 x ( 1000 - 13 ) = 2056 x 1000 - 2056 x 13 = 2056000 - 26728 = 2029272 answer is b"
Answer: b
Problem: a rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn . the area of the lawn is 2109 sq . m . what is the width of the road ?
Options: a ) 5 m , b ) 4 m , c ) 2 m , d ) 3 m , e ) 6 m
Rationale: "area of the park = 60 * 40 = 2400 m ^ 2 given area of the lawn = 2109 m ^ 2 total area of the cross roads = 2400 - 2109 = 291 m ^ 2 assume that the width of the cross road = x = area of road 1 + road 2 - common area cross road = 60 x + 40 x - x ^ 2 total area of cross road = 60 x + 40 x - x ^ 2 = 291 m ^ 2 ( x - 97 ) ( x - 3 ) = 0 x = 3 answer d"
Answer: d
Problem: a train is moving at 6 / 7 of its usual speed . the train is 30 minutes too late . what is the usual time for the train to complete the journey ?
Options: a ) 1 hour , b ) 30 minutes , c ) 3 hours , d ) 2 hours 30 min , e ) 2 hours
Rationale: "new time = d / ( 6 v / 7 ) = 7 / 6 * usual time 30 minutes represents 1 / 6 of the usual time . the usual time is 3 hours . the answer is c ."
Answer: c
Problem: we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 530 . how many green hats did we buy ?
Options: a ) a ) 36 , b ) b ) 20 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44
Rationale: let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 530 . 6 ( 85 - g ) + 7 g = 530 . 510 - 6 g + 7 g = 530 . g = 530 - 510 = 20 . the answer is b .
Answer: b
Problem: a volunteer organization is recruiting new members . in the fall they manage to increase their number by 5 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ?
Options: a ) 16.16 % , b ) 15.15 % , c ) 14.95 % , d ) 13.33 % , e ) 12.52 %
Rationale: "( 100 % + 5 % ) * ( 100 % - 19 % ) = 1.05 * . 81 = 0.8505 . 1 - 0.8505 = 14.95 % lost = - 14.95 % the answer is c the organization has lost 14.95 % of its total volunteers from fall to spring ."
Answer: c
Problem: two cars are driving toward each other . the first car is traveling at a speed of 90 km / h , which is 50 % faster than the second car ' s speed . if the distance between the cars is 975 km , how many hours will it take until the two cars meet ?
Options: a ) 6 , b ) 6.5 , c ) 7 , d ) 7.5 , e ) 8
Rationale: "the speed of the first car is 90 km / h . the speed of the second car is 90 / 1.5 = 60 km / h . the two cars complete a total of 150 km each hour . the time it takes the cars to meet is 975 / 150 = 6.5 hours . the answer is b ."
Answer: b
Problem: find the annual income derived by investing $ 6800 in 40 % stock at 136 .
Options: a ) 550 , b ) 2000 , c ) 250 , d ) 3000 , e ) 400
Rationale: "by investing $ 136 , income obtained = $ 40 . by investing $ 6800 , income obtained = $ [ ( 40 / 136 ) * 6800 ] = $ 2000 . answer b ."
Answer: b
Problem: in 1982 and 1983 , company b ’ s operating expenses were $ 12.0 million and $ 14.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 16 2 / 3 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 %
Rationale: "profit in 1982 = 15.6 - 12.0 = 3.6 profit in 1983 = 18.8 - 14.0 = 4.8 increase in profit = 4.8 - 3.6 = 1.2 percentage increase 12 * 100 / 36 = 33.33 ; answer : d"
Answer: d
Problem: what is the difference between local value & face value of 7 in the numeral 65793 ?
Options: a ) 693 , b ) 656 , c ) 691 , d ) 9890 , e ) 10000
Rationale: ( local value of 7 ) - ( face value of 7 ) = ( 700 - 7 ) = 693 a
Answer: a
Problem: mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 14 miles , how many miles was mike ' s ride ?
Options: a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 14 ) = $ 11 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 11 0.25 * x = 8.5 x = 34 miles the answer is d .
Answer: d
Problem: at 1 : 00 pm , a truck left city p and headed toward city q at a constant speed of 35 km / h . one hour later , a car left city q and headed toward city p along the same road at a constant speed of 40 km / h . if the distance between city p and city q is 335 km , at what time will the truck and the car meet each other ?
Options: a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 30 , e ) 7 : 00
Rationale: "at 2 : 00 pm , the truck and the car are 300 km apart . the truck and the car complete a distance of 75 km each hour . the time it takes to meet is 300 / 75 = 4 hours . they will meet at 6 : 00 pm . the answer is c ."
Answer: c
Problem: a license plate in the country kerrania consists of 4 digits followed by two letters . the letters a , b , and c are used only by government vehicles while the letters d through z are used by non - government vehicles . kerrania ' s intelligence agency has recently captured a message from the country gonzalia indicating that an electronic transmitter has been installed in a kerrania government vehicle with a license plate starting with 79 . if it takes the police 10 minutes to inspect each vehicle , what is the probability that the police will find the transmitter within 3 hours ?
Options: a ) 18 / 79 , b ) 1 / 6 , c ) 1 / 25 , d ) 1 / 50 , e ) 1 / 900
Rationale: if it takes 10 minutes to inspect one vehicle , the # of vehicles that can be inspected in 3 hours ( 180 minutes ) = 180 / 10 = 18 . hence , for calculating the probability that the police will find the transmitter within three hours , the favorable cases = 18 . now , we need to figure out the total # of cases . the total # of cases = total # of such cars possible . the details given about the car is that it starts with 79 , which leaves 2 more digits , both of which can be filled by all 10 numbers ( 0 - 9 ) . in addition , we have 3 letters , each of which can be filled by any from the set { a , b , c } . hence the total # of such cars possible = 10 * 10 * 3 * 3 = 900 so , the probability that the police will find the transmitter within three hours = 18 / 900 = 1 / 50 . option d
Answer: d
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 61 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: "the total number of books is 75 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 61 books , thus the number of un - returned books is 75 - 61 = 14 books . 0.35 x = 14 x = 40 the answer is d ."
Answer: d
Problem: one - sixth of the light switches produced by a certain factory are defective . 4 - fifths of the defective switches are rejected and 1 / 15 of the non defective switches are rejected by mistake . if all the switches not rejected are sold , what percent of the switches sold by the factory are defective ?
Options: a ) 1.8 % , b ) 2.9 % , c ) 4.1 % , d ) 5.6 % , e ) 6.4 %
Rationale: 1 / 6 of the switches are defective . the defective switches that are not rejected are 1 / 5 * 1 / 6 = 1 / 30 = 3 / 90 of all switches . the non defective switches that are sold are 5 / 6 * 14 / 15 = 70 / 90 of all switches . the percent of switches sold that are defective is 3 / 73 which is about 4.1 % . the answer is c .
Answer: c
Problem: a man buys a cycle for rs . 1600 and sells it at a loss of 12 % . what is the selling price of the cycle ?
Options: a ) 1410 , b ) 1420 , c ) 1430 , d ) 1408 , e ) 1540
Rationale: s . p . = 88 % of rs . 1600 = 88 / 100 x 1600 = rs . 1408 answer : d
Answer: d
Problem: at milk factory , each employee working the second shift produced 2 / 3 as many widgets as each employee working the first shift . if the first shift has 3 / 4 as many employees , what fraction of the total widgets did the second shift produce ?
Options: a ) 8 / 17 , b ) 1 / 2 , c ) 8 / 9 , d ) 9 / 8 , e ) 17 / 8
Rationale: at milk factory , let the first shift have 3 employee and each produce 3 widgets , so the total number of widgets produced by the first shift is 3 * 3 = 9 ; then the second shift would have 4 employees and each second shift employee would produce 3 * 2 / 3 = 2 widgets , so the total number of widgets produced by the second shift employees would be 4 * 2 = 8 ; the ratio of the second shift production to the total is 8 / ( 9 + 8 ) = 8 / 17 . answer : a .
Answer: a
Problem: the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if steve and david have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?
Options: a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54
Rationale: "if steve and david submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combined ` ` no discount cost ' ' . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ."
Answer: b
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets $ 500 more than d , what is a ' s share ?
Options: a ) $ 1200 , b ) $ 1600 , c ) $ 2000 , d ) $ 2500 , e ) $ 3000
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 a ' s share = 5 x = 5 * $ 500 = $ 2500 the answer is d ."
Answer: d
Problem: when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 7 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?
Options: a ) 3 / 10 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5
Rationale: say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 7 ) ( 4 + 4 x ) or , x = 2 / 5 answer b
Answer: b
Problem: a , b and c have rs . 500 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) 50 , b ) 88 , c ) 77 , d ) 66 , e ) 51
Rationale: "a + b + c = 500 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 500 - - - - - - - - - - - - - - - - c = 50 answer : a"
Answer: a
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 18 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 277 , c ) 187 , d ) 180 , e ) 271
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 18 sec = 18 * 10 = 180 m . the length of the faster train = 180 m . answer : d"
Answer: d
Problem: matt gets a $ 1,000 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 550 , how many sales has matt made ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1000 new average = ( xy + 1000 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1000 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1000 ) = ( xy + x + 150 y + 150 ) i . e . ( 850 ) = ( x + 150 y ) new commission = 550 = 150 + x i . e . x = 400 i . e . y = 3 new sales = y + 1 = 4 answer : option b"
Answer: b
Problem: a man invested rs . 14400 in rs . 100 shares of a company at 20 % premium . if his company declares 5 % dividend at the end of the year , then how much does he get ?
Options: a ) 234 , b ) 600 , c ) 388 , d ) 278 , e ) 129
Rationale: explanation : number of shares = = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = = rs . 600 answer : b ) rs . 600
Answer: b
Problem: the distance between two cities a and b is 1140 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 09 am , b ) 07 am , c ) 11 am , d ) 05 pm , e ) 03 pm
Rationale: "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 1140 . therefore , 60 x + 75 ( x - 1 ) = 1140 . = > x = 9 . so , they meet at ( 8 + 9 ) i . e , 5 pm answer : d"
Answer: d
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 15 % , then the cost price of the article is :
Options: a ) 500 , b ) 334 , c ) 555 , d ) 536 , e ) 5598
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 115 = rs . 536 answer : option d"
Answer: d
Problem: pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 7 : 00 am and pipe b at 8 : 00 am , at what time will the pool be full ?
Options: a ) 16 : 00 , b ) 18 : 00 , c ) 19 : 00 , d ) 20 : 00 , e ) 17 : 00
Rationale: "pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 7 : 00 a . m and pipe b at 8 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 8 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 7 : 00 a . m , pool is full at 17 : 00 hrs answer : e"
Answer: e
Problem: selling an kite for rs . 30 , a shop keeper gains 35 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?
Options: a ) 8 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 21.5 %
Rationale: "explanation : marked price = rs . 30 c . p . = 100 / 135 * 30 = rs . 22.22 sale price = 90 % of rs . 30 = rs . 27 required gain % = 4.77 / 22.22 * 100 = 21.5 % . answer : e"
Answer: e
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 58 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) s . 59.45 , b ) s . 56.22 , c ) s . 51.219 , d ) s . 59.18 , e ) s . 51.11
Rationale: "explanation : sum = ( 58 * 100 ) / ( 2 * 5 ) = rs . 580 amount = [ 580 * ( 1 + 5 / 100 ) 2 ] = rs . 639.45 c . i . = ( 639.45 - 580 ) = rs . 59.45 answer : a"
Answer: a
Problem: if a = 105 and a ^ 3 = 21 × 25 × 45 × d , what is the value of d ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × d = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x d = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x d = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x d d = 7 ^ 2 = 49 answer d"
Answer: d
Problem: a present value of a machine is $ 40000 . its value depletiation rate is 5 % per annum then find the machine value after 2 years ?
Options: a ) $ 36540 , b ) $ 36100 , c ) $ 29580 , d ) $ 31256 , e ) $ 41250
Rationale: "p = $ 40000 r = 5 % t = 2 years machine value after 3 years = p / ( 1 - r / 100 ) ^ t = 40000 * 19 / 20 * 19 / 20 * 19 / 20 = $ 36100 answer is b"
Answer: b
Problem: find the compound ratio of ( 3 : 4 ) , ( 4 : 5 ) and ( 1 : 2 ) is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 10 , d ) 4 : 10 , e ) 3 : 2
Rationale: "required ratio = 3 / 4 * 4 / 5 * 1 / 2 = 3 / 10 = 3 : 10 answer is c"
Answer: c
Problem: at veridux corporation , there are 218 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 47
Rationale: "well , first let â € ™ s take care of the â € œ totals â €  . the numbers in the â € œ totals â €  row must add up . if 90 are females , the other 218 â € “ 90 = 128 must be males . similarly , the numbers in the â € œ totals â €  column must add up . if 40 are managers , then the other 218 â € “ 40 = 178 must be associates . now , in the â € œ associate â €  row , 135 + e = 178 , which means e = 43 â € ” the other 43 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the â € œ female â €  column : b + 43 = 90 , which means b = 47 . there are fifteen female managers in this company . thus , the answer = 47 ( e ) ."
Answer: e
Problem: find a sum for 1 st 9 prime number ' s ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 34 , e ) 100
Rationale: required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 ) = 100 note : 1 is not a prime number option e
Answer: e
Problem: if d = 1 / ( 2 ^ 3 * 5 ^ 11 ) is expressed as a terminating decimal , how many nonzero digits will d have ?
Options: a ) one , b ) two , c ) three , d ) seven , e ) ten
Rationale: "another way to do it is : we know x ^ a * y ^ a = ( x * y ) ^ a given = 1 / ( 2 ^ 3 * 5 ^ 11 ) = multiply and divide by 2 ^ 8 = 2 ^ 8 / ( 2 ^ 3 * 2 ^ 8 * 5 ^ 11 ) = 2 ^ 8 / 10 ^ 11 = > non zero digits are 256 = > ans c"
Answer: c
Problem: a man is 25 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 11 , b ) 23 , c ) 27 , d ) 22 , e ) 91
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 25 ) years . ( x + 25 ) + 2 = 2 ( x + 2 ) x + 27 = 2 x + 4 = > x = 23 . answer : b"
Answer: b
Problem: calculate the sum of first 89 natural numbers .
Options: a ) 2017 , b ) 2647 , c ) 2147 , d ) 2045 , e ) 4005
Rationale: "solution we know that ( 1 + 2 + 3 + . . . . . + 89 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 89 ) = ( 89 × 90 / 2 ) = 4005 . answer e"
Answer: e
Problem: a jogger running at 10 km / hr along side a railway track is 340 m ahead of the engine of a 120 m long train running at 46 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 76 sec , b ) 67 sec , c ) 98 sec , d ) 46 sec , e ) 23 sec
Rationale: "speed of train relative to jogger = 46 - 10 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 340 + 120 = 460 m . time taken = 460 / 10 = 46 sec . answer : d"
Answer: d
Problem: an amount of rs . 10000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 3 / 4 % , then the amount invested at 11 % was ?
Options: a ) 2377 , b ) 3750 , c ) 2997 , d ) 2677 , e ) 1987
Rationale: let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 10000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 10000 - x ) * 11 * 1 ] / 100 = ( 10000 * 39 / 4 * 1 / 100 ) ( 9 x + 110000 - 11 x ) / 100 = 3900 / 4 = 975 ( 9 x + 110000 - 11 x ) = 97500 x = 6250 sum invested at 9 % = rs . 6250 sum invested at 11 % = rs . ( 10000 - 6250 ) = rs . 3750 . answer : b
Answer: b
Problem: the present population of a town is 300 . 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 ) 330
Rationale: p = 300 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 300 * ( 1 + 10 / 100 ) = 300 * ( 11 / 10 ) = 330 answer is e
Answer: e
Problem: in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 600 m ?
Options: a ) 236 , b ) 127.5 , c ) 267 , d ) 268 , e ) 281
Rationale: "when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 600 m , the number of meters by which a beats c = ( 600 * 212.5 ) / 1000 = 127.5 m answer : b"
Answer: b
Problem: a powder tin has a square base with side 8 cm and height 14 cm . another tin has a circular base with diameter 8 cm and height 14 cm . the difference in their capacities is :
Options: a ) 168 cm ³
b ) 192 cm ³
c ) 228 cm ³
d ) 236 cm ³
e ) none
Rationale: sol . difference in capacities = [ 8 * 8 * 14 - 22 / 7 * 4 * 4 * 14 ] cm ³ = 192 cm ³ answer b
Answer: b
Problem: today david , who is 40 years old , and his daughter , who is 12 years old , celebrate their birthdays . how many years will pass before david ’ s age is twice his daughter ’ s age ?
Options: a ) 22 , b ) 20 , c ) 16 , d ) 18 , e ) 14
Rationale: forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . after x years passes david ’ s age will be ( 40 + x ) years old , and his daughter ’ s age will be ( 12 + x ) years old . since the david ’ s age is twice his daughter ’ s age ( 40 + x ) = 2 * ( 12 + x ) - - - > 40 + x = 24 + 2 x - - - > x = 16 the answer is ( c ) .
Answer: c
Problem: ( 17 ) 3.5 x ( 17 ) ? = 178
Options: a ) 2.29 , b ) 2.75 , c ) 4.25 , d ) 4.5 , e ) none of these
Rationale: "solution let ( 17 ) 3.5 * ( 17 ) x = 178 . then , ( 17 ) 3.5 + x = ( 17 ) 8 . ∴ 3.5 + x = 8 ⇔ x = ( 8 - 3.5 ) ⇔ x = 4.5 answer d"
Answer: d
Problem: earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 120 envelopes
Options: a ) 2 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: "earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envelopes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 120 envelopes they will take 120 / 60 mins . i . e . , 2 mins . answer : a"
Answer: a
Problem: if ( 400 ) ( 7000 ) = ( 28000 ) ( 100 ^ x ) , what is the value of x ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: ( 400 ) ( 7,000 ) = ( 2,800 ) ( 100 ^ x ) = > ( 400 ) ( 7,000 ) / 2,800 = 100 ^ x = > 100 = 100 ^ x = > 100 ^ 1 = 100 ^ x since , base is same so powers will be same too . so , x = 1 answer will be e
Answer: e
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.64 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.40 , b ) $ 3.00 , c ) $ 3.20 , d ) $ 3.60 , e ) $ 4.80
Rationale: "total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.64 therefore , x = $ 2.40 . answer a"
Answer: a
Problem: a number of 41 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?
Options: a ) 13 , b ) 12 , c ) 15 , d ) 16 , e ) 17
Rationale: "to maximize # of boxes we should minimize marbles per box : 12 * 3 + 1 * 5 = 41 - - > 12 + 1 = 13 . answer : a ."
Answer: a
Problem: the sum of the present age of henry and jill is 41 . what is their present ages if 7 years ago henry was twice the age of jill ?
Options: a ) and 25 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these
Rationale: let the age of jill 7 years ago be x , age of henry be 2 x x + 7 + 2 x + 7 = 41 x = 9 present ages will be 16 and 25 answer : a
Answer: a
Problem: set x consists of the integers from 0 to 12 , inclusive , while set y consists of the integers from 6 to 10 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 4 , b ) 10 , c ) 5 , d ) 9 , e ) 8
Rationale: "x = { 0 , 1,2 , 3,4 , 5,6 , 7 , 8 , 9 , 10 , 11 , 12 } y = { 6 , 7 , 8 , 9 , 10 } common elements = { 6 , 7 , 8 , 9 , 10 } = 5 elements answer : option c ."
Answer: c
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 500 more , there would have been a gain of 10 % . what is the cost price ?
Options: a ) 1000 , b ) 2998 , c ) 2500 , d ) 2788 , e ) 2991
Rationale: "90 % 110 % - - - - - - - - 20 % - - - - 500 100 % - - - - ? = > rs . 2500 answer : c"
Answer: c
Problem: what is the area of a square field whose diagonal of length 26 m ?
Options: a ) 287 , b ) 269 , c ) 338 , d ) 200 , e ) 230
Rationale: "d 2 / 2 = ( 26 * 26 ) / 2 = 338 answer : c"
Answer: c
Problem: a book is bought for $ 600 and sold for $ 624 . what is the profit in percentage ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "624 / 600 = 1.04 the answer is b ."
Answer: b
Problem: a store owner estimates that the average price of type a products will increase by 35 % next year and that the price of type b products will increase by 20 % next year . this year , the total amount aid for type a products was $ 3500 and the total price paid for type b products was $ 6300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,755 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 12,285 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.35 * 3500 = 4725 cost of type b products next year = 1.2 * 6300 = 7560 total 4725 + 7560 = 12285 answer : d"
Answer: d
Problem: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 75 , the runs scored by a are ?
Options: a ) 11 , b ) 18 , c ) 13 , d ) 17 , e ) 12
Rationale: "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 4 / 25 * 75 = 12 answer : e"
Answer: e
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 10 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 288 , c ) 100 , d ) 299 , e ) 126
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 10 * 10 = 100 m . the length of the faster train = 100 m . answer : c"
Answer: c
Problem: a trader sells 78 meters of cloth for rs . 6788 at the profit of rs . 29 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 22 , b ) 75 , c ) 60 , d ) 58 , e ) 11
Rationale: "sp of 1 m of cloth = 6788 / 78 = rs . 87 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 87 - rs . 29 = rs . 58 . answer : d"
Answer: d
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 50 % ?
Options: a ) s . 429 , b ) s . 480 , c ) s . 320 , d ) s . 128 , e ) s . 419
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 50 % = 50 % of 640 = rs . 320 sp = cp - loss = 640 - 320 = rs . 320 answer : c"
Answer: c
Problem: a ( 8 , w ^ 2 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 17 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .
Rationale: "y = x ^ 2 + 17 w ^ 2 = 8 ^ 2 + 17 w ^ 2 = 81 w = 9 answer e"
Answer: e
Problem: on a certain transatlantic crossing , 40 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 50 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %
Rationale: let t be the total number of passengers . let x be the number of people with round trip tickets . 0.4 t had round trip tickets and took their cars . 0.5 x had round trip tickets and took their cars . 0.5 x = 0.4 t x = 0.8 t the answer is d .
Answer: d
Problem: if log 2 = 0.30103 , the number of digits in 2128 is .
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 56
Rationale: log ( 2128 ) = 128 log ( 2 ) = 128 × 0.30103 ≈ 38.4 ie , its characteristic = 38 hence , number of digits in 2128 = 38 + 1 = 39 answer : option b
Answer: b
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 40 white marbles . how many red marbles could be in bag a ?
Options: a ) 8 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 3 let w in bag b be 4 k w = 30 = 6 k + 4 k = > k = 40 / 10 = 4 total red ' s in bag a will be 2 k = 8 a"
Answer: a
Problem: if a person walks at 5 km / hr instead of 4 km / hr , he would have walked 6 km more . the actual distance traveled by him is ?
Options: a ) 14 , b ) 20 , c ) 18 , d ) 24 , e ) 21
Rationale: "let the actual distance traveled be x km . then , x / 4 = ( x + 6 ) / 5 x - 24 = > x = 24 km . answer : d"
Answer: d
Problem: if tim had lunch at $ 60.80 and he gave 20 % tip , how much did he spend ?
Options: a ) $ 30.60 , b ) $ 60.60 , c ) $ 72.96 , d ) $ 40.60 , e ) $ 50.60
Rationale: the tip is 20 % of what he paid for lunch . hence tip = 20 % of 60.80 = ( 20 / 100 ) * 60.80 = $ 12.16 total spent 60.80 + 12.16 = $ 72.96 correct answer c
Answer: c
Problem: when asked what the time is , a person answered that the amount of time left is 1 / 3 of the time already completed . what is the time .
Options: a ) 2 pm , b ) 9 pm , c ) 3 pm , d ) 8 pm , e ) 6 pm
Rationale: "a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 1 / 3 x ⇒ x = 18 time is 6 pm answer : e"
Answer: e
Problem: a ladder 18 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 6 feet from the base of the wall . if the top of the ladder slips down 4 feet , how many feet will the bottom of the ladder slip ?
Options: a ) 12.5 , b ) 15 , c ) 18 , d ) 19 , e ) 25
Rationale: "18 ^ 2 - 6 ^ 2 = 288 it means that the height is equal to 16.9 . since the top of the ladder slips down 4 feet , then the height of the wall = 16.9 - 4 = 12.9 the bottom = sqrt ( 18 ^ 2 - 12.9 ^ 2 ) = sqrt ( 324 - 166.41 ) = 12.5 ans is a"
Answer: a
Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be even ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "in order to make even nos . by multiplication , we should have even * odd , odd * even or even * even total even nos . possible by multiplying nos . from the 2 sets : ( 1 * 6 ) ; 2 * any of the three from set b ; 3 * 6 ; & 4 * any of the three from set b 1 + 3 + 1 + 3 = 8 total possibilities = 4 * 3 = 12 p ( event ) = 8 / 12 or 2 / 3 ans d"
Answer: d
Problem: johnny makes $ 3.25 per hour at his work . if he works 8 hours , how much money will he earn ?
Options: a ) $ 30 , b ) $ 54 , c ) $ 26 , d ) $ 12 , e ) $ 9.60
Rationale: 3.25 * 8 = 26 . answer is c .
Answer: c
Problem: an article is bought for rs . 1280 and sold for rs . 900 , find the loss percent ?
Options: a ) 28 % , b ) 29 % , c ) 16 % , d ) 26 % , e ) 32 %
Rationale: "1280 - - - - 380 100 - - - - ? = > 29 % answer : b"
Answer: b
Problem: what is the rate percent when the simple interest on rs . 800 amount to rs . 160 in 3 years ?
Options: a ) 5 % , b ) 6.6 % , c ) 9 % , d ) 2 % , e ) 4 %
Rationale: "160 = ( 800 * 3 * r ) / 100 r = 6.6 % answer : b"
Answer: b
Problem: solve below question 2 x + 1 = - 17
Options: a ) - 8 , b ) - 9 , c ) 9 , d ) 8 , e ) - 7
Rationale: "1 . subtract 1 from both sides : 2 x + 1 - 1 = - 17 - 1 2 . simplify both sides : 2 x = - 18 3 . divide both sides by 2 : 4 . simplify both sides : x = - 9 b"
Answer: b
Problem: what is the difference between the largest number and the least number written with the digits 9 , 3 , 1 , 2 ?
Options: a ) 6084 , b ) 3788 , c ) 2077 , d ) 8082 , e ) 1812
Rationale: "explanation : 1239 9321 - - - - - - - - - - - - 8082 answer : d"
Answer: d
Problem: if m and n are positive integer , and 1800 m = n ^ 3 , what is the least possible value of m ?
Options: a ) 2 , b ) 3 , c ) 15 , d ) 30 , e ) 45
Rationale: 1800 * m = n ^ 3 m = n ^ 3 / 1800 = n ^ 3 / ( 3 ^ 2 * 5 ^ 2 * 2 ^ 3 ) so n has to be 3 * 5 * 2 so that n ^ 3 is divisible by 1800 . so m = ( 2 * 3 * 5 ) ^ 3 / ( 3 ^ 2 * 5 ^ 2 * 2 ^ 3 ) m = 15 answer : c
Answer: c
Problem: the moon revolves around the earth at a speed of approximately 1.04 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 61.2 , c ) 3,744 , d ) 3,600 , e ) 3,672
Rationale: "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 1.04 * 3600 = 3744 kilometers per hour . option c is correct"
Answer: c
Problem: rates for having a manuscript typed at a certain typing service are $ 6 per page for the first time a page is typed and $ 3 per page each time a page is revised . if a certain manuscript has 100 pages , of which 30 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 690 , b ) $ 620 , c ) $ 650 , d ) $ 640 , e ) $ 770
Rationale: "for 100 - 30 - 10 = 60 pages only cost is 6 $ per page for the first time page is typed - 60 * 5 = 300 $ ; for 30 pages the cost is : first time 6 $ + 3 $ of the first revision - 30 * ( 6 + 3 ) = 270 $ ; for 10 pages the cost is : first time 5 $ + 3 $ of the first revision + 3 $ of the second revision - 10 ( 6 + 3 + 3 ) = 120 $ ; total : 300 + 270 + 120 = 690 $ . answer : a ."
Answer: a
Problem: a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 15 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 90 , b ) rs . 76 , c ) rs . 98 , d ) rs . 18 , e ) rs . 02
Rationale: "sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 15 = rs . 90 . answer : c"
Answer: c
Problem: 20 % of a number is added to 120 , the result is the same number . find the number ?
Options: a ) 150 , b ) 288 , c ) 1687 , d ) 997 , e ) 121
Rationale: "( 20 / 100 ) * x + 120 = x 2 x = 300 x = 150 answer : a"
Answer: a
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 5830 , what is the length of the plot in metres ?
Options: a ) 333 , b ) 200 , c ) 288 , d ) 276 , e ) 220
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 5830 [ 4 l - 40 ] = 5830 / 26.50 = 220 4 l = 260 l = 260 / 4 = 65 meters . answer : e"
Answer: e
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 much distance will the car cover in 5 hours ?
Options: a ) 300 km , b ) 325 km , c ) 375 km , d ) 425 km , e ) 450 km
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 5 hours is 75 × 5 = 375 km the answer is c ."
Answer: c
Problem: if a town of 65,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) a . 66000 , b ) b . 67000 , c ) c . 68000 , d ) d . 69000 , e ) e . 70000
Rationale: 1 % is quite small and hence the answer is a )
Answer: a
Problem: two trains , a and b , started simultaneously from opposite ends of a 75 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 75 - mile trip in 3 hours ; train b , traveling at a constant rate , completed the 75 - mile trip in 2 hours . how many miles had train a traveled when it met train b ?
Options: a ) 20 , b ) 22.5 , c ) 30 , d ) 37.5 , e ) 45
Rationale: "as the ratio of the rates of a and b is 2 to 3 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that x would cover 2 / ( 2 + 3 ) = 2 / 5 of 75 miles : 75 * 2 / 5 = 30 miles . answer : c ."
Answer: c
Problem: in one alloy there is 12 % chromium while in another alloy it is 8 % . 15 kg of the first alloy was melted together with 30 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 9.4 % , b ) 9.33 % , c ) 9.6 % , d ) 9.8 % , e ) 10 %
Rationale: "the amount of chromium in the new 15 + 30 = 45 kg alloy is 0.12 * 15 + 0.08 * 30 = 4.2 kg , so the percentage is 4.2 / 45 * 100 = 9.33 % . answer : b ."
Answer: b
Problem: what is the remainder when 135 ^ 77 is divided by 7 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "( 15 ^ 77 * 9 ^ 77 ) / 7 ; ( 15 ^ 77 ) / 7 * ( 9 ^ 77 ) / 7 ; 1 * 2 ^ 77 / 7 ; ( ( 2 ^ 3 ) ^ 25 * 2 ^ 2 ) / 7 ; 1 * 4 = 4 answer : e"
Answer: e
Problem: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 45 . what is the difference between the two digits of that number ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 45 ⇔ 9 ( x - y ) = 45 ⇔ x - y = 5 answer b"
Answer: b
Problem: if 42.30 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "42.30 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.30 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.30 = km / 50 . . . . . . 40 / 100 = 3 m / 50 . . . . . . m = 5 k + m = 3 + 5 = 8 answer : c"
Answer: c
Problem: a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many j cubes are painted on only 2 faces ?
Options: a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16
Rationale: "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . j = 4 + 4 + 4 = 12 . answer a"
Answer: a
Problem: at present the ratio between the ages of arun and deepak is 5 : 7 . after 6 years , arun ' s age will be 36 years . what is the age of deepak at present ?
Options: a ) 35 years , b ) 25 years , c ) 42 years , d ) 39 years , e ) 40 years
Rationale: "let the present ages of arun and deepak be 5 x years and 7 x years respectively 5 x + 6 = 36 5 x = 30 x = 6 deepak ' s age = 7 x = 42 years answer is c"
Answer: c
Problem: the average age of 15 students of a class is 16 years . out of these , the average age of 5 students is 14 years and that of the other 10 students is 16 years . tee age of the 15 th student is ?
Options: a ) 18 years , b ) 16 years , c ) 14 years , d ) 12 years , e ) 10 years
Rationale: "age of the 15 th student = [ 15 * 16 - ( 14 * 5 + 16 * 10 ) ] = ( 240 - 230 ) = 10 years . answer : e"
Answer: e
Problem: excluding stoppages , the speed of a bus is 75 kmph and including stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 15 , b ) 24 , c ) 17 , d ) 19 , e ) none of these
Rationale: "due to stoppages , it covers 30 km less . time taken to cover 30 km = ( ( 30 / 75 ) ã — 60 ) = 24 min . option ( b ) is correct"
Answer: b
Problem: the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 130 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?
Options: a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 520
Rationale: if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 130 group # 2 = ( like understood ) = 3 / 4 ( 1 / 4 ) n = 130 n = 520 answer = ( e )
Answer: e
Problem: when a certain perfect square is increased by 148 , the result is another perfect square . what is the value of the original perfect square ?
Options: a ) 1296
b ) 1369
c ) 1681
d ) 1764
e ) 2500
Rationale: let ’ s call the two perfect squares x ^ 2 and y ^ 2 , respectively . then the given information translates as x ^ 2 + 148 = y ^ 2 . subtracting x ^ 2 gives 148 = y ^ 2 − x ^ 2 , a difference of squares . this , in turn , factors as ( y + x ) ( y − x ) = 148 . the next step is tricky . it begins with factoring 148 , which breaks down as 2 ∗ 2 ∗ 37 . since we ’ re dealing with perfect squares , x and y are positive integers , and ( y + x ) and ( y − x ) must be paired integer factors of 148 . the options are 148 ∗ 1,74 ∗ 2 , and 37 ∗ 4 . but our number properties establish that ( y + x ) and ( y − x ) must be either both odd or both even , so only 74 ∗ 2 is an actual possibility . and because for any positive integers ( y + x ) > ( y − x ) , we can conclude that y + x = 74 and y – x = 2 . solving by elimination , 2 y = 76 , y = 38 , and x = 36 . finally , we just need to square 36 . but rather than multiplying it out , note that 36 ^ 2 ends in 6 – as does only one answer , choice a . this answer must be the one we want .
Answer: a
Problem: train a is 13 miles ahead of train b , which is traveling the same direction along the same route as train a . if train a is traveling at an average speed of 37 miles per hour and train b is traveling at an average speed of 43 miles per hour , how long will it take train b to overtake and drive 17 miles ahead of train a ?
Options: a ) 4 hours , b ) 2 hours , c ) 2 hours 30 minutes , d ) 5 hours , e ) 3 hours 20 minutes
Rationale: relative speed = 43 - 37 = 6 miles per hour dist required = 13 + 17 = 30 miles time taken to overtake = 30 / 6 = 5 hours . d is the answer .
Answer: d
Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?
Options: a ) 1 / 20 , b ) 1 / 12 , c ) 2 / 15 , d ) 3 / 10 , e ) 1 / 7
Rationale: "p ( x is prime ) = 1 / 3 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 3 * 1 / 4 = 1 / 12 the answer is b ."
Answer: b
Problem: on increasing the price of t . v . sets by 30 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 4 , b ) 5 , c ) 56 , d ) 2 , e ) 7
Rationale: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 130 × 80 ) = rs . 10400 increase % = 4001000040010000 × 100 = 4 % answer : a"
Answer: a
Problem: if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 10 percent , how much would she earn per week ?
Options: a ) $ 374 , b ) $ 330 , c ) $ 385 , d ) $ 392 , e ) $ 399
Rationale: "( 348 / 116 ) 110 = 330 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 110 = 330 ( 300 + 30 ) answer b"
Answer: b