regisss/math_qa huggingface dataset:
Problem: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 11 percent . overall he make a .
Options: a ) 228 , b ) 288 , c ) 27 , d ) 200 , e ) 280
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 11 / 100 ) = 8000 + 880 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 880 = rs . 280 as this is positive , an overall profit of rs . 280 was made . answer : e"
Answer: e
Problem: in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 5 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24 % , d ) 25 % , e ) 34 %
Rationale: "since 5 % of the customers who sample the candyare notcaught , then 88 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.95 = 0.22 ; { % of customers who sample candy } = 0.231 . answer : b ."
Answer: b
Problem: the average of first 22 natural numbers is ?
Options: a ) 11.6 , b ) 11.5 , c ) 12.9 , d ) 15.4 , e ) 15.1
Rationale: "sum of 22 natural no . = 506 / 2 = 253 average = 253 / 22 = 11.5 answer : b"
Answer: b
Problem: in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 10 and 400 , then the least and greatest integer on the card would be
Options: a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 13 , d ) 4 and 14 , e ) 5 and 14
Rationale: "given : 10 < x ( x + 1 ) < 400 . now , it ' s better to test the answer choices here rather than to solve : if x = 3 then x ( x + 1 ) = 12 > 10 - - > so , the least value is 3 . test for the largest value : if x = 20 then x ( x + 1 ) = 20 * 21 = 420 > 400 answer : b ."
Answer: b
Problem: p , q and r have $ 4000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2400 , b ) 2403 , c ) 3998 , d ) 2539 , e ) 1600
Rationale: "e 1600 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 4000 - r ) = > 3 r = 8000 - 2 r = > 5 r = 8000 = > r = 1600 ."
Answer: e
Problem: rahul and sham together can complete a task in 35 days , but rahul alone can complete same work in 60 days . calculate in how many days sham can complete this work ?
Options: a ) 84 days , b ) 82 days , c ) 76 days , d ) 68 days , e ) 60 days
Rationale: explanation : as rahul and sham together can finish work in 35 days . 1 days work of rahul and sham is 1 / 35 rahul can alone complete this work in 60 days , so , rahul one day work is 1 / 60 clearly , sham one day work will be = ( rahul and sham one day work ) - ( rahul one day work ) = 1 / 35 - 1 / 60 = 1 / 84 hence sham will complete the given work in 84 days . answer is a
Answer: a
Problem: a train running at the speed of 60 km / hr crosses a pole in 6 sec . what is the length of the train ?
Options: a ) 356 , b ) 278 , c ) 127 , d ) 100 , e ) 150
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 6 = 100 m answer : d"
Answer: d
Problem: lucy bought a 1 - year , 10000 certificate of deposit that paid interest at an annual rate of 8 percent compunded semiannually . what was the total amount of interest paid on this certificate at maturity ?
Options: a ) 10464 , b ) 864 , c ) 816 , d ) 800 , e ) 480
Rationale: solution : it says , 8 percent per annum per compounded semi annually . therefore r = 8 / 2 = 4 % . so , p = 10000 r = 4 n = 2 net amount a = 10816 , i = 800 . answer : d
Answer: d
Problem: if x ^ 2 + ( 1 / x ^ 2 ) = 6 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 34 , e ) 15
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 6 ^ 2 - 2 = 34 . thus , the answer is d ."
Answer: d
Problem: a bag marked at $ 125 is sold for $ 120 . the rate of discount is ?
Options: a ) 10 % , b ) 25 % , c ) 20 % , d ) 50 % , e ) 4 %
Rationale: rate of discount = 5 / 125 * 100 = 4 % answer is e
Answer: e
Problem: the radius of a cylindrical vessel is 8 cm and height is 3 cm . find the whole surface of the cylinder ?
Options: a ) 308 sq cm , b ) 220 sq cm , c ) 440 sq cm , d ) 553.1 sq cm , e ) 138 sq cm
Rationale: "r = 8 h = 3 2 π r ( h + r ) = 2 * 22 / 7 * 8 ( 11 ) = 553.1 answer : d"
Answer: d
Problem: the marks obtained by vijay and amith are in the ratio 6 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 1 : 5 , b ) 4 : 5 , c ) 9 : 5 , d ) 9 : 8 , e ) 9 : 7
Rationale: "6 : 5 3 : 2 - - - - - - - 18 : 15 : 10 18 : 10 9 : 5 answer : c"
Answer: c
Problem: for what value of x , is | x – 3 | + | x + 1 | + | x | = 10 ?
Options: a ) 0 , b ) 3 , c ) - 3 , d ) 4 , e ) - 2
Rationale: "there are 3 transition points : - 1 , 0 , 3 when x > 3 , | x − 3 | + | x + 1 | + | x | = 10 | x − 3 + x + 1 + x = 10 x = 4 satisfies when 0 < x < 3 | x − 3 | + | x + 1 | + | x | = 10 − ( x − 3 ) + ( x + 1 ) + x = 10 x = 6 ( not possible since 0 < x < 3 ) when - 1 < x < 0 | x − 3 | + | x + 1 | + | x | = 10 − ( x − 3 ) + − ( x + 1 ) + x = 10 x = - 8 ( not possible since - 1 < x < 0 ) when x < - 1 | x − 3 | + | x + 1 | + | x | = 10 - ( x - 3 ) - ( x + 1 ) - x = 10 x = - 8 / 3 satisfies answer : d"
Answer: d
Problem: when n is divided by 5 the remainder is 3 . what is the remainder when ( n + 3 ) ^ 2 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "n = 5 x + 3 , for some integer x ( n + 3 ) ^ 2 = ( 5 x + 6 ) ^ 2 = 5 y + 36 , for some integer y when we divide this by 5 , the remainder is 1 . the answer is b ."
Answer: b
Problem: right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 66 years . what is molly ' s age right now ?
Options: a ) 15 years , b ) 35 years , c ) 25 years , d ) 45 years , e ) 55 years
Rationale: "now , sandy is 66 - 6 = 60 molly ' s age is ( 3 / 4 ) * 60 = 45 the answer is d ."
Answer: d
Problem: a and b can do a work in 5 days and 10 days respectively . a starts the work and b joins him after 4 days . in how many days can they complete the remaining work ?
Options: a ) 6 days , b ) 2 / 3 days , c ) 8 days , d ) 3 days , e ) 9 days
Rationale: "work done by a in 4 days = 4 / 5 remaining work = 1 / 5 work done by both a and b in one day = 1 / 5 + 1 / 10 = 3 / 10 remaining work = 1 / 5 * 10 / 3 = 2 / 3 days . answer : b"
Answer: b
Problem: ( 935421 x 625 ) = ?
Options: a ) 542622125 , b ) 584632125 , c ) 544638125 , d ) 584638125 , e ) none of these
Rationale: "explanation : 935421 × 625 = 935421 × 54 = 935421 × ( 10 / 2 ) 4 = ( 935421 × 10000 ) / 16 = 584638125 . answer : option d"
Answer: d
Problem: a certain fraction is equivalent to 3 / 5 . if the numerator of the fraction is increased by 4 and the denominator is doubled , the new fraction is equivalent to 1 / 3 . what is the sum of the numerator and denominator of the original fraction ?
Options: a ) 49 , b ) 35 , c ) 28 , d ) 56 , e ) 21
Rationale: "x / y = 3 / 5 - > 1 ( x + 4 ) / 2 y = 1 / 3 - > 2 divide 1 by 2 : = > 2 x / ( x + 4 ) = 9 / 5 = > 10 x = 9 x + 36 = > x = 36 = > y = 5 / 3 * 12 = 20 so x + y = 56 the answer is d ."
Answer: d
Problem: a survey was sent to 65 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 4 % , c ) 14 % , d ) 28 % , e ) 63 %
Rationale: "case 1 : ( 7 / 65 ) = x / 100 x = 10 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 10 ) % = 4 % answer is b"
Answer: b
Problem: bert and rebecca were looking at the price of a condominium . the price of the condominium was 100 % more than bert had in savings , and separately , the same price was also 60 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .
Options: a ) 1 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 4 : 5 , e ) 1 : 1
Rationale: "suppose bert had 100 so price becomes 200 , this 200 = 1.6 times r ' s saving . . so r ' s saving becomes 125 so required ratio is 100 : 125 = 4 : 5 answer : d"
Answer: d
Problem: a man swims downstream 30 km and upstream 20 km taking 5 hours each time , what is the speed of the man in still water ?
Options: a ) 7 , b ) 8 , c ) 2 , d ) 5 , e ) 4
Rationale: "30 - - - 5 ds = 6 ? - - - - 1 20 - - - - 5 us = 4 ? - - - - 1 m = ? m = ( 6 + 4 ) / 2 = 5 answer : d"
Answer: d
Problem: andrew purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1000 , b ) 1055 , c ) 1060 , d ) 1075 , e ) 1080
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 b"
Answer: b
Problem: how many integers v are prime numbers in the range 200 < v < 220 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: my friend , every single odd number greater than can be written either as 4 v + 1 or as 4 v + 3 . if you divide any odd number by 4 , you will get a remainder of either 1 or 3 . that ' s not a rule unique to prime numbers at all . the 6 v + 1 or 6 v - 1 rule is basically every odd number that is not divisible by three , so it narrows the search a little . here ' s how i thought about the problem . first , eliminate all the even numbers and the odd multiples of 5 in that range . that leaves us with : { 201 , 203 , 207 , 209 , 211 , 213 , 217 , 219 } eliminate the four multiples of 3 . notice that 21 is a multiple of 3 , so 210 is also a multiple of 3 . if we add or subtract 3 or 9 , we get more multiples of three . when we eliminate those , we are left with . { 203 , 209 , 211 , 217 } now , notice that a cool thing about this range is that 210 is also a multiple 7 ( again , because 21 is a multiple of 7 ) . this means that 210 - 7 = 203 210 + 7 = 217 those two numbers are also multiples of 7 , so eliminate them from the list . now , we are left with { 209 , 211 } . we ' ve already checked all the prime numbers less than 10 , so we know that neither of these numbers is divisible by anything less than 10 . we have to check 11 now . we know that 22 is a multiple of 11 , so 220 is also a multiple of 11 . this means that 220 - 11 = 209 is also a multiple of 11 . we can eliminate this from the list also . that leaves us with just 211 . there ' s no zero option in the question , so this must be a prime number . answer = ( a )
Answer: a
Problem: if the average of 20 digits is 500 and the average of 14 of them is 390 , calculate the average of the remaining 6 numbers ?
Options: a ) 756.7 , b ) 751.7 , c ) 753.7 , d ) 752.7 , e ) 722.7
Rationale: "explanation : total of the 20 digits - 20 * 500 = 10000 total of the 14 digits - 14 * 390 = 5460 total of the remaining 6 digits - 10000 - 5460 = 4540 average of the remaining 6 numbers = 4540 / 6 = 756.7 answer : a"
Answer: a
Problem: two bullet train s 140 m and 180 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 11.52 sec . , c ) 11.8 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: "relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 180 ) m = 320 m . required time = 320 x 9 / 250 = 11.52 sec . answer b"
Answer: b
Problem: a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 25 per kg , then his gain percent is
Options: a ) 12 % , b ) 33 % , c ) 14 % , d ) 15 % , e ) 16 %
Rationale: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 25 ) = rs . 200 . profit = 200 - 150 = 50 so , profit % = ( 50 / 150 ) * 100 = 33 % option b"
Answer: b
Problem: the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 768 sq meters , then what is the width ( in meters ) of the rectangular plot ?
Options: a ) 24 m , b ) 16 m , c ) 35 m , d ) 54 m , e ) 43 m
Rationale: "area = l * w = 3 w ^ 2 = 768 w ^ 2 = 256 w = 16 the answer is b ."
Answer: b
Problem: a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 500 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "given that p is smallest integer greater than 200 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 b"
Answer: b
Problem: if p / q = 4 / 5 , then the value of 25 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 4 , b ) 34 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer given exp . = 25 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 25 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 25 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 25 / 7 + 6 / 14 = 25 / 7 + 3 / 7 = 28 / 7 = 4 correct option : a"
Answer: a
Problem: a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price r of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price r = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"
Answer: c
Problem: bottle r contains 350 capsules and costs $ 6.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
Options: a ) $ 0.25 , b ) $ 0.12 , c ) $ 0.0052 , d ) $ 0.003 , e ) $ 0.002
Rationale: "cost per capsule in r is 6.25 / 350 = 0.0178 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.0052 the answer is c"
Answer: c
Problem: the milk level in a rectangular box measuring 58 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 5437.5 , e ) 5635.5
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 58 * 25 * 1 / 2 = 725 feet ^ 3 of milk must be removed , which equals to 725 * 7.5 = 5437.5 gallons . answer : d ."
Answer: d
Problem: on a certain date , pat invested $ 7,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 28,000 , in how many years total will the total value of the investment plus interest increase to $ 56,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "28,000 = 7,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 56,000 = 7,000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."
Answer: a
Problem: on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 160,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 80 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 160,000 = 6 years total 24 years . answer e"
Answer: e
Problem: a rectangular block 15 cm by 30 cm by 75 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 6
b ) 40
c ) 15
d ) 10
e ) 22
Rationale: volume of the block = 15 * 30 * 75 = 33750 cm ^ 3 side of the largest cube = h . c . f of 15 , 30,75 = 15 cm volume of the cube = 15 * 15 * 15 = 3375 cm ^ 3 number of cubes = 33750 / 3375 = 10 answer is d
Answer: d
Problem: after replacing an old member by a new member , it was found that the average age of 5 members of a club is the same as it was 3 years ago . what is the difference between the ages of the replaced and the new member ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: explanation : i ) let the ages of the five members at present be a , b , c , d & e years . and the age of the new member be f years . ii ) so the new average of five members ' age = ( a + b + c + d + f ) / 5 - - - - - - - ( 1 ) iii ) their corresponding ages 3 years ago = ( a - 3 ) , ( b - 3 ) , ( c - 3 ) , ( d - 3 ) & ( e - 3 ) years so their average age 3 years ago = ( a + b + c + d + e - 15 ) / 5 = x - - - - - ( 2 ) = = > a + b + c + d + e = 5 x + 15 = = > a + b + c + d = 5 x + 15 - e - - - - - - ( 3 ) iv ) substituting this value of a + b + c + d = 5 x + 15 - e in ( 1 ) above , the new average is : ( 5 x + 15 - e + f ) / 5 equating this to the average age of x years , 3 yrs , ago as in ( 2 ) above , ( 5 x + 15 - e + f ) / 5 = x = = > ( 5 x + 15 - e + f ) = 5 x solving e - f = 15 years . thus the difference of ages between replaced and new member = 15 years . answer : d
Answer: d
Problem: zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 26.1 kg of zinc has been consumed in it ?
Options: a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none
Rationale: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 26.1 kg zinc , mixture , melted = [ 20 / 9 x 26.1 ] kg = 58 kg . answer a"
Answer: a
Problem: the ratio of boys to girls is 6 : 4.60 % of the boys and 40 % of girls take lunch in the canteen . what % of class takes lunch ?
Options: a ) 51 % , b ) 52 % , c ) 53 % , d ) 54 % , e ) 55 %
Rationale: let total no of students 100 , boy 60 and girl 40 , so lunch taken by boy and girl respectively 60 * 60 / 100 = 36 and 40 * 40 / 100 = 16 so total 52 students takes lunch out of 100 students . . so required % is 52 % answer : b
Answer: b
Problem: a person x started at 3 hours earlier at 40 km / h from a place p , then another person y followed him at 60 km / h . started his journey at 3 o ' clock , afternoon . what is the diference in time when x was 30 km ahead of y and when y was 30 km ahead of x ?
Options: a ) 8 h , b ) 3 h , c ) 6 h , d ) 3 h , e ) 1 h
Rationale: explanation : time ( when x was 30 km ahead of y ) = ( 120 - 30 ) / 20 = 4.5 h time ( when y was 30 km ahead of x ) = ( 120 + 30 ) / 20 = 7.5 h thus , required difference in time = 3 h answer : b
Answer: b
Problem: a room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with squre tiles . find the least number of squre tiles required to cover the floor ?
Options: a ) 178 , b ) 128 , c ) 127 , d ) 176 , e ) 171
Rationale: "area of the room = 544 * 374 sq cm size of largest square tile = h . c . f of 544 cm and 374 cm = 34 cm area of 1 tile = 34 * 34 sq cm no . of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer : d"
Answer: d
Problem: if i walk at 6 km / h , i miss the bus by 12 minutes . if i walk at 5 km / h , i reach 14 minutes before the arrival of the bus . how far i walk to reach the bus stand ?
Options: a ) 13 km , b ) 12 km , c ) 11 km , d ) 6.5 km , e ) 5.5 km
Rationale: "d = product of speed difference of time / difference of speed [ here , â € “ ve sign indicates before the schedule time ] d = 6 ã — 5 / 60 [ 12 â ˆ ’ ( â ˆ ’ 14 ) / 6 - 5 ] â ‡ ’ d = 13 km answer a"
Answer: a
Problem: if 35 % of a number is 24 less than 50 % of that number , then the number is ?
Options: a ) 180 , b ) 450 , c ) 160 , d ) 170 , e ) 185
Rationale: explanation : let the number be n . then , 50 % of n - 35 % of n = 24 50 / 100 n - 35 / 100 n = 24 n = ( 24 x 100 ) / 15 = 160 . answer c
Answer: c
Problem: tom opened a shop investing rs . 3000 . jose joined him 2 months later , investing rs . 4500 . they earned a profit of rs . 5400 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 3000 , b ) 2200 , c ) 2309 , d ) 2400 , e ) 3200
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 5400 = 3000 a"
Answer: a
Problem: if the selling price of 60 articles is equal to the cost price of 30 articles , then the loss or gain percent is :
Options: a ) 55 % , b ) 35 % , c ) 66 % , d ) 45 % , e ) 50 %
Rationale: "let c . p . of each article be re . 1 . then , c . p . of 60 articles = rs . 60 ; s . p . of 60 articles = rs . 30 . loss % = 30 / 60 * 100 = 50 % answer : e"
Answer: e
Problem: there are 5 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 150 , d ) 180 , e ) 200
Rationale: number of ways of selecting 2 fiction books = 5 c 2 number of ways of selecting 2 non fiction books = 6 c 2 5 c 2 * 6 c 2 = 10 * 15 = 150 answer : c
Answer: c
Problem: in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1,155 , and if 1 < p < q < r < s , how many students in the class are accounting majors ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 17
Rationale: "prime factorization of the product pqrs = 1155 = 3 * 5 * 7 * 11 since 1 < p < q < r < s number of students who are accounting majors , p = 3 answer a"
Answer: a
Problem: the area of a triangle is with base 4 m and height 6 m ?
Options: a ) 11 m 2 , b ) 10 m 2 , c ) 18 m 2 , d ) 19 m 2 , e ) 12 m 2
Rationale: "1 / 2 * 4 * 6 = 12 m 2 answer : e"
Answer: e
Problem: if 40 sheep eat 40 bags of grass in 40 days . in how many days one sheep will eat one bag of grass ?
Options: a ) 1 , b ) 20 , c ) 40 , d ) 80 , e ) 70
Rationale: explanation : let the required number of days be x . less sheep , more days ( indirect proportion ) less bags , less days ( direct proportion ) sheep 1 : 40 : : 40 : x bags 40 : 1 1 x 40 x x = 40 x 1 x 40 x = 40 . answer : c
Answer: c
Problem: increasing the original price of an article by 20 percent and then increasing the new price by 20 percent is equivalent to increasing the original price by
Options: a ) 40 % , b ) 41 % , c ) 42 % , d ) 43 % , e ) 44 %
Rationale: "1.2 * 1.2 * x = 1.44 * x the answer is e ."
Answer: e
Problem: the age of somu is one - third his father ' s . 6 years back he was one - fifth of his father ' s age . what is his persent age ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 10
Rationale: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 6 = 3 x - 6 / 5 = x = 12 answer : option d"
Answer: d
Problem: john builds a square with a side of 12 cm from some wire . if from the same wire , he builds a rectangle with a width of 6 cm , what will be the length of the rectangle ?
Options: a ) 18 cm
b ) 19 cm
c ) 20 cm
d ) 21 cm
e ) none
Rationale: solution : if the side of the square is 12 cm , then its perimetre will be 48 cm . we build the rectangle from the same wire , so it will have the same perimetre . its width is 6 cm , so its length will be ( 48 - 12 ) ÷ 2 = 36 ÷ 2 = 18 cm answer a
Answer: a
Problem: a train 560 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 28 , e ) 32
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 560 * 2 / 35 = 32 sec answer : option e"
Answer: e
Problem: the banker â € ™ s gain on a sum due 3 years hence at 12 % per annum is rs . 180 . the banker â € ™ s discount is
Options: a ) rs . 960 , b ) rs . 840 , c ) rs . 1020 , d ) rs . 680 , e ) none
Rationale: solution t . d = ( b . g x 100 / r x t ) = rs . ( 180 x 100 / 12 x 3 ) = rs . 500 . b . d = rs ( 500 + 180 ) = rs . 680 . answer d
Answer: d
Problem: 12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 10 .
Options: a ) 150 , b ) 152 , c ) 154 , d ) 163 , e ) 144
Rationale: "d = d * q + r d = 17 * 9 + 10 d = 153 + 10 d = 163 answer d"
Answer: d
Problem: a lady builds 8 cm length , 15 cm width , and 5 cm height box using 10 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 107 , b ) 60 , c ) 70 , d ) 89 , e ) 78
Rationale: "number of cubes required = volume of box / volume of cube = 8 * 15 * 5 / 10 = 60 cubes answer : b"
Answer: b
Problem: a furniture dealer purchased a desk for $ 100 and then set the selling price equal to the purchase price plus a markup that was 40 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: "anyway , in this question , there is no discount but the mark up is given as 40 % of the selling price . so it is not 40 % of $ 100 but instead , 40 % of selling price which is obtained by adding mark up to $ 100 . so if selling price is s , 100 + 40 % of s = s or 100 = 0.6 s therefore s = 100 / 0.6 = s = profit = 100 / 0.6 - 100 which is calculated on cost price in % terms . so 40 / 100 * 100 = 40 % is profit . a"
Answer: a
Problem: there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total w of the book ?
Options: a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018
Rationale: "first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) w 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ."
Answer: a
Problem: the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 33 kmph ?
Options: a ) 210 , b ) 220 , c ) 125 , d ) 240 , e ) 250
Rationale: "distance covered in 1 min = ( 33 * 1000 ) / 60 = 550 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 550 / 4.4 = 125 answer : c"
Answer: c
Problem: the population of a bacteria colony doubles every day . if it was started 8 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 1024 , d ) 2048 , e ) 4096
Rationale: "8 days ago - 2 7 days ago - 4 6 days ago - 8 5 days ago - 16 4 days ago - 32 3 days ago - 64 2 days ago - 128 yesterday - 256 today - 512 ans : a"
Answer: a
Problem: how many quarters are equal to 7 dollars ?
Options: a ) 1 , b ) 28 , c ) 12 , d ) 9 , e ) 7
Rationale: "7 * 4 = 28 quarters answer : b"
Answer: b
Problem: what is 0.1 percent of 12,356 ?
Options: a ) 0.12356 , b ) 1.2356 , c ) 12.356 , d ) 0.012356 , e ) 0.0012356
Rationale: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.1 ( 1 / 100 ) 12,356 . the answer is 12.356 . hence , the correct answer is c .
Answer: c
Problem: the difference between the value of a number increased by 25 % and the value of the original number decreased by 30 % is 22 . what is the original number ?
Options: a ) 40 , b ) 50 , c ) 65 , d ) 70 , e ) 90
Rationale: "let the original # be x then 1.25 x − 0.7 x = 22 - - > x = 40 answer : a ."
Answer: a
Problem: if a - b = 3 and a ^ 2 + b ^ 2 = 33 , find the value of ab .
Options: a ) 12 , b ) 15 , c ) 10 , d ) 18 , e ) 13
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 33 - 9 = 24 ab = 12 . answer is a ."
Answer: a
Problem: 1 : 3 = 1 2 / 3 : x . the value of x is ?
Options: a ) 1 , b ) 6 , c ) 7 , d ) 5 , e ) 8
Rationale: x * 1 = 3 * 5 / 3 x = 5 answer : d
Answer: d
Problem: how many figures are required to number the pages the pages of a book containing 709 pages ?
Options: a ) 2020 , b ) 2019 , c ) 1019 , d ) 2029 , e ) 2039
Rationale: "1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 709 = 610 * 3 = 1830 - - - - - - - - - - - 2019 answer : b"
Answer: b
Problem: a cone of height 9 cm with diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm . the percentage of the wood wasted is :
Options: a ) 45 %
b ) 56 %
c ) 67 %
d ) 75 %
e ) none of these
Rationale: explanation : we will first subtract the cone volume from wood volume to get the wood wasted . then we can calculate its percentage . sphere volume = 4 / 3 π r 3 cone volume = 1 / 3 π r 2 h volume of wood wasted = ( 4 / 3 π ∗ 9 ∗ 9 ∗ 9 ) − ( 1 / 3 π ∗ 9 ∗ 9 ∗ 9 ) = π ∗ 9 ∗ 9 ∗ 9 cm 3 required percentage = π ∗ 9 ∗ 9 ∗ 9 / 4 / 3 π ∗ 9 ∗ 9 ∗ 9 ∗ 100 % = 3 / 4 ∗ 100 % = 75 % option d
Answer: d
Problem: of the votes cast on a certain proposal , 66 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )
Options: a ) 290 , b ) 310 , c ) 330 , d ) 350 , e ) 370
Rationale: "let x be the total number of votes cast . 0.6 x = 0.4 x + 66 0.2 x = 66 x = 330 the answer is c ."
Answer: c
Problem: a can finish a work in 72 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
Options: a ) 30 days , b ) 12 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: "b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 24 work is done by a in 1 day 5 / 12 work is done by a in 72 * 5 / 12 = 30 days answer is a"
Answer: a
Problem: the average earning of amechanic for the first 4 days of a week is rs . 25 and for the last 4 days is rs . 22 . if heearns rs . 20 on the fourth day , his average earning forthe whole week is ?
Options: a ) s . 10 , b ) s . 24 , c ) s . 30 , d ) s . 40 , e ) s . 50
Rationale: total earning for the week = sum of earning of first four days + sum of earning of last four days - earning of 4 th day = 4 x 25 + 4 x 22 - 20 = rs . 168 â ˆ ´ average earning = 168 / 7 = rs . 24 b
Answer: b
Problem: a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 3025 in 3 years . find the rate percent ?
Options: a ) 11 , b ) 10 , c ) 28 , d ) 25 , e ) 82
Rationale: "explanation : 2420 - - - 605 100 - - - ? = > 25 % answer : option d"
Answer: d
Problem: 9 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) 33 , b ) 66 , c ) 88 , d ) 11 , e ) 281
Rationale: "( 9 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 20 20 – 9 = 11 answer : d"
Answer: d
Problem: a building contractor employs 20 male , 15 female and 5 child workers . to a male worker he pays rs . 25 per day , to a female worker rs . 20 per day and a child worker rs . 8 per day . the average wage per day paid by the contractor is ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: explanation : 20 15 5 25 20 8 500 + 300 + 40 = 840 / 40 = 21 b
Answer: b
Problem: what is the remainder when 3 ^ 33 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of powers of 3 follow a repeating cycle of four : { 3 , 9 , 7 , 1 } 33 has the form 4 k + 1 , so the units digit of 3 ^ 33 is 3 . the remainder when dividing by 5 is 3 . the answer is d ."
Answer: d
Problem: find ( 7 x + 2 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?
Options: a ) 23 , b ) 25 , c ) 26 , d ) 27 , e ) 29
Rationale: "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 2 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 2 y ) / ( 3 y - 2 y ) = > 23 y / y = 23 answer : a"
Answer: a
Problem: john left home and drove at the rate of 45 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 45 mph to reach his destination . how many miles did john drive ?
Options: a ) 235 miles . , b ) 245 miles . , c ) 225 miles . , d ) 265 miles . , e ) 275 miles .
Rationale: "the total distance d traveled by john is given by d = 45 * 2 + 3 * 45 = 225 miles . answer c"
Answer: c
Problem: a statue is being carved by a sculptor . the original piece of marble weighed 190 kg . in the first week 25 percent is cut away . in the second week 15 percent of the remainder is cut away . in the third week the statue is completed when 10 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 105 kg , b ) 103 kg , c ) 109 kg , d ) 125 kg , e ) 117 kg
Rationale: "c 109 kg 190 ã — 0.75 ã — 0.85 ã — 0.9 = 109 kg ."
Answer: c
Problem: the population of a town increased from 1 , 75,000 to 2 , 97,500 in a decade . the average percent increase of population per year is
Options: a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) 7 %
Rationale: solution increase in 10 years = ( 297500 - 175000 ) = 122500 increase % = ( 122500 / 175000 ã — 100 ) % = 70 % . required average = ( 70 / 10 ) % = 7 % . answer e
Answer: e
Problem: in an exam , gibi scored 59 percent , jigi scored 55 percent , mike scored 99 percent and lizzy 67 percent . the maximum score awarded in the exam is 700 . find the average mark scored by all the 4 students ?
Options: a ) 471 , b ) 490 , c ) 480 , d ) 453 , e ) 456
Rationale: average mark scored by all the three boys = [ 59 / 100 ( 700 ) + 55 / 100 ( 700 ) + 99 / 100 ( 700 ) + 67 / 100 ( 700 ) ] / 4 ( 413 + 385 + 693 + 469 ) / 4 = 490 answer : b
Answer: b
Problem: in how many no . between 10 and 50 exactly two of the digits is 5 ?
Options: a ) 47 , b ) 65 , c ) 1 , d ) 35 , e ) 65
Rationale: "it ' s simple can be solved by elimination of answer choices . option b and d are too large , not possible . even ae are large to have correct choice . ans : c"
Answer: c
Problem: john and david work at a hospital with 8 other workers . for an internal review , 2 of the 8 workers will be randomly chosen to be interviewed . what is the probability that john and david will both be chosen ?
Options: a ) 1 / 30 , b ) 1 / 25 , c ) 1 / 20 , d ) 1 / 28 , e ) 1 / 30
Rationale: probability that john and david will both be chosen out of 8 workers = ( 2 / 8 ) * ( 1 / 7 ) = 1 / 28 answer d
Answer: d
Problem: by selling 8 pens for a rupee a woman loses 25 % . how many for a rupee should he sell in order to gain 25 % ?
Options: a ) 2 , b ) 14 , c ) 3 , d ) 5 , e ) 6
Rationale: "d 75 % - - - 8 125 % - - - ? 75 / 125 * 8 = 5"
Answer: d
Problem: 3.20 can be expressed in terms of percentage as
Options: a ) 3.20 % , b ) 30.2 % , c ) 320.00 % , d ) 0.320 % , e ) none of these
Rationale: explanation : while calculation in terms of percentage we need to multiply by 100 , so 3.20 * 100 = 320 answer : option c
Answer: c
Problem: a person was asked to subtract 25 % of a number from the original but he subtracted 25 from the number . his answer was 25 more than correct one . what was the original number ?
Options: a ) 288 , b ) 266 , c ) 288 , d ) 200 , e ) 111
Rationale: 25 + 25 = 50 25 % - - - - - - 50 100 % - - - - - ? = > 200 answer : d
Answer: d
Problem: if x : y is 1 : 5 and y : z is 5 : 7 then x : z is equal to
Options: a ) 1 : 6 , b ) 1 : 5 , c ) 1 : 4 , d ) 1 : 7 , e ) 1 : 3
Rationale: the two ratios given are having the same number 5 for y in both the ratios . hence - x : y = 1 : 5 y : z = 5 : 7 = > x : z = 1 : 7 answer d
Answer: d
Problem: divide $ 1000 among a , b in the ratio 1 : 3 . how many $ that a get ?
Options: a ) $ 50 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600
Rationale: "sum of ratio terms = 1 + 3 = 4 a = 1000 * 1 / 4 = $ 250 answer is d"
Answer: d
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 72 kilometers , maxwell ' s walking speed is 6 km / h , and brad ' s running speed is 12 km / h . what is the distance traveled by maxwell when they meet in the middle ?
Options: a ) 14 , b ) 24 , c ) 16 , d ) 18 , e ) 20
Rationale: "consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 6 xt = 72 - 12 xt ( i . e distance = speed x time ) = > 18 t = 72 hence t = 4 oa = 6 x 4 = 24 km answer : b"
Answer: b
Problem: carolyn bought 17 gumballs , lew bought 12 gumballs , and carey bought x gumballs . the average ( arithmetic mean ) number of gumballs the 3 bought is between 19 and 25 , inclusive . what is the difference between the greatest number and the smallest number of gumballs carey could have bought ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: smallest gumballs = ( 19 - 17 ) + ( 19 - 12 ) + 19 = 28 largest gumballs = ( 25 - 17 ) + ( 25 - 12 ) + 25 = 46 difference = 46 - 28 = 18 a
Answer: a
Problem: a train 250 m long passed a pole in 10 sec . how long will it take to pass a platform 1250 m long ?
Options: a ) 60 sec , b ) 90 sec , c ) 120 sec , d ) 150 sec , e ) 180 sec
Rationale: speed = 250 / 10 = 25 m / sec . required time = ( 250 + 1250 ) / 25 = 60 sec answer : a
Answer: a
Problem: one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 225 cm when it touches the floor on third time . what is the value of the original height ?
Options: a ) 80 cm , b ) 90 cm , c ) 100 cm , d ) 120 cm , e ) 130 cm
Rationale: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 225 2.5 h = 225 h = 90 . b is the answer ."
Answer: b
Problem: a man fell in a 30 meter deep well , in one day he climbs 4 meters up and slips 3 meters down . how many days would it take for him to come out of the well ?
Options: a ) 22 , b ) 46 , c ) 17 , d ) 27 , e ) 33
Rationale: d i will take 27 days to come out of that well for that man , he climbs 4 meter every day and slips 3 meter down that means he climbs 1 meter in total each day , so like this on 26 th day he would have climbed 26 meter and on 27 th day he will climb 4 meeter again so total 30 meter he will climb in 27 days .
Answer: d
Problem: if a mixture is 2 ⁄ 7 alcohol by volume and 3 ⁄ 7 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?
Options: a ) 3 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 5 , e ) 4 / 5
Rationale: should be a sub - 600 level q . . volume = { 2 / 7 } / { 3 / 7 } = 2 / 3 c
Answer: c
Problem: 20 percent of country y ' s yearly exports come from fruit exports . one - sixth of all fruit exports from country y are orange exports . if country y generates $ 4.25 million from its orange exports , how much money does it generate from its yearly total of exports ?
Options: a ) $ 21.25 m , b ) $ 25.5 m , c ) $ 106.25 m , d ) $ 127.5 m , e ) $ 153 m
Rationale: 2 / 10 * 1 / 6 * ( total ) = 4.25 1 / 30 * ( total ) = 4.25 ( total ) = 4.25 * 30 = 127.5 answer : d .
Answer: d
Problem: what is the value of n if the sum of the consecutive odd intergers w from 1 to n equals 169 ?
Options: a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29
Rationale: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."
Answer: b
Problem: indu gave bindu rs . 7500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 5 , b ) 2 , c ) 9 , d ) 5 , e ) 12
Rationale: "7500 = d ( 100 / 4 ) 2 d = 12 answer : e"
Answer: e
Problem: evaluate : 7899665 - 12 * 3 * 2 = ?
Options: a ) 2455835 , b ) 2789255 , c ) 6868575 , d ) 7899657 , e ) 1023666
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 7899665 - 12 * 3 * 2 = 7899665 - 8 = 7899657 correct answer d"
Answer: d
Problem: a can do a half of certain work in 70 days and b one third of the same in 35 days . they together will do the whole work in ?
Options: a ) 1 / 65 , b ) 1 / 62 , c ) 1 / 63 , d ) 1 / 60 , e ) 1 / 61
Rationale: a = 140 days b = 105 days 1 / 140 + 1 / 105 = 7 / 420 = 1 / 60 = > 60 days answer : d
Answer: d
Problem: if 9 / ( 1 + 4 / x ) = 1 , then x =
Options: a ) 3 , b ) 1 / 2 , c ) 1 / 3 , d ) - 1 / 3 , e ) - 3
Rationale: "the expression 9 / ( 1 + 4 / x ) = 1 should have been equal to something . if 9 / ( 1 + 4 / x ) = 1 = 1 = > 9 x / ( x + 4 ) = 1 = > 9 x = x + 4 = > 8 x = 4 = > x = 1 / 2 correct option : b"
Answer: b
Problem: what is the prime factors ’ number of 12 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "prime factors ’ number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 24 = 2 ^ 2 * 3 ^ 1 prime factors ’ number will be 2 + 1 = 3 . hence , answer is b ."
Answer: b
Problem: in 2 bags , there are to be put together 5 red and 12 white balls , neither bag being empty . how must the balls be divided so as to give a person who draws 1 ball from either bag - the least chance of drawing a red ball ?
Options: a ) 1 / 32 , b ) 2 / 32 , c ) 3 / 32 , d ) 4 / 32 , e ) 5 / 32
Rationale: "least chance . p = 1 / 2 * 5 / 16 + 1 / 2 * 0 = 5 / 32 answer : e"
Answer: e
Problem: what is the sum of the odd integers from 55 to 75 , inclusive ?
Options: a ) 495 , b ) 550 , c ) 555 , d ) 600 , e ) 715
Rationale: "the mean is 65 . sum = mean ( # of elements ) there are 11 odd numbers between 55 - 75 inclusive . 11 * 65 = 715 e"
Answer: e
Problem: in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 1 : 2 . in the subsequent n games , the ratio of the team ´ s wins to losses was 2 : 3 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ?
Options: a ) 7 : 18 , b ) 9 : 23 , c ) 10 : 17 , d ) 23 : 54 , e ) 31 : 77
Rationale: "m = 4 / 9 of total games n = 5 / 9 of total games wins = 1 / 3 * 4 / 9 + 2 / 5 * 5 / 9 = 4 / 27 + 6 / 27 = 10 / 27 losses = 1 - 10 / 27 = 17 / 27 the ratio of wins to losses is 10 : 17 . the answer is c ."
Answer: c
Problem: for all even integers n , h ( n ) is defined to be the sum of the even integers between 2 and n , inclusive . what is the value of h ( 20 ) / h ( 10 ) ?
Options: a ) 1.8 , b ) 60 , c ) 6 , d ) 18 , e ) 3
Rationale: "concept : when terms are in arithmetic progression ( a . p . ) i . e . terms are equally spaced then mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 20 ) = [ ( 2 + 20 ) / 2 ] * 9 = 99 h ( 10 ) = ( 2 + 10 ) / 2 ] * 5 = 30 h ( 18 ) / h ( 10 ) = ( 99 ) / ( 30 ) ~ 3 answer : e"
Answer: e
Problem: a shopkeeper sold an article at $ 1170 and gained a 20 % profit . what was the cost price ?
Options: a ) $ 950 , b ) $ 975 , c ) $ 1000 , d ) $ 1025 , e ) $ 1050
Rationale: "let x be the cost price . 1.2 x = 1170 x = 1170 / 1.2 = 975 the answer is b ."
Answer: b
Problem: how many positive integers less than 70 have a reminder 01 when divided by 3 ?
Options: a ) 13 , b ) 24 , c ) 35 , d ) 16 , e ) 17
Rationale: "1 also gives the remainder of 1 when divided by 3 . so , there are total of 24 numbers . answer : b ."
Answer: b
Problem: an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 15 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?
Options: a ) 1340 , b ) 1445 , c ) 1375 , d ) 1415 , e ) 1455
Rationale: $ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 15 % of the gaskets to x = 9 gaskets = 25 * 9 = 225 2 . he sold 15 % of the gaskets to y = 9 gaskets = 25 * 9 = 225 3 . he sold remaining 70 % to z = 42 gaskets = 25 * 10 = 250 + 20 * 32 = 890 thus , total money earned 225 + 225 + 890 = 1340 answer is a
Answer: a