regisss/math_qa huggingface dataset:
Problem: there are two positive numbers in the ratio 2 : 7 . if the larger number exceeds the smaller by 30 , then find the larger number ?
Options: a ) 42 , b ) 38 , c ) 44 , d ) 36 , e ) 46
Rationale: "let the two positive numbers be 2 x and 7 x respectively . 7 x - 2 x = 30 5 x = 30 = > x = 6 = > larger number = 7 x = 42 . answer : a"
Answer: a
Problem: one night 17 percent of the female officers on a police force were on duty . if 204 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 420 , b ) 480 , c ) 540 , d ) 600 , e ) 660
Rationale: "let x be the number of female police officers on the police force . the number of female police officers on duty was 102 . 0.17 x = 102 x = 600 the answer is d ."
Answer: d
Problem: the contents of a certain box consist of 20 apples and 30 oranges . how many oranges must be added to the box so that exactly 20 % of the pieces of fruit in the box will be apples ?
Options: a ) 50 , b ) 55 , c ) 75 , d ) 85 , e ) 100
Rationale: "apple = ( apple + orange + x ) * 0.2 20 = ( 30 + 20 + x ) * 0.2 x = 50 answer : a"
Answer: a
Problem: the workforce of company x is 60 % female . the company hired 24 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 288 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 24 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 24 ) 0.05 x = 13.2 x = 264 - this is quantity of employees before adding 24 men so after adding it will be 288 answer is c"
Answer: c
Problem: whats the reminder when 58 , 458,965 , 231,457 , 895,684 , 525,465 , 985,445 is divided by 16
Options: a ) 5 , b ) 7 . , c ) 2 . , d ) 3 , e ) 9
Rationale: "a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . a number ending in 3 zeroes is divisible by 8 . a number ending in 4 zeroes in divisible by 16 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 58 , 458,965 , 231,457 , 895,684 , 525,465 , 985,445 = 58 , 458,965 , 231,457 , 895,684 , 525,465 , 980,000 + 5,445 the first number is divisible by 16 . you just have to find the remainder when you divide 5445 by 16 . that will be the remainder when you divide the original number by 16 . 5445 / 16 gives remainder 5 . answer ( a )"
Answer: a
Problem: the ratio of the volumes of two cubes is 1000 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 100 : 121 , b ) 100 : 127 , c ) 81 : 191 , d ) 81 : 161 , e ) 100 : 182
Rationale: "explanation : ratio of the sides = ³ √ 1000 : ³ √ 1331 = 10 : 11 ratio of surface areas = 10 ^ 2 : 11 ^ 2 = 100 : 121 answer : option a"
Answer: a
Problem: what is the smallest positive integer x such that 720 - x is the cube of a positive integer
Options: a ) 5 , b ) 7 , c ) 47 , d ) 9 , e ) 12
Rationale: "given 738 - x is a perfect cube so we will take 729 = 9 * 9 * 9 738 - x = 729 x = 738 - 729 = 9 correct option is d"
Answer: d
Problem: 1370 , x , 1070 , - 180 , - 6430
Options: a ) 1320 , b ) 6530 , c ) 6630 , d ) 6730 , e ) 6830
Rationale: 1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 answer : a .
Answer: a
Problem: if 75 percent of a class answered the first question on a certain test correctly , 45 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 10 % , b ) ( 8 ) 40 % , c ) 30 % , d ) 50 % , e ) 65 %
Rationale: "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 45 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 120 x = 40 ans : b"
Answer: b
Problem: the perimeter of a square is equal to the perimeter of a rectangle of length 17 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 23.57 , b ) 23.54 , c ) 23.5 , d ) 24.35 , e ) 24.51
Rationale: "let the side of the square be a cm . perimeter of the rectangle = 2 ( 17 + 14 ) = 62 cm perimeter of the square = 62 cm i . e . 4 a = 62 a = 15.5 diameter of the semicircle = 15.5 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 15.5 ) = 1 / 2 ( 22 / 7 ) ( 15.5 ) = 24.35 cm to two decimal places answer : d"
Answer: d
Problem: ? % of 360 = 180
Options: a ) 277 , b ) 36 , c ) 50 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 180 or , ? = 180 × 100 / 360 = 50 answer c"
Answer: c
Problem: the average of runs of a cricket player of 10 innings was 33 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 77 , b ) 79 , c ) 85 , d ) 87 , e ) 89
Rationale: "explanation : average = total runs / no . of innings = 33 so , total = average x no . of innings = 33 x 10 = 330 . now increase in avg = 4 runs . so , new avg = 33 + 4 = 37 runs total runs = new avg x new no . of innings = 37 x 11 = 407 runs made in the 11 th inning = 407 - 330 = 77 answer : a"
Answer: a
Problem: if y exceeds x by 25 % , then x is less than y by ?
Options: a ) 28 % , b ) 21 % , c ) 20 % , d ) 30 % , e ) 29 %
Rationale: "x = 100 y = 125 125 - - - - - - - - 25 100 - - - - - - - - ? = > 20 % answer : c"
Answer: c
Problem: the average score of a cricketer in 2 matches is 60 and in other 3 matches is 50 . then find the average score in all the 5 matches ?
Options: a ) 54 , b ) 27 , c ) 30 , d ) 35 , e ) 42
Rationale: "average in 5 matches = ( 2 * 60 + 3 * 50 ) / 2 + 3 = 120 + 150 / 5 = 270 / 5 = 54 answer is a"
Answer: a
Problem: the largest three digit number which is a perfect cube , is :
Options: a ) 125 , b ) 999 , c ) 343 , d ) 512 , e ) 729
Rationale: "explanation : 9 * 9 * 9 = 729 answer : e"
Answer: e
Problem: a 160 meter long train crosses a man standing on the platform in 18 sec . what is the speed of the train ?
Options: a ) 96 kmph , b ) 94 kmph , c ) 32 kmph , d ) 56 kmph , e ) 76 kmph
Rationale: "s = 160 / 18 * 18 / 5 = 32 kmph answer : c"
Answer: c
Problem: albert invested rs . 8000 in a scheme for 2 years at compound interest rate 5 % p . a . how much amount will albert get on maturity of the fixed deposit ?
Options: a ) 8840 , b ) 2776 , c ) 2998 , d ) 2662 , e ) 8820
Rationale: "amount = [ 8000 * ( 1 + 5 / 100 ) 2 ] = 8000 * 21 / 20 * 21 / 20 = rs . 8820 answer : e"
Answer: e
Problem: a person buys an article at $ 600 . at what price should he sell the article so as to make a profit of 8 % ?
Options: a ) 670 , b ) 689 , c ) 648 , d ) 740 , e ) 889
Rationale: "c 648 cost price = $ 600 profit = 8 % of 600 = $ 48 selling price = cost price + profit = 600 + 48 = 648"
Answer: c
Problem: what is the remainder when ( 63 ) ( 65 ) is divided by 8 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7
Rationale: "( 63 ) ( 65 ) = ( 64 - 1 ) ( 64 + 1 ) = 64 ^ 2 - 1 which is 1 less than a multiple of 8 . then the remainder will be 7 . the answer is e ."
Answer: e
Problem: if shares of two persons in profits are rs . 1600 and rs . 1200 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "profit = time * capital so 1600 : 1200 = 4 : 3 answer : c"
Answer: c
Problem: irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 148 cookies , what percent of the cookies did ingrid bake ?
Options: a ) 0.125 % , b ) 1.25 % , c ) 31.7 % , d ) 125 % , e ) 0.152 %
Rationale: 9.18 x + 5.17 x + 2.05 x = 16.4 x = 148 cookies x = 148 / 16.4 = 9 ( approx ) so , ingrid baked 9 * 5.17 cookies or 47 cookies ( approx ) % share = 47 / 148 = 31.7 approx hence , answer is c .
Answer: c
Problem: two integers are in the ratio of 1 to 4 . if 6 is added to the smaller number , the ratio becomes 1 to 3 . find the larger integer .
Options: a ) 4 , b ) 24 , c ) 30 , d ) 72 , e ) 80
Rationale: "one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 4 , then 4 x = y , where x is the smaller integer . if adding 6 to the smaller integer makes the ratio 1 to 3 , then 3 ( x + 6 ) = y . substituting y = 4 x into the second equation yields 3 x + 18 = 4 x . so , x = 18 ( smaller integer ) and , y = 4 x = 72 ( larger integer ) so d is the correct answer . another option is to test the answer choices . a ) the larger number is 4 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 1 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 1 ) , we get 7 . so , the new ratio is 7 to 4 . no good . we want a resulting ratio of 1 to 3 eliminate a b ) the larger number is 24 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 6 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 6 ) , we get 12 so , the new ratio is 12 to 24 which is 1 to 2 . no good . we want a resulting ratio of 1 to 3 eliminate b c ) the larger number is 30 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 7.5 ( which is not an integer ) since both numbers are integers , the larger number can not be 30 . eliminate c d ) the larger number is 72 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 18 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 18 ) , we get 24 so , the new ratio is 24 to 72 . this is the same as the ratio of 1 to 3 therefore ( d ) is correct e ) the larger number is 80 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 20 if 6 is added to the smaller number , the ratio becomes 1 to 3 if we add 6 to the smaller number ( 20 ) , we get 26 so , the new ratio is 26 to 80 which is 13 to 40 . no good . we want a resulting ratio of 1 to 3 eliminate e therefore d is the only correct choice ."
Answer: d
Problem: a , b and c are partners in a business . their capitals are respectively , rs . 5000 , rs . 6000 and rs . 4000 . a gets 30 % of the total profit for managing the business . the remaining profit is divided among 3 in the ratio of their capitals . in the end of the year , the profit of a is rs . 200 more than the sum of the profits of b and c . find the total profit ?
Options: a ) 3089 , b ) 3098 , c ) 3057 , d ) 3000 , e ) 3012
Rationale: a : b : c = 5 : 6 : 4 let the total profit = 100 - 30 = 70 5 / 15 * 70 = 70 / 3 a share = 70 / 3 + 30 = 160 / 3 b + c share = 100 - 160 / 3 = 140 / 3 a - ( b + c ) = 160 / 3 - 140 / 3 = 20 / 3 20 / 3 - - - - 200 100 - - - - ? = > 3000 answer : d
Answer: d
Problem: $ 100 is divided amongst a , b and c so that a may get 1 / 4 as much as b and c together , b may get 3 / 5 as much as a and c together , then the share of a is
Options: a ) $ 15 , b ) $ 20 , c ) $ 25 , d ) $ 18 , e ) $ 30
Rationale: "a : ( b + c ) = 1 : 4 a ' s share = 100 * 1 / 5 = $ 20 answer is b"
Answer: b
Problem: an urn contains 5 red , 6 blue and 8 green balls . 4 balls are randomly selected from the urn , find the probability that the drawn ball are 1 blue and 3 red ?
Options: a ) 1 / 969 , b ) 2 / 969 , c ) 4 / 969 , d ) 5 / 323 , e ) 21 / 789
Rationale: sample space = no . of ways 4 balls were drawn from urn = 19 c 4 = 3876 no . ways 1 blue balls and 3 red were drawn from bag = 6 c 1 * 5 c 3 = 60 probability = 60 / 3876 = 5 / 323 ans - d
Answer: d
Problem: how many positive even integers less than 100 contain digits 5 or 9 ?
Options: a ) 16 , b ) 10 , c ) 18 , d ) 19 , e ) 20
Rationale: two digit numbers : 5 at tens place : 50 , 52,54 , 56,58 9 at tens place : 90 , 92,94 , 96,98 if 5 and 9 is at units place , the number cant be even total : 5 + 5 = 10 answer b
Answer: b
Problem: farm tax is levied on the 45 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 15.125 % , d ) 27.78 % , e ) none
Rationale: "only trick n this question is to ignore 45 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 45 ) = 27.78 % and the answer is not there in the options . the correct answer is ( d ) ."
Answer: d
Problem: 30 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :
Options: a ) 33 , b ) 34 , c ) 26 , d ) 10 , e ) 19
Rationale: "explanation : let the two parts be ( 30 - x ) and x . then , 10 ( 30 - x ) + 22 x = 780 = > 12 x = 480 = > x = 40 . bigger part = ( 30 - x ) = 10 . answer : d ) 10"
Answer: d
Problem: the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 30,000 is made ?
Options: a ) 328897 , b ) 120000 , c ) 877888 , d ) 277768 , e ) 126000
Rationale: "the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 30,000 is made = 96,000 + 30,000 = rs . 1 , 26,000 answer : e"
Answer: e
Problem: johnson completes a piece of work in 10 days , vincent completes the same work in 40 days . if both of them work together , then the number of days required to complete the work is
Options: a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 12 days
Rationale: if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 10 × 40 / 50 = 8 days . b )
Answer: b
Problem: in triangle pqr , the angle q = 90 degree , pq = 4 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz
Options: a ) 1.2 cm , b ) 2.4 cm , c ) 4.8 cm , d ) 2.16 cm , e ) 3.2 cm
Rationale: "look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 4 = 8 : 10 - - > qy = 3.2 . answer : e"
Answer: e
Problem: a local elementary school has 1049 students and 9 teachers , how many students would have to be added to the school to make sure each teacher has the same amount of students in their classroom ?
Options: a ) 4 , b ) 6 , c ) 5 , d ) 1 , e ) 2
Rationale: using the rule on the divisibility of nine , we add the digits of 1049 together to get 14 . since we are doing addition , the next number that is divisible by nine would be 18 . therefore , our answer 4 ( option a )
Answer: a
Problem: the average marks of 30 students in a class is 100 . but a student mark is wrongly noted as 70 instead of 10 then find the correct average marks ?
Options: a ) a ) 78 , b ) b ) 82 , c ) c ) 98 , d ) d ) 91 , e ) e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 70 ) / 30 avg = 100 - 2 = 98 answer is c"
Answer: c
Problem: if a and b are positive real numbers , and a ^ 3 + b ^ 3 = 25 , then the greatest possible value of a is between :
Options: a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9
Rationale: if a > 3 , then a ^ 3 + b ^ 3 > 25 . the answer is a .
Answer: a
Problem: a 440 - liter solution of kola is made from 88 % water , 8 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 10 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 4.52 % . , b ) 7.5 % . , c ) 9.2 % . , d ) 10.5 % . , e ) 11 % .
Rationale: "denominator : 440 + 10 + 3.2 + 6.8 = 460 numerator : 440 ( 1 - . 88 - . 08 ) + 3.2 440 ( 0.04 ) + 3.2 17.6 + 3.2 20.8 ratio : 20.8 / 460 = 0.045 answer : a"
Answer: a
Problem: a wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule , whose length and breadth are in the ratio of 6 : 5 . what is the area of the rectangle ?
Options: a ) 65 cm 2
b ) 30 cm 2
c ) 76 cm 2
d ) 68 cm 2
e ) 46 cm 2
Rationale: the circumference of the circle is equal to the permeter of the rectangle . let l = 6 x and b = 5 x 2 ( 6 x + 5 x ) = 2 * 22 / 7 * 3.5 = > x = 1 therefore l = 6 cm and b = 5 cm area of the rectangle = 6 * 5 = 30 cm 2 answer : b
Answer: b
Problem: sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 50 marks . how many sums did sandy get correct ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 50 5 x = 110 x = 22 the answer is b ."
Answer: b
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 6 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "if the units digit of a ^ 2 is 9 , then the units digit of a is either 3 or 7 . if the units digit of ( a + 1 ) ^ 2 is 6 , then the units digit of a + 1 is either 4 or 6 . to satisfy both conditions , the units digit of a must be 3 . then a + 2 has the units digit of 5 , thus the units digit of ( a + 2 ) ^ 2 will be 5 . the answer is c ."
Answer: c
Problem: a person borrows 20000 for 6 years at 8 % p . a . simple interest . he immediately lends it to another person at 9 % p . a . for 6 years . find his gain in the transaction per year .
Options: a ) 200 , b ) 250 , c ) 210 , d ) 190 , e ) 180
Rationale: gain in 6 years = [ ( 20000 ã — 9 ã — 6 / 100 ) â ˆ ’ ( 20000 ã — 6 ã — 8 / 100 ) ] = ( 10800 â € “ 9600 ) = 1200 â ˆ ´ gain in 6 year = ( 1200 / 6 ) = 200 answer a
Answer: a
Problem: a solid yellow stripe is to be painted in the middle of a certain highway . if 1 gallon of paint covers an area of w square feet of highway , how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long ? ( 1 mile = 5,280 feet and 1 foot = 12 inches )
Options: a ) ( 5,280 mt ) / 12 w
b ) ( 5,280 pt ) / 12 m
c ) ( 5,280 pmt ) / 12
d ) ( 5,280 ) ( 12 m ) / pt
e ) ( 5,280 ) ( 12 p ) / mt
Rationale: given that : 1 gallon of paint covers an area ofwsquare feet . question : how many gallonsof paint will be needed . . . in any case you will have : ( total area in square feet ) / ( gallons per feet ) = ( total area in square feet ) / w , so w must be in the denominator : eliminate all but a and d . now , lets see where should be t : ( area in square feet ) = ( width in feet ) * ( length in feet ) - - > width = tinchesas 1 feet = 12 inchesthent inches = t / 12 feet , so ( area in square feet ) = ( t / 12 ) * ( length in feet ) , so t must be in the nominator : only a is left . answer : a .
Answer: a
Problem: what is the units digit of 23 ^ 2 * 17 ^ 2 * 39 ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the units digit of 23 ^ 2 is the units digit of 3 * 3 = 9 which is 9 . the units digit of 17 ^ 2 is the units digit of 7 * 7 = 49 which is 9 . the units digit of 39 ^ 2 is the units digit of 9 * 9 = 81 which is 1 . the units digit of 9 * 9 * 1 = 81 is 1 . the answer is a ."
Answer: a
Problem: if the probability of rain on any given day in chicago during the summer is 50 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 8 , inclusive ?
Options: a ) 1 / 32 , b ) 2 / 25 , c ) 5 / 16 , d ) 8 / 25 , e ) 3 / 4
Rationale: "from july 4 to july 8 , we have total of 5 days . prob of raining on exactly 3 days = 5 c 3 ∗ ( 1 / 2 ) 3 ∗ ( 1 / 2 ) 25 c 3 ∗ ( 1 / 2 ) 3 ∗ ( 1 / 2 ) 2 = 5 / 16 ans : c"
Answer: c
Problem: if m is a positive integer and m ^ 2 is divisible by 24 , then the largest positive integer that must divide m is ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 16
Rationale: "m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 8 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is c but if m = 48 then answer should be 16 . is the question right ? or am i missing some thing ? c"
Answer: c
Problem: a flagstaff 17.5 m high casts a shadow of length 40.25 m . the height of the building , which casts a shadow of length 28.75 m under similar conditions will be ?
Options: a ) 10 m , b ) 12.5 m , c ) 12 m , d ) 13 m , e ) 14 m
Rationale: "let the height of the building x metres . less lengthy shadow , less in the height ( direct proportion ) 40.25 : 28.75 : : 17.5 : x 40.25 x x = 28.75 x 17.5 x = 28.75 x 17.5 / 40.25 x = 12.5 answer : b"
Answer: b
Problem: average monthly income of a family of 4 earning members was rs . 840 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?
Options: a ) rs . 692.80 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1410 , e ) none
Rationale: answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 840 x 4 - 650 x 3 rs . = 1410 rs . correct option : d
Answer: d
Problem: x and y are two towns . ganesh covers the distance from x to y at an average speed of 43 km / hr . however , he covers the distance from y to x at an average speed of 34 km / hr . his average speed during the whole journey in km / hr . is :
Options: a ) 34 , b ) 43 , c ) 40 , d ) 38 , e ) 29
Rationale: "solution : average speed = 2 xy / x + y = 2 * 43 * 34 / 43 + 34 = 2924 / 77 = 37.974 . . . = 38 answer : d"
Answer: d
Problem: what is the measure of the angle q made by the diagonals of the any adjacent sides of a cube .
Options: a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90
Rationale: "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be q = 60 . c"
Answer: c
Problem: visitors to show were charged rs . 15 each on the first day . rs . 7.50 on the second day , rs . 2.50 on the third day and total attendance on the 3 days were in ratio 2 : 5 : 13 respectively . the average charge per person for the whole show is ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: 2 : 5 : 13 2 x 5 x 13 x 15 7.5 2.5 30 x + 37.5 x + 32.5 x = 100 x / 20 x average = 5 answer : c
Answer: c
Problem: hillary and eddy are climbing to the summit of mt . everest from a base camp 4,900 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 900 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?
Options: a ) 10.0 , b ) 11.0 , c ) 13.0 , d ) 12.0 , e ) 14.0
Rationale: "solution : h stopped 900 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . d"
Answer: d
Problem: a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 70 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?
Options: a ) 1 : 120 , b ) 67 : 120 , c ) 67 : 8 , d ) 8 : 120 , e ) 1 : 2
Rationale: "first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 20 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.70 = $ 36 cost = 36 / 1.7 = 360 / 12 = $ 30 if he wants a 70 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 21.17 well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 21.17 / 33 = 120 / 187 of a liter . if milk is 120 / 87 of the liter , then water is 67 / 187 of the liter , and the ratio of water to milk is 67 : 120 . answer choice ( b )"
Answer: b
Problem: the price of a book is increased from $ 300 to $ 390 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 35 % , e ) 45 %
Rationale: "explanation : change in the price = rs 390 – rs 300 = rs 90 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 90 / 300 ) * 100 = 30 % c"
Answer: c
Problem: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 1170 , what will be b ' s share of the earnings ?
Options: a ) $ 390 , b ) $ 520 , c ) $ 1080 , d ) $ 1170 , e ) $ 630
Rationale: "explanatory answer a , b and c will share the amount of $ 1170 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 1170 will be 4 : 3 : 2 . hence , b ' s share will be 3 * 1170 / 9 = 390 . correct choice is ( a )"
Answer: a
Problem: 12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 27 cm height . what is the diameter of each sphere ?
Options: a ) 2 cm , b ) 4 cm , c ) 6 cm , d ) 8 cm , e ) 10 cm
Rationale: "volume of cylinder = pi * r ^ 2 * h volume of a sphere = 4 * pi * r ^ 3 / 3 12 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 16 = 27 cm ^ 3 r = 3 cm d = 6 cm the answer is c ."
Answer: c
Problem: what is the units digit of 32 ! + 50 ! + 4 ! + 4 ! ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 4 + 4 = 8 the units digit is 8 . the answer is e ."
Answer: e
Problem: if jack walked 8 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?
Options: a ) 4 , b ) 4.5 , c ) 6 , d ) 6.4 , e ) 15
Rationale: "distance walked in 1 hour and 15 mins = 8 miles speed per hour = distance / time = 8 / ( 5 / 4 ) = 6.4 miles per hour answer 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 , 80 percent of books that were loaned out are returned and there are 67 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: "there are 8 books less ( 75 - 68 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 40 answer d"
Answer: d
Problem: if a farmer wants to plough a farm field on time , he must plough 120 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 600 , b ) 490 , c ) 720 , d ) 435 , e ) 679
Rationale: let x be the number of days in the initial plan . therefore , the whole field is 120 ⋅ x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 120 x = 85 ( x + 2 ) + 40 35 x = 210 x = 6 so the farmer planned to have the work done in 6 days , and the area of the farm field is 120 ⋅ 6 = 720 hectares correct answer c
Answer: c
Problem: for each color copy , print shop x charges $ 1.20 and print shop y charges $ 1.70 . how much greater is the charge for 40 color copies at print shop y than at print shop x ?
Options: a ) $ 14 , b ) $ 16 , c ) $ 18 , d ) $ 20 , e ) $ 22
Rationale: "the difference in the two prices is $ 1.70 - $ 1.20 = $ 0.50 for each color copy . each color copy will cost an extra $ 0.50 at print shop y . 40 * $ 0.50 = $ 20 the answer is d ."
Answer: d
Problem: in a school of 300 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) 54 , b ) 63 , c ) 70 , d ) 42 , e ) 31
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 300 * 18 / 100 = 54 answer : a"
Answer: a
Problem: a number x is 12 times another number y . the percentage that y is less than x is
Options: a ) 91.6 % , b ) 87.5 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 12 . then y = 1 is less than x = 12 by ( 12 - 1 ) / 12 * 100 = 11 / 12 * 100 = 91.6 % . answer : a ."
Answer: a
Problem: a train 90 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 5 , e ) 4
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 90 * 3 / 55 = 5 sec . answer d"
Answer: d
Problem: the average age of a family of 5 members is 20 years . if the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member ?
Options: a ) 13.5 , b ) 14 , c ) 15 , d ) 12.5 , e ) none
Rationale: solution : at present the total age of the family = 5 * 20 = 100 . the total age of the family at the time of the birth of the youngest member , = [ 100 − 10 − ( 10 * 4 ) ] = 50 . therefore , average age of the family at the time of birth of the youngest member , = 50 / 4 = 12.5 . answer : option d
Answer: d
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with five times the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.80 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.27 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 5 units of water was used to make 6 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 6 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 6 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 6 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.8 = 6 * x - - > x = $ 0.27 . answer : b ."
Answer: b
Problem: how many unique positive odd integers less than 90 are equal to the product of a positive multiple of 5 and an odd number ?
Options: a ) 4 , b ) 9 , c ) 11 , d ) 12 , e ) 15
Rationale: "the question basically asks how many positive odd integers less than 90 are odd multiples of 5 so we have 5 , 15,25 , 35,45 , 55,65 , 75,85 = 9 ans b"
Answer: b
Problem: if # is an operation which results in adding the digits of integer until a single digit is left , what is the probability that a number picked up in first 90 positive integers will have the result of # as an odd digit ? ( example 99 = 9 + 9 = 18 = 1 + 8 = 9 , so # = 9 )
Options: a ) 4 / 10 , b ) 4 / 9 , c ) 1 / 2 , d ) 6 / 10 , e ) 5 / 9
Rationale: first of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90 . that will be 17 ( 8 + 9 + 17 ) why did i calculate this ? i will come to that in a moment . so to get an odd digit by carrying out the operation # , the sum of the digits of the integer should be 1 , 3 , 5 , 7 , 9 , 10 , 12 , 14 , and 16 ( why not 18 ? because we know the maximum sum can be 17 ) number of integers , whose digits add to 1 : 1 and 10 = 2 number of integers , whose digits add to 3 : 3 , 12 , 21 , 30 = 4 number of integers , whose digits add to 5 : 5 , 14 , 23 , 32 , 41 , 50 = 6 number of integers , whose digits add to 7 : 7 , 16 , 25 , 34 , 43 , 52 , 61 , 70 = 8 number of integers , whose digits add to 9 : 10 multiples of 9 up to 90 = 10 number of integers , whose digits add to 10 : 19 , 28 , 37 , 46 , 55 , 64 , 73 , 82 = 8 number of integers , whose digits add to 12 : 39 , 48 , 57 , 66 , 75 , 84 = 6 number of integers , whose digits add to 14 : 59 , 68 , 77 , 86 = 4 number of integers , whose digits add to 16 : 79 , 88 = 2 so in total there are 2 + 4 + 6 + 8 + 10 + 8 + 6 + 4 + 2 = 50 such numbers probability = 50 / 90 = 5 / 9 correct answer e
Answer: e
Problem: operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 6 , when a # b = 100 ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 11 , e ) 17
Rationale: "official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 6 = 10 / 2 + 6 = 11 . the correct answer is d ."
Answer: d
Problem: jerry and michelle play a card game . in the beginning of the game they have an equal number of cards . each player , at her turn , gives the other a third of her cards . michelle plays first , giving jerry a third of her cards . jerry plays next , and michelle follows . then the game ends . jerry ended up with 14 more cards than michelle . how many cards did each player have originally ?
Options: a ) 27 , b ) 30 , c ) 34 , d ) 36 , e ) 38
Rationale: game michelle jerry michelle initially 2727 assume after game 1 1836 after game 2 3024 after game 3 2034 now jerry has 14 cards more than michelle . so the answer is a
Answer: a
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 50 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 411 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 50 ) = 21 + 390 = > 411 hence answer will be ( e )"
Answer: e
Problem: a circular swimming pool is surrounded by a concrete wall 4 feet wide . if the area of the wall is 11 / 25 of the area of the pool , then the radius of the pool in feet is ?
Options: a ) 22
b ) 20
c ) 9
d ) 8
e ) 1
Rationale: let the radius of the pool be r . then area of the wall and pool = π ( r + 4 ) 2 π ( r + 4 ) 2 area of the pool = π ( r ) 2 π ( r ) 2 area of the wall = π ( r + 4 ) 2 − π ( r ) 2 π ( r + 4 ) 2 − π ( r ) 2 given π ( r + 4 ) 2 − π ( r ) 2 π ( r + 4 ) 2 − π ( r ) 2 = 1125 ( π r 2 ) 1125 ( π r 2 ) r 2 + 8 r + 16 − r 2 = 1125 r 2 r 2 + 8 r + 16 − r 2 = 1125 r 2 11 r 2 − 200 r − 400 = 011 r 2 − 200 r − 400 = 0 solving r = 20 answer : b
Answer: b
Problem: the population of a town increases 25 % and 40 % respectively in two consecutive years . after the growth the present population of the town is 1750 . then what is the population of the town 2 years ago ?
Options: a ) a ) 750 , b ) b ) 800 , c ) c ) 850 , d ) d ) 900 , e ) e ) 950
Rationale: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1750 * 100 / 125 * 100 / 140 = 1000 answer : option b"
Answer: b
Problem: a truck travels 20 miles due north , 30 miles due east , and then 20 miles due north . how many miles is the truck from the starting point ?
Options: a ) 20.3 , b ) 44.7 , c ) 50 , d ) 70 , e ) 120
Rationale: we have two right angle triangles with sides 20 and 15 the distance between starting and end point = sum of the hypotenuse of both the triangles . hypotenuse = [ 400 + 225 ] ^ ( 1 / 2 ) = 25 hence the total distance between end point and starting point = 25 + 25 = 50 correct option : c
Answer: c
Problem: find the area of a parallelogram with base 22 cm and height 14 cm ?
Options: a ) 298 cm 2 , b ) 384 cm 2 , c ) 308 cm 2 , d ) 286 cm 2 , e ) 276 cm 2
Rationale: "area of a parallelogram = base * height = 22 * 14 = 308 cm 2 answer : c"
Answer: c
Problem: the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 4180 . what was his original salary ?
Options: a ) 2277 , b ) 2999 , c ) 4000 , d ) 2651 , e ) 1971
Rationale: "x * ( 110 / 100 ) * ( 95 / 100 ) = 4180 x * ( 11 / 10 ) * ( 1 / 100 ) = 44 x = 4000 answer : c"
Answer: c
Problem: the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum t of all the digits of the integers from 0 to 99 inclusive ?
Options: a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just t = 900 : the answer is c ."
Answer: c
Problem: in δ pqs above , if pq = 2 and ps = 3 , then
Options: a ) 3 / 2 , b ) 12 / 5 , c ) 16 / 5 , d ) 15 / 4 , e ) 20 / 3
Rationale: there are two ways to calculate area of pqs . area remains same , so both are equal . 2 * 3 / 2 = pr * 4 / 2 pr = 3 / 2 a
Answer: a
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 11000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 14 , b ) 21 , c ) 22 , d ) 23 , e ) none
Rationale: "sol . let the total number of workers be x . then , 8000 x = ( 10000 × 7 ) + 6000 ( x – 7 ) ‹ = › 2000 x = 28000 ‹ = › x = 14 . answer a"
Answer: a
Problem: a man whose speed is 8 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 3 kmph , find his average speed for the total journey ?
Options: a ) 1 kmph , b ) 5 kmph , c ) 6 kmph , d ) 4 kmph , e ) 6.8 kmph
Rationale: "explanation : speed of man = 8 kmph speed of stream = 3 kmph speed in downstream = 11 kmph speed in upstream = 5 kmph average speed = ( 2 x 11 x 5 ) / 16 = 6.8 kmph . answer : e"
Answer: e
Problem: of 30 applicants for a job , 9 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 10 , c ) 9 , d ) 7 , e ) 5
Rationale: "b . 10 30 - 3 = 27 27 - 9 - 18 = - 10 then 5 are in the intersection between 4 years experience and degree . answer b"
Answer: b
Problem: a fruit seller had some apples . he sells 50 % apples and still he has 5000 . originally he had how many apples ?
Options: a ) 10000 , b ) 15200 , c ) 11005 , d ) 12540 , e ) 12450
Rationale: "suppose originally he had x apples then ( 100 - 50 ) % of x = 5000 50 x / 100 = 5000 x = 10000 answer is a"
Answer: a
Problem: in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 9 feet between each tree . how many trees can be planted if the road is 151 feet long ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 16
Rationale: "let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 14 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 9 feet spaces will be t - 1 . then , the length of sidewalk required for 9 feet spaces will be 9 * ( t - 1 ) it is given that total lenght of sidewalk is 151 feet . or 9 ( t - 1 ) + t = 151 or 9 t - 9 + t = 151 or 10 t = 160 or t = 16 answer : - e"
Answer: e
Problem: the slant height of a cone is 35 cm and radius of the base is 14 cm , find the curved surface of the cone .
Options: a ) 4150
b ) 1780
c ) 1540
d ) 1500
e ) 6100
Rationale: π * 14 * 35 = 1540 answer : c
Answer: c
Problem: if a ã — b = 2 a - 3 b + ab , then 3 ã — 2 + 2 ã — 3 is equal to :
Options: a ) 7 , b ) 8 , c ) 9 , d ) 25 , e ) 26
Rationale: "explanation : 3 ã — 2 + 2 ã — 3 = ( 2 ã — 3 - 3 ã — 2 + 2 ã — 3 ) + ( 2 ã — 2 - 3 ã — 3 + 2 ã — 3 ) = ( 6 + 4 - 9 + 6 ) = 7 . answer : a"
Answer: a
Problem: a 20 % stock yielding 12 % is quoted at :
Options: a ) rs . 83.33 , b ) rs . 167 , c ) rs . 112 , d ) rs . 120 , e ) rs . 140
Rationale: "income of rs 12 on investment of rs 100 income of rs 20 on investment of ? = ( 20 * 100 ) / 12 = 167 answer : b"
Answer: b
Problem: if the length of the sides of two cubes are in the ratio 6 : 1 , what is the ratio of their total surface area ?
Options: a ) 6 : 1 , b ) 12 : 1 , c ) 24 : 1 , d ) 36 : 1 , e ) 72 : 1
Rationale: "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 6 x ) ^ 2 = 216 x ^ 2 . the ratio of surface areas is 36 : 1 . the answer is d ."
Answer: d
Problem: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 12 seconds . the length of the faster train is
Options: a ) 80 m , b ) 270 m , c ) 120 m , d ) 180 m , e ) none
Rationale: "solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 12 ) m = 270 m . answer b"
Answer: b
Problem: the ratio of number of boys and girls in a school is 2 : 5 . if there are 350 students in the school , find the number of girls in the school ?
Options: a ) 150 , b ) 250 , c ) 300 , d ) 370 , e ) 280
Rationale: "let the number of boys and girls be 2 x and 5 x total students = 350 number of girls in the school = 5 * 350 / 7 = 250 answer is b"
Answer: b
Problem: if the perimeter of a rectangular garden is 1800 m , its length when its breadth is 400 m is ?
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) 900
Rationale: 2 ( l + 400 ) = 1800 = > l = 500 m answer : a
Answer: a
Problem: solve for x and check : - 3 x = 12
Options: a ) - 4 , b ) - 2 , c ) 1 , d ) 3 , e ) none of these
Rationale: "solution : dividing each side by - 3 , we obtain ( - 3 x / - 3 ) = ( 12 / - 3 ) therefore : x = - 4 check : - 3 x = 12 ( - 3 * - 4 ) = 12 12 = 12 answer : a"
Answer: a
Problem: sarah is driving to the airport . after driving at 15 miles per hour for one hour , she realizes that if she continues at that same average rate she will be an hour late for her flight . she then travels 60 miles per hour for the rest of the trip , and arrives 30 minutes before her flight departs . how many miles did she drive in all ?
Options: a ) 45 , b ) 175 , c ) 210 , d ) 245 , e ) 280
Rationale: after driving at 15 miles per hourfor one hour , this distance left to cover is d - 15 . say this distance is x miles . now , we know that the difference in time between covering this distance at 15 miles per hour and 60 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 15 - x / 60 = 3 / 2 - - > 4 x / 60 - x / 60 = 3 / 2 - - > 3 x / 60 = 3 / 2 - - > x = 30 . total distance = x + 15 = 45 miles . answer : a
Answer: a
Problem: on dividing a number by 48 , we get 29 as remainder . on dividing the same number by 8 , what will be the remainder ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "number = 48 x + 29 ( ∵ since the number gives 29 as remainder on dividing by 48 ) = ( 6 × 8 × x ) + ( 3 × 8 ) + 5 hence , if the number is divided by 8 , we will get 5 as remainder . answer : d"
Answer: d
Problem: a shopkeeper sells 600 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) 12 , b ) 27 , c ) 29 , d ) 35 , e ) 21
Rationale: sp per metre = 18000 / 600 = rs . 40 loss per metre = rs . 5 cp per metre = 40 + 5 = rs . 45 . answer : d
Answer: d
Problem: obra drove 140 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 6.67 % , b ) 12.5 % , c ) 18.75 % , d ) 29.16 % , e ) 33.3 %
Rationale: "area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 140 π / 480 π = 29.16 % hence , answer is d ."
Answer: d
Problem: a certain number of men can finish a piece of work in 100 days . if there were 10 men less , it would take 10 days more for the work to be finished . how many men were there originally ?
Options: a ) 120 , b ) 105 , c ) 115 , d ) 110 , e ) 140
Rationale: originally let there be x men . less men , more days ( indirect proportion ) therefore ( x - 10 ) : x : : 100 : 110 = ( x - 10 ) x 110 - x ( 100 ) = 10 x = 1100 x = 110 answer is d .
Answer: d
Problem: find the cost of fencing around a circular field of diameter 16 m at the rate of rs . 3 a meter ?
Options: a ) 150.84 , b ) 160.6 , c ) 150.45 , d ) 160.99 , e ) 180.4
Rationale: "2 * 22 / 7 * 8 = 50.28 50.28 * 3 = rs . 150.84 answer : a"
Answer: a
Problem: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 3200 . with the help of c , they completed the work in 3 days . how much is to be paid to c
Options: a ) rs . 300 , b ) rs . 400 , c ) rs . 500 , d ) rs . 600 , e ) none of these
Rationale: "explanation : c ' s 1 day ' s work = 1 / 3 − ( 1 / 6 + 1 / 8 ) = ( 1 / 3 − 7 / 24 ) = 1 / 24 a : b : c = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ′ sshare = 1 / 8 ∗ 3200 = 400 option b"
Answer: b
Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 30 is a prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 30 , b ) 1 / 30 , c ) 8 / 30 , d ) 3 / 30 , e ) 7 / 30
Rationale: "let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23,29 } n ( x ) = 10 , n ( s ) = 30 hence , the required probability is 10 / 30 . answer : c"
Answer: c