Cheukting/mathqa huggingface dataset:
Question (other): a bag contains 5 green balls and 8 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?
Options: a ) 3 / 7 , b ) 6 / 11 , c ) 12 / 21 , d ) 19 / 39 , e ) 29 / 49
Rationale: "the total number of ways to draw two balls is 13 c 2 = 78 the number of ways to draw two green balls is 5 c 2 = 10 the number of ways to draw two white balls is 8 c 2 = 28 p ( two balls of the same colour ) = 38 / 78 = 19 / 39 the answer is d ."
Answer: d
Question (gain): if 60 % of 3 / 5 of a number is 36 , then the number is ?
Options: a ) 80 , b ) 100 , c ) 75 , d ) 90 , e ) none of these
Rationale: "let the number be x . then 60 % of 3 / 5 of x = 36 60 / 100 * 3 / 5 * x = 36 x = ( 36 * 25 / 9 ) = 100 required number = 100 . correct option : b"
Answer: b
Question (gain): a sum of money amounts to rs . 9800 after 5 years and rs . 12005 after 8 years at the same rate of simple interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 15 % , c ) 12 % , d ) 22 % , e ) 19 %
Rationale: "s . i . for 3 years = ( 12005 - 9800 ) = rs . 2205 s . i . for 5 years = rs . 2205 / 3 * 5 = rs . 3675 . principal = ( 9800 - 3675 ) = rs . 6125 hence , rate = ( 100 * 3675 ) / ( 6125 * 5 ) = 12 % answer : c"
Answer: c
Question (gain): two years ago , ram put $ 1,000 into a savings account . at the end of the first year , his account had accrued $ 200 in interest bringing his total balance to $ 1,200 . the next year , his account balance increased by 20 % . at the end of the two years , by what percent has ram ' s account balance increased from his initial deposit of $ 1,000 ?
Options: a ) 19 % , b ) 30 % , c ) 42 % , d ) 45 % , e ) 25 %
Rationale: "investment 1000 dollars 1 st year total gained = 200 total amount end of first year = 1200 second year account increased by 20 % = 1200 * 0.2 = 240 therefore total amount by second year end = 1420 so total percentage increase in money = ( 1420 - 1000 ) * 100 / 1000 = 42 % correct answer c = 42 %"
Answer: c
Question (gain): in a college , 1 percent of students hate math , 2 percent of students hate english , 1 percent hate french and 4 percent hate german . can you find out the percentage of students who hate all 4 subjects ?
Options: a ) 8 % , b ) 5 % , c ) 7 % , d ) 12 % , e ) 19 %
Rationale: a 8 % of student hate all four subjects .
Answer: a
Question (physics): walking at 6 / 7 th of his usual speed , a man is 25 mins too late . his usual time is
Options: a ) 7.5 hrs , b ) 1.5 hrs , c ) 2.5 hrs , d ) 1.67 hrs , e ) 2.67 hrs
Rationale: "as the distance is same s * t = 6 / 7 s * ( t + 25 ) solving this we get t = 150 sec 150 / 60 = 2.5 hrs answer : c"
Answer: c
Question (physics): amit and ananthu can do a work in 15 days and 30 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?
Options: a ) 28 days , b ) 20 days , c ) 23 days , d ) 25 days , e ) 27 days
Rationale: "amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 30 ananthu can do work in = 4 / 5 * 30 = 24 days so total days = 24 + 3 = 27 days answer : e"
Answer: e
Question (general): if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 39 , find the value of ab .
Options: a ) 15 , b ) 8 , c ) 4 , d ) 10 , e ) 3
Rationale: "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 39 - 9 = 30 ab = 15 . answer is a ."
Answer: a
Question (gain): a cylinder of height h is 2 / 3 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ?
Options: a ) 25 % , b ) 50 % , c ) 60 % , d ) 80 % , e ) 90 %
Rationale: "basically we can disregard the radius is 25 % information , as we are only asked about the height of the original and the new cylinder . this is becausethe new cylinder is 3 / 5 fullmeans the same as that it ' s height is 3 / 5 . original cylinder 2 / 3 new cylinder 3 / 5 so 3 / 5 / 2 / 3 = 3 / 5 * 3 / 2 = 0.90 or 90 % . answer e"
Answer: e
Question (other): a and b together have $ 1210 . if of a ' s amount is equal to of b ' s amount , what is the ratio between a and b ?
Options: a ) 2 : 3 , b ) 3 : 2 , c ) 4 : 5 , d ) 5 : 3 , e ) can not be determined
Rationale: "( 4 / 15 ) a = ( 2 / 5 ) b a = ( ( 2 / 15 ) * ( 15 / 4 ) ) b a = ( 3 / 2 ) b a / b = 3 / 2 a : b = 3 : 2 option b"
Answer: b
Question (geometry): the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 294 sq . cm , what is the width of the rectangle ?
Options: a ) 10 cm , b ) 12 cm , c ) 14 cm , d ) 16 cm , e ) 18 cm
Rationale: "2 l + 2 w = 5 w l = 3 w / 2 w * l = 294 3 w ^ 2 / 2 = 294 w ^ 2 = 196 w = 14 the answer is c ."
Answer: c
Question (physics): express a speed of 108 kmph in meters per second ?
Options: a ) 30 mps , b ) 76 mps , c ) 26 mps , d ) 97 mps , e ) 16 mps
Rationale: "108 * 5 / 18 = 30 mps answer : a"
Answer: a
Question (other): the ratio of the two natural numbers is 6 : 5 . if a certain number is subtracted to both the numbers , the ratio becomes 5 : 4 . if the larger number exceeds the smaller number by 5 , find the number subtracted ?
Options: a ) 8 , b ) 5 , c ) 15 , d ) 22 , e ) 6
Rationale: let the two numbers be 6 x and 5 x . let the numbers subtracted to both so that their ratio becomes 5 : 4 be k . ( 6 x - k ) / ( 5 x - k ) = 5 / 4 = > 24 x - 4 k = 25 x - 5 k = > k = x . 6 x - 5 x = 5 = > x = 5 k = x = 5 . answer : b
Answer: b
Question (gain): 200 is what percent of 50 ?
Options: a ) 0.2 % , b ) 2 % , c ) 5 % , d ) 20 % , e ) 400 %
Rationale: "200 = x * 50 / 100 x = 400 % ans ; e"
Answer: e
Question (general): a big container is 30 % full with water . if 54 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 120 liters
Rationale: "a big container is 30 % full with water and after 54 liters of water is added , the container becomes 75 % full . hence these 54 liters account for 45 % of the container , which means that the capacity of it is 54 / 0.45 = 120 liters . or : if the capacity of the container is x liters then : 0.3 x + 54 = 0.75 x - - > x = 120 liters . answer : e"
Answer: e
Question (gain): at what rate percent per annum will the simple interest on a sum of money be 6 / 5 of the amount in 10 years ?
Options: a ) 4 % , b ) 7 % , c ) 9 % , d ) 3 % , e ) 12 %
Rationale: "let sum = x . then , s . i . = 6 x / 5 , time = 10 years . rate = ( 100 * 6 x ) / ( x * 5 * 10 ) = 12 % answer : e"
Answer: e
Question (general): if x is real , find the maximum value of the expression - 2 x ^ 2 + 5 x + 7 .
Options: a ) 6.125 , b ) 8.125 , c ) 10.125 , d ) 12.125 , e ) 14.125
Rationale: this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 5 x + 7 = ( - 2 x + 7 ) ( x + 1 ) the roots are 7 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 1.25 the maximum value is - 2 ( 1.25 ) ^ 2 + 5 ( 1.25 ) + 7 = 10.125 the answer is c .
Answer: c
Question (geometry): the perimeter of one face of a cube is 40 cm . its volume will be :
Options: a ) 125 cm 3 , b ) 400 cm 3 , c ) 250 cm 3 , d ) 1000 cm 3 , e ) none of these
Rationale: "explanation : edge of cude = 40 / 4 = 10 cm volume = a * a * a = 10 * 10 * 10 = 1000 cm cube option d"
Answer: d
Question (other): a starts business with rs . 3500 and after 10 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?
Options: a ) 24887 , b ) 20778 , c ) 23788 , d ) 31500 , e ) 2811
Rationale: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 10 = 2 months . so there profit ratio = ( 3500 ã — 12 ) : ( 2 x ) = 2 : 3 â ‡ ’ x = 31500 answer : d"
Answer: d
Question (gain): if the personal income tax rate is lowered from 45 % to 30 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 48000 ?
Options: a ) $ 3500 , b ) $ 5000 , c ) $ 3150 , d ) $ 7200 , e ) $ 10000
Rationale: saving = ( 45 - 30 ) % of 48000 = 7200 . answer : d
Answer: d
Question (physics): a trader sells 45 meters of cloth for rs . 4500 at the profit of rs . 12 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 80 , b ) rs . 85 , c ) rs . 88 , d ) rs . 100 , e ) none of these
Rationale: sp of 1 m of cloth = 4500 / 45 = rs . 100 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 100 - rs . 12 = rs . 88 . answer : c
Answer: c
Question (general): subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 10 pages .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 4 , e ) 16
Rationale: "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 10 / 2.5 ) = 4 hrs answer : d"
Answer: d
Question (physics): two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 16 seconds , the speed of each train ( in km / hr ) is
Options: a ) 42 , b ) 27 , c ) 28 , d ) 20 , e ) 24
Rationale: "explanation : distance covered = 120 + 120 = 240 m time = 16 s let the speed of each train = v . then relative speed = v + v = 2 v 2 v = distance / time = 240 / 16 = 15 m / s speed of each train = v = 15 / 2 = 7.5 m / s = 7.5 × 36 / 10 km / hr = 27 km / hr answer : option b"
Answer: b
Question (general): how much is 80 % of 60 is greater than 4 / 5 of 25 ?
Options: a ) 15 , b ) 28 , c ) 16 , d ) 12 , e ) 73
Rationale: "( 80 / 100 ) * 60 â € “ ( 4 / 5 ) * 25 48 - 20 = 28 answer : b"
Answer: b
Question (gain): a 6 litre sol is 30 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?
Options: a ) a . 0.6 , b ) b . 1 , c ) c . 2.1 , d ) d . 3 , e ) e . 2.4
Rationale: 30 % of 6 = 1.8 50 % of 6 = 3 shortage is 1.2 so we need to have 1.2 / 50 % to get 50 % alcohol content . = 2.4 e
Answer: e
Question (physics): a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 470 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 400 , b ) 475 , c ) 550 , d ) 560 , e ) 700
Rationale: "let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 470 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 770 a + b + c = 70 per hour so for eight hrs = 70 * 8 = 560 = answer = d"
Answer: d
Question (physics): can you find a 7 digit number which describes itself . the first digit is the number of zeros in the number . the second digit is the number of ones in the number , etc . for example , in the number 21200 , there are 2 zeros , 1 one , 2 twos , 0 threes and 0 fours .
Options: a ) 4211000 , b ) 1211000 , c ) 5211000 , d ) 2211000 , e ) 3211000
Rationale: e 3211000
Answer: e
Question (physics): what decimal fraction is 50 ml of a litre ?
Options: a ) . 5 , b ) . 05 , c ) . 05 , d ) 0.05 , e ) none of these
Rationale: "answer required fraction = 50 / 1000 = 5 / 100 = . 05 correct option : b"
Answer: b
Question (physics): gary ’ s gas station serves an average of 13 cars per hour on saturdays , 10 cars per hour on sundays , and 9 cars per hour on all other days of the week . if the station is open from 6 a . m . to 10 p . m . every day , how many cars does gary ’ s station serve over the course of a typical week ?
Options: a ) 1,088 , b ) 1,200 , c ) 1,240 , d ) 1,280 , e ) 1,320
Rationale: "6 a . m . to 10 p . m . = 16 hours number of cars serviced on weekdays = ( 16 * 9 * 5 ) number of cars serviced on saturday = ( 16 * 13 ) number of cars serviced on sunday = ( 16 * 10 ) number of cars served in a week = 16 ( 45 + 13 + 10 ) = 16 * 68 = 1088 answer : a"
Answer: a
Question (gain): a man ' s speed with the current is 15 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is
Options: a ) 8.5 km / hr , b ) 9 km / hr , c ) 10 km / hr , d ) 12.5 km / hr , e ) none
Rationale: sol . man ' s rate in still in water = ( 15 - 2.5 ) km / hr = 12.5 km / hr . man ' s rate against the current = ( 12.5 - 2.5 ) km / hr = 10 km / hr . answer c
Answer: c
Question (physics): in what time will a train 100 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 2.8 sec , c ) 8.5 sec , d ) 2.2 sec , e ) 4.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 100 / 40 = 2.5 sec . answer : a"
Answer: a
Question (general): if r is a positive integer , and r / 15 = 8.2 , what is the remainder when r is divided by 15 ?
Options: a ) a . 1 , b ) b . 2 , c ) c . 3 , d ) d . 4 , e ) e . 8
Rationale: if r were a multiple of 15 , the quotient r / 15 would be an integer . the fact that it ' s a decimal tells us that 15 goes into r eight whole times and some decimal part of a time . this decimal part , 0.2 is the remainder divided by the divisor . let b be the remainder . b / 15 = 0.2 = 1 / 5 b = ( 15 ) * ( 1 / 5 ) = 3 answer = ( c )
Answer: c
Question (general): working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 15 , 12 , and 18 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 4 / 15 , b ) 1 / 2 , c ) 15 / 22 , d ) 25 / 12 , e ) 11 / 4
Rationale: "the time it takes printer x is 15 hours . the combined rate of y and z is 1 / 12 + 1 / 18 = 5 / 36 the time it takes y and z is 36 / 5 the ratio of times is 15 / ( 36 / 5 ) = 5 * 15 / 36 = 25 / 12 the answer is d ."
Answer: d
Question (general): what is the 20 - fifth decimal to the right in the fraction 10 / 11 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: 10 / 11 = 0.9090909090 . . . the odd - numbered decimal places are 9 . the answer is e .
Answer: e
Question (physics): one cutting machine cuts 100 metal bars in 30 minutes . another machine does the same job in 30 seconds . what time will it take if both machines are put on the same work ?
Options: a ) 25.0 seconds , b ) 29.5 seconds , c ) 30.0 seconds , d ) 30.5 seconds , e ) 30.7 seconds
Rationale: by guess it is clear that the time taken will be less than 30 seconds and very near to it . therefore , answer 29.5 seconds will be correct . answer - b
Answer: b
Question (general): what is the average ( arithmetic mean ) of the numbers 16 , 17 , 17 , 18 , 19 , 19 and 20 ?
Options: a ) 18 , b ) 17 , c ) 16 , d ) 15 , e ) 19
Rationale: "{ 16 , 17 , 17 , 18 , 19 , 19 , 20 } = { 18 - 2,18 - 1,18 - 1 , 18 , 18 + 1 , 18 + 1,18 + 2 } - - > the average = 18 . answer : a ."
Answer: a
Question (general): the sum of 5 th and 21 th term of a . p . is equal to the sum of 8 th , 15 th and 13 th term . find the term which is 0
Options: a ) 11 , b ) 10 , c ) 12 , d ) 13 , e ) 14
Rationale: "t 5 + t 21 = t 8 + t 15 + t 13 = > a + 4 d + a + 20 d = a + 7 d + a + 14 d + a + 12 d = > a + 9 d = 0 = > t 10 = 0 i . e . 10 th term is zero . answer : b"
Answer: b
Question (gain): what is 0.01 percent of 15,356 ?
Options: a ) 0.15356 , b ) 1.5356 , c ) 15.356 , d ) 0.015356 , e ) 0.0015356
Rationale: since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.01 ( 1 / 100 ) 15,356 . the answer is 1.5356 . hence , the correct answer is b .
Answer: b
Question (general): evaluate : 12 + sqrt ( - 5 + 7 ã — 8 ã · 4 ) = ?
Options: a ) 90 , b ) 91 , c ) 92 , d ) 93 , e ) 94
Rationale: "according to order of operations , inner brackets first where 7 x 8 ã · 4 is first calculated since it has a multiplication and a division . 7 x 8 ã · 4 = 56 ã · 4 = 14 hence 12 + sqrt ( - 5 + 7 ã — 8 ã · 4 ) = 12 + sqrt ( - 5 + 14 ) = 12 + sqrt ( 9 ) = 12 + 81 = 93 correct answer d ) 93"
Answer: d
Question (general): in 5 football games thus far this season , barry has run for 98 , 107 , 85 , 89 , and 91 yards . at a minimum , how many yards n will he need to gain this sunday if he wants to keep his season average above 100 yards ?
Options: a ) 101 , b ) 116 , c ) 130 , d ) n = 131 , e ) n = 141
Rationale: sorry the answer n = 131 is d .
Answer: d
Question (general): ab + cd = jjj , where ab and cd are two - digit numbers and jjj is a 3 digit number ; a , b , c , and d are distinct positive integers . in the addition problem above , what is the value of c ?
Options: a ) 1 , b ) 3 , c ) 7 , d ) 9 , e ) can not be determined
Rationale: ab and cd are two digit integers , their sum can give us only one three digit integer of a kind of jjj it ' s 111 . so , a = 1 . 1 b + cd = 111 now , c can not be less than 9 , because no to digit integer with first digit 1 ( mean that it ' s < 20 ) can be added to two digit integer less than 90 to have the sum 111 ( if cd < 90 meaning c < 9 cd + 1 b < 111 ) - - > c = 9 answer : d .
Answer: d
Question (general): 8 friends went to a hotel and decided to pay the bill amount equally . but 7 of them could pay rs . 80 each as a result 8 th has to pay rs . 70 extra than his share . find the amount paid by him .
Options: a ) 140 , b ) 121 , c ) 110 , d ) 160 , e ) none
Rationale: "explanation : average amount paid by 7 persons = rs . 80 increase in average due to rs . 70 paid extra by the 8 th men = rs . 70 / 7 = rs . 10 therefore , average expenditure of 8 friends = rs . 80 + rs . 10 = rs . 90 therefore , amount paid by the 11 th men = rs . 90 + rs . 70 = rs . 160 correct option : d"
Answer: d
Question (physics): if 4 men can colour 48 m long cloth in 2 days , then 8 men can colour 36 m long cloth in
Options: a ) 0.75 day , b ) 2 days , c ) 1.2 days , d ) 4 days , e ) 5 days
Rationale: "the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 8 = 0.75 day . a"
Answer: a
Question (gain): a person lent a certain sum of money at 6 % per annum at simple interest and in 8 years the interest amounted to $ 572 less than the sum lent . what was the sum lent ?
Options: a ) 1000 , b ) 1100 , c ) 1200 , d ) 1300 , e ) 1400
Rationale: "p - 572 = ( p * 6 * 8 ) / 100 p = 1100 the answer is b ."
Answer: b
Question (geometry): a circular ground whose diameter is 35 metres , has a 1.4 metre - broad garden around inside of it . what is the area of the garden in square metres ?
Options: a ) 301.5 , b ) 484.12 , c ) 401.84 , d ) 301.0 , e ) 301.84
Rationale: "req . area = ï € [ ( 35 ) 2 â € “ ( 33.6 ) 2 ] = 22 â  „ 7 ã — ( 68.6 ã — 1.4 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = ( 22 ã — 68.6 ã — 0.2 = 301.84 sq m . answer e"
Answer: e
Question (physics): the edges of three metal cubes are 4 cm , 5 cm , and 6 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ?
Options: a ) 6.6 , b ) 6.8 , c ) 7.0 , d ) 7.2 , e ) 7.4
Rationale: "the total volume is 4 ^ 3 + 5 ^ 3 + 6 ^ 3 = 405 the edge of the new cube is the cube root of 405 which is about 7.4 cm . the answer is e ."
Answer: e
Question (gain): mr . hernandez , who was a resident of state x for only 8 months last year , had a taxable income of $ 22,500 for the year . if the state tax rate were 10 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ?
Options: a ) $ 1500 , b ) $ 1720 , c ) $ 1600 , d ) $ 1300 , e ) $ 1160
Rationale: "total tax for the year = 22,500 x 10 % = 2250 as stated annual tax is prorated as per the duration of stay . prorated tax = 900 ( 8 / 12 ) = 1500 answer a"
Answer: a
Question (physics): walking at 3 / 4 of her normal speed , a worker is 12 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
Options: a ) 36 , b ) 48 , c ) 60 , d ) 62 , e ) 66
Rationale: let v be her normal speed and let t be her normal time . d = ( 3 / 4 ) v * ( t + 12 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 3 / 4 ) v * ( t + 12 ) t / 4 = 9 t = 36 the answer is a .
Answer: a
Question (general): if a : b = 4 : 1 , then find ( a - 3 b ) / ( 2 a - b ) ?
Options: a ) 6 / 7 , b ) 1 / 7 , c ) 5 / 7 , d ) 3 / 2 , e ) 4 / 7
Rationale: answer : option b a / b = 4 / 1 = > a = 4 b ( a - 3 b ) / ( 2 a - b ) = ( 4 b - 3 b ) / ( 8 b - b ) = b / 7 b = > 1 / 7
Answer: b
Question (other): log 3 n + log 12 n what is 3 digit number n that will be whole number
Options: a ) 6291 , b ) 7292 , c ) 1728 , d ) 1929 , e ) 1727
Rationale: "no of values n can take is 1 12 ^ 3 = 1728 answer : c"
Answer: c
Question (general): the average weight of a , b , c is 45 kg . the avgwgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .
Options: a ) 23 , b ) 43 , c ) 21 , d ) 31 , e ) 43
Rationale: sol . let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer d
Answer: d
Question (gain): the price of a shirt is increased by 15 % and then reduced by 15 % . the final price of the shirt is ?
Options: a ) $ 97.75 , b ) $ 90 , c ) $ 91.56 , d ) $ 95.62 , e ) $ 93.45
Rationale: let the original price be $ 100 new final price = 85 % of ( 115 % of $ 100 ) = 85 / 100 * 115 / 100 * 100 = $ 97.75 answer is a
Answer: a
Question (general): if two integers x , y ( x > y ) are selected from - 3 to 4 ( inclusive ) , how many cases are there ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: there are 8 integers from - 3 to 4 inclusive . 8 c 2 = 28 . the answer is e .
Answer: e
Question (physics): in 100 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 10 , b ) 12 , c ) 30 , d ) 40 , e ) 20
Rationale: dist = ( 100 / 45 * 9 ) = 20 m answer e
Answer: e
Question (physics): the citizens of planet nigiet are 5 fingered and have thus developed their decimal system in base 8 . a certain street in nigiet contains 1000 ( in base 5 ) buildings numbered 1 to 1000 . how many 3 s are used in numbering these buildings ? express result in terms of base 10 .
Options: a ) 54
b ) 64
c ) 75
d ) 85
e ) 100
Rationale: no of 3 s b / w 1 - 99 is 20,100 - 199 is 20 and so on . so leavn d range b / w 300 - 399 total no of 3 s is ( 9 * 20 = ) 180 . no of 3 s b / w 300 - 399 is ( 20 + 100 = ) 120 . total no of 3 s b / w 1 - 1000 = 120 + 180 = 300 in base 10 300 = 3 * 5 ^ 2 = 75 . answer : c
Answer: c
Question (other): of the people who responded to a market survey , 150 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 5 to 1 , how many people responded to the survey ?
Options: a ) 80 , b ) 180 , c ) 240 , d ) 360 , e ) 480
Rationale: ratio = 5 : 1 = > 5 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 150 = > 5 x = 150 = > x = 30 hence total no . of respondents = 150 + 30 = 180 hence b is the answer .
Answer: b
Question (other): the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 9 and 10 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 230 , d ) 345 , e ) 395
Rationale: "clearly , the numbers are ( 23 x 9 ) and ( 23 x 10 ) . larger number = ( 23 x 10 ) = 230 . answer : option c"
Answer: c