Cheukting/mathqa huggingface dataset:
Question (other): how many positive integers e between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?
Options: a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26
Rationale: 1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e .
Answer: e
Question (other): the hcf of two numbers is 23 and the other two factors of their lcm are 13 and 14 . what is the largest number ?
Options: a ) 280 , b ) 284 , c ) 292 , d ) 320 , e ) 322
Rationale: hcf of the two numbers = 23 since hcf will be always a factor of lcm , 23 is a factor of the lcm . given that other two factors in the lcm are 13 and 14 . hence factors of the lcm are 23 , 13 , 14 so , numbers can be taken as ( 23 × 13 ) and ( 23 × 14 ) = 299 and 322 hence , largest number = 322 e )
Answer: e
Question (probability): in a throw of dice what is the probability of ge æ « ng number greater than 2
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these
Rationale: explanation : number greater than 2 is 3 , 4 , 5 & 6 , so only 4 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 4 / 6 = 2 / 3 answer : b
Answer: b
Question (gain): a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 50 percent greater than the wholesale price . if the retailer decreases the retail price by 30 percent this will have the same effect as increasing the wholesale price by what percent ?
Options: a ) 15 , b ) 20 , c ) 10 , d ) 5 , e ) 8
Rationale: answer : d = 5 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 50 % increase makes retail price = 150 . now 30 % decrease - > ( 1 - 30 / 100 ) * 150 = 105 . now compared to the wholesale price of 100 , 5 % increase is what will have the same effect as increasing the wholesale price .
Answer: d
Question (general): on dividing 172 by a number , the quotient is 10 and the remainder is 2 . find the divisor .
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17
Rationale: "d = ( d - r ) / q = ( 172 - 2 ) / 10 = 170 / 10 = 17 e"
Answer: e
Question (gain): in what time a sum of money double itself at 4 % per annum simple interest ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 83 1 / 3 % , d ) 33 4 / 3 % , e ) 73 1 / 3 %
Rationale: "p = ( p * 4 * r ) / 100 r = 25 % answer : a"
Answer: a
Question (general): a big container is 35 % full with water . if 48 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?
Options: a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120
Rationale: "48 liters is 40 % of the capacity c . 48 = 0.4 c c = 48 / 0.4 = 120 liters . the answer is e ."
Answer: e
Question (general): in a box , there are 8 orange , 7 black and 6 white balls . if one ball is picked up randomly . what is the probability that it is neither orange nor white ?
Options: a ) 2 / 3 , b ) 3 / 4 , c ) 7 / 19 , d ) 8 / 21 , e ) 10 / 21
Rationale: total balls are 21 and neither black nor white . so favor case will be only 8 c 1 and total case 21 c 1 probability will be 8 c 1 / 21 c 1 = 8 / 21 answer : d
Answer: d
Question (general): suraj has a certain average of runs for 12 innings . in the 13 th innings he scores 96 runs thereby increasing his average by 5 runs . what is his average after the 13 th innings ?
Options: a ) 48 , b ) 64 , c ) 36 , d ) 72 , e ) 27
Rationale: "to improve his average by 5 runs per innings he has to contribute 12 x 5 = 60 runs for the previous 12 innings . thus , the average after the 13 th innings = 96 - 60 = 36 . answer : c"
Answer: c
Question (general): total number of boys and girls in a school is 150 . if the number of boys is x , then girls become x % of the total number of students . the number of boys is
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: explanation : clearly , x % of 150 = 150 - x [ as x is number of boys ] = > x + x / 100 ∗ 150 = 150 = > 5 / 2 x = 150 = > x = 60 option b
Answer: b
Question (gain): $ 20000 will become $ 60000 at 20 % p . a . find the time ?
Options: a ) 2 years , b ) 5 years , c ) 7 years , d ) 8 years , e ) 10 years
Rationale: "si = simple interest = a - p = 60000 - 20000 = $ 40000 r = 100 si / pt = 100 * 40000 / 20000 * 20 = 10 years answer is e"
Answer: e
Question (other): a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 6 : 2 . the ratio of economy cars to sport utility vehicles is 5 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 6 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: the ratio of economy to luxury cars is 6 : 2 - - > e : l = 6 : 2 = 30 : 10 . the ratio of economy cars to sport utility vehicles is 5 : 3 - - > e : s = 5 : 3 = 30 : 18 . thus , l : s = 10 : 18 = 5 : 6 . answer : b .
Answer: b
Question (general): what is the smallest integer that satisfies the inequality ( ( x - 3 ) / ( x ^ 2 - 8 x - 20 ) ) > 0 ?
Options: a ) - 2 , b ) 10 , c ) - 1 , d ) 3 , e ) 0
Rationale: let us factorize the denominator and rewrite the expression as ( x â ˆ ’ 3 ) / ( ( x â ˆ ’ 10 ) ( x + 2 ) ) > 0 equate each of the terms of the expression to zero to identify the values of x that are relevant to test whether the inequality holds good . the values that are relevant to us are x = 3 , x = 10 and x = - 2 . let us arrange these values in ascending order : - 2 , 3 and 10 . the quickest way to solve inequalities questions after arriving at these values is verifying whether the inequality holds good at the following intervals . interval 1 : x < - 2 . pick a value in that range and check whether the inequality holds good . let us take x = - 10 . when x = - 10 , ( x â ˆ ’ 3 ) / ( ( x â ˆ ’ 10 ) ( x + 2 ) ) < 0 ; the inequality does not hold good in this interval . interval 2 : - 2 < x < 3 . let us take x = 0 . when x = 0 , ( x â ˆ ’ 3 ) / ( ( x â ˆ ’ 10 ) ( x + 2 ) ) = ( 0 â ˆ ’ 3 ) / ( ( 0 â ˆ ’ 10 ) ( 0 + 2 ) ) > 0 ; the inequality holds good in this interval . the least integer value that x can take if x > - 2 is x = - 1 . answer : c .
Answer: c
Question (general): the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 80 , and what number ?
Options: a ) 35 , b ) 30 , c ) 25 , d ) 20 , e ) 15
Rationale: a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 90 = 15 e
Answer: e
Question (general): if a = 105 and a ^ 3 = 21 * 49 * 45 * b , what is the value of b ?
Options: a ) 25 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 49 = 7 * 7 45 = 3 * 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 7 * 7 * 3 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 * 7 ^ 3 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 * 7 ^ 3 b = 5 ^ 2 = 25 correct answer a ."
Answer: a
Question (physics): james took a 3 - hour bike ride . in the second hour he traveled 30 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
Options: a ) 54.0 , b ) 54.9 , c ) 92.5 , d ) 57.0 , e ) 63.0
Rationale: let the distance travelled in the first hour be x . thus , 1.2 x = 30 , x = 25 . now , the distance travelled in the 3 rd hour = 30 + 1 / 4 â ˆ — 30 = 37.5 the only option ending with a 0.5 in the decimal place is c . answer : c
Answer: c
Question (general): calculate the value of n from the below equation : n ^ 3 â ˆ ’ 10 n + 20 = 44
Options: a ) 1 , b ) 5 , c ) 3 , d ) 2 , e ) 4
Rationale: "use elimination method to find the correct option . you find that of all the options when 4 is the correct value for n answer : e"
Answer: e
Question (physics): due to construction , the speed limit along an 9 - mile section of highway is reduced from 45 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 5.61 , b ) b ) 3.42 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 9 miles stretch = 9 * 60 / 45 = 9 * 4 / 3 = 12 new time in minutes to cross 9 miles stretch = 9 * 60 / 35 = 9 * 12 / 7 = 15.42 time difference = 3.42 ans : b"
Answer: b
Question (general): a number x is multiplied by 5 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?
Options: a ) 25 / 9 , b ) 9 / 5 , c ) 5 / 3 , d ) 3 / 5 , e ) 9 / 25
Rationale: "sqrt ( 5 x / 3 ) to be perfect square x has to 5 / 3 ans : c"
Answer: c
Question (gain): what amount does an investor receive if the investor invests $ 4000 at 10 % p . a . compound interest for two years , compounding done annually ?
Options: a ) $ 4720 , b ) $ 4840 , c ) $ 4920 , d ) $ 5080 , e ) $ 5160
Rationale: "a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 5000 = 1.21 * 5000 = 4840 the answer is b ."
Answer: b
Question (general): a store owner estimates that the average price of type a products will increase by 40 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,755 , b ) $ 15,430 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.40 * 4500 = 6300 cost of type b products next year = 1.1 * 8300 = 9130 total 6300 + 9130 = 15430 option b"
Answer: b
Question (other): the school soccer team looks at their record and finds that they win , lose , and tie games in a ratio of 4 : 3 : 1 . how many games did they play if they lost 9 games ?
Options: a ) 3 , b ) 9 , c ) 12 , d ) 18 , e ) 24
Rationale: the ratio is 4 wins : 3 losses : 1 tie . think of ratio as ` ` parts . ' ' divide 9 ( total losses ) by 3 ( ratio losses ) to find 1 ` ` part ' ' of the ratio . 9 / 3 = 3 this means the team tied 3 games . multiply 3 ( 1 ` ` part ' ' of ratio ) by 4 ( ratio wins ) to find total wins . 3 * 4 = 12 . this mean the team won 12 games . add up wins , losses , and ties . 12 + 9 + 3 = 24 the answer is e
Answer: e
Question (general): if 9 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?
Options: a ) 20 , b ) 24 , c ) 36 , d ) 40 , e ) 54
Rationale: "let the capacity of the tank = c ( 3 / 4 ) c + 9 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 9 = > ( 3 / 20 ) c = 9 = > c = ( 9 * 20 ) / 3 = 60 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 9 = 45 + 9 = 54 answer e"
Answer: e
Question (general): what is the remainder when 121212 . . . . . . . ( 300 ) digits is divided by 99 .
Options: a ) 18 , b ) 36 , c ) 72 , d ) 0 , e ) 1
Rationale: 12 / 99 = 12 1212 / 99 = 24 121212 / 99 = 36 . . . 121212 . . . ( 300 ) / 99 = ( 12 * 300 ) % 99 = 36 if they say 300 digits then ( 12 * 150 ) % 99 = 18 answer : a
Answer: a
Question (gain): walking 9 / 8 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 99 , c ) 27 , d ) 36 , e ) 20
Rationale: "speed ratio = 1 : 9 / 8 = 8 : 9 time ratio = 9 : 8 1 - - - - - - - - 9 4 - - - - - - - - - ? 36 m . answer : d"
Answer: d
Question (general): the average of 30 numbers is 48 . if three numbers namely 45 , 55 and 43 are discarded , the average of remaining numbers is ?
Options: a ) 47 , b ) 47.03 , c ) 48.03 , d ) 48 , e ) 49
Rationale: "explanation : total of 30 numbers = 30 * 48 = 1440 average o 27 numbers = 1440 - ( 45 + 55 + 43 ) / 27 = 48.03 answer : option c"
Answer: c
Question (physics): a man rows his boat 95 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 5 kmph , b ) 7 kmph , c ) 9 kmph , d ) 8 kmph , e ) 10 kmph
Rationale: "speed downstream = d / t = 95 / ( 2 1 / 2 ) = 38 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 38 - 18 ) / 2 = 10 kmph answer : e"
Answer: e
Question (general): a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 210,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 45,000 , c ) $ 55,000 , d ) $ 60,000 , e ) $ 75,000
Rationale: "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 7 a * 1 + a * 5 ) / 6 = 12 a / 6 = 2 a = 60000 answer is d . $ 60,000"
Answer: d
Question (general): a batsman scored 1 runs in his 18 th innings and that makes his average 18 . find his average upto the 17 th innings ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: avg = sum of the value / no . of the value 18 = ( sum of the first 17 innings score + 1 ) / 18 ( 18 * 18 - 1 ) = sum of the first 17 innings score sum of the first 17 innings score = 323 ave upto 17 innings = 323 / 17 = 19 answer : a
Answer: a
Question (physics): if jack walked 9 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 ) 6.25 , e ) 7.2
Rationale: "distance walked in 1 hour and 15 mins = 9 miles speed per hour = distance / time = 9 / ( 5 / 4 ) = 7.2 miles per hour answer e"
Answer: e
Question (general): a student chose a number , multiplied it by 2 , then subtracted 148 from the result and got 110 . what was the number he chose ?
Options: a ) 90 , b ) 129 , c ) 120 , d ) 160 , e ) 200
Rationale: "solution : let x be the number he chose , then 2 * x * 148 = 110 2 x = 258 x = 129 correct answer b"
Answer: b
Question (geometry): a crate measures 3 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 27 , b ) 3 , c ) 6 , d ) 8 , e ) 12
Rationale: "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 3 for the surface 8 * 12 face . volume = 27 pi answer b"
Answer: b
Question (gain): what percent of 17 is 17 percent of 1 ?
Options: a ) 0.001 , b ) 0.01 , c ) 0.1 , d ) 14 , e ) 1
Rationale: "17 % of 1 = ( 17 / 100 ) * 1 = 17 / 100 to determine what percentage of 17 this is : [ 17 ] [ / 100 * 17 ] * 100 = 1 % ans : e"
Answer: e
Question (general): if [ x ] is the greatest integer less than or equal to x , what is the value of [ 1.6 ] + [ - 3.4 ] + [ 10.7 ] ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "you are asked what the closest lesser integer value to [ x ] is . [ 1.6 ] = 1.0 [ - 3.4 ] = - 4.0 [ 10.7 ] = 10.0 therefore , answer is : 1.0 - 4.0 + 10.0 = 7.0 option e ."
Answer: e
Question (other): a firm is comprised of partners and associates in a ratio of 2 : 61 . if 75 more associates were hired , the ratio of partners to associates would be 4 : 137 . how many partners are currently in the firm ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the ratio 2 : 61 = 4 : 122 so the ratio changed from 4 : 122 to 4 : 137 . 137 - 122 = 15 which is 1 / 5 of the increase in 75 associates . the ratio changed from 20 : 610 to 20 : 685 . thus the number of partners is 20 . the answer is e ."
Answer: e
Question (general): evaluate : 37 - 18 ÷ 3 × 2 =
Options: a ) 20 , b ) 25 , c ) 27 , d ) 22 , e ) 17
Rationale: "according to order of operations , 18 ÷ 3 × 2 ( division and multiplication ) is done first from left to right 18 ÷ 3 × 2 = 6 × 2 = 12 hence 37 - 18 ÷ 3 × 2 = 37 - 12 = 25 correct answer b ) 25"
Answer: b
Question (physics): a train 225 m long running at 90 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 271 , b ) 266 , c ) 400 , d ) 277 , e ) 232
Rationale: "length of the platform = 90 * 5 / 18 * 25 = 625 – 225 = 400 answer : c"
Answer: c
Question (general): in an election only two candidates contested 20 % of the voters did not vote and 120 votes were declared as invalid . the winner got 200 votes more than his opponent thus he secured 41 % votes of the total voters on the voter list . percentage votes of the defeated candidate out of the total votes casted is :
Options: a ) 22 , b ) 389 , c ) 38 , d ) 45 , e ) 01
Rationale: let there be x voters and k votes goes to loser then 0.8 x - 120 = k + ( k + 200 ) k + 200 = 0.41 x \ inline \ rightarrow k = 1440 and ( k + 200 ) = 1640 therefore \ inline \ frac { 1440 } { 3200 } \ times 100 = 45 % answer : d ) 45 %
Answer: d
Question (physics): a 600 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 800 , b ) 700 , c ) 360 , d ) 370 , e ) 380
Rationale: "speed = 600 / 18 = 100 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 100 / 3 = > x = 1300 m . l = 1300 - 600 = 700 m answer : option b"
Answer: b
Question (general): 17 times a number gives 187 . the number is
Options: a ) 11 , b ) 12 , c ) 13.2 , d ) none , e ) can not be determined
Rationale: "explanation : let the number be ' n ' 17 × n = 187 ⇒ n = 11 correct option : a"
Answer: a
Question (general): 0.0008154 / 0.00205 x 16.5 = ?
Options: a ) 8.5 , b ) 6.6 , c ) 7.6 , d ) 6.4 , e ) 5.7
Rationale: "explanation : ? = 0.0008154 / 0.00205 x 16.5 = 6.6 answer : option b"
Answer: b
Question (geometry): if the area of a circle is 144 pi square feet , find its circumference .
Options: a ) 65 pi feet
b ) 24 pi feet
c ) 42 pi feet
d ) 18 pi feet
e ) 64 pi feet
Rationale: the area is given by pi * r * r . hence pi * r * r = 144 pi r * r = 81 ; hence r = 12 feet the circumference is given by 2 * pi * r = 2 * pi * 12 = 24 pi feet correct answer b
Answer: b
Question (physics): tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , how many r kilometers per hour did tammy walk on the second day ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 6
Rationale: "ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5"
Answer: c
Question (physics): a man sitting in a train which is traveling at 80 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 32 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 75 kmph
Rationale: "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 80 ) kmph = 32 kmph . answer : a"
Answer: a
Question (general): howmany 3 digit numbers are there tens digit place is more than hundreds digit place and units place less than hundreds digit place ?
Options: a ) 80 , b ) 100 , c ) 110 , d ) 120 , e ) 140
Rationale: we have numbers { 01 , 23 , 45 , 67 , 89 } now we would decide the cases on behalf of value of hundred place digit . and accordingly choose unit ' s digit and ten ' s digit . value of hundred place digit must be choosen in such a manner that there should exist a greater digit for ten ' s place and a smaller digit for unit place . thus we can have values of hundred ' s digit from 12 , 34 , 56 , 78 only now starting from hundred ' s digit = 8 : hundred ' s digit possible values for ten ' s digit possible values for unit digit total ways 8 9 01 , 23 , 45 , 67 1 * 1 * 8 = 8 7 89 0 , 12 , 34 , 56 1 * 2 * 7 = 14 6 7 , 89 01 , 23 , 45 1 * 3 * 6 = 18 5 67 , 89 0 , 12 , 34 1 * 4 * 5 = 20 4 5 , 67 , 89 01 , 23 1 * 5 * 4 = 20 3 45 , 67 , 89 0 . 1.2 1 * 6 * 3 = 18 2 3 , 45 , 67 , 89 01 1 * 7 * 2 = 14 1 23 , 45 , 67 , 89 0 1 * 8 * 1 = 8 so , total no of cases = 8 + 14 + 18 + 20 + 20 + 18 + 14 + 8 = 120 hence total no of possible 3 digit numbers = 120 answer : d
Answer: d
Question (general): a = 7 ^ 15 - 625 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itself . on the other hand the stem says that x could get how many different number not must get different number ( this is very important issue ) as our friends say , if we simplify numerator more we can obtain : 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 ( 124 ) = 5 ^ 12 ( 31 * 2 * 2 ) divided by x and we are told that this fraction is an integer . so , x could be ( not must be ) 5 , 31 , or 2 ! ! ! so , x could get 4 different values and answer is e . . . ."
Answer: e
Question (geometry): what is the total surface area in square meters of a rectangular solid whose length is 6 meters , width is 5 meters , and depth is 2 meters ?
Options: a ) 100 m 2
b ) 104 m 2
c ) 106 m 2
d ) 108 m 2
e ) 160 m 2
Rationale: surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 6 * 5 + 5 * 2 + 6 * 2 ) = 2 ( 30 + 10 + 12 ) = 2 * 52 = 104 m 2 answer : b
Answer: b
Question (general): average of 10 matches is 32 , how many runs one should should score to increase his average by 4 runs .
Options: a ) 70 , b ) 76 , c ) 78 , d ) 80 , e ) 88
Rationale: "explanation : average after 11 innings should be 36 so , required score = ( 11 * 36 ) - ( 10 * 32 ) = 396 - 320 = 76 answer : option b"
Answer: b
Question (gain): a particular library has 300 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 244 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 120 , b ) 140 , c ) 160 , d ) 180 , e ) 200
Rationale: "the total number of books is 300 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 244 books , thus the number of un - returned books is 300 - 244 = 56 books . 0.35 x = 56 x = 160 the answer is c ."
Answer: c