Cheukting/mathqa huggingface dataset:
Question (probability): what is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously ?
Options: a ) 1 / 6 , b ) 1 / 4 , c ) 1 / 2 , d ) 21 / 216 , e ) 32 / 216
Rationale: "the other way would be to list out each option . the options for a sum of 8 : ( 6 , 1,1 ) has 3 options ie ( 6 , 1,1 ) , ( 1 , 6,1 ) , ( 1 , 1,6 ) ; ( 5 , 2,1 ) has 6 options , ( 4 , 3,1 ) has 6 options , ( 4 , 2,2 ) has 3 options , ( 3 , 3,2 ) has 3 options . we have 21 options to get 8 . the options for a sum of 14 : ( 6 , 4,4 ) has 3 options , ( 6 , 5,3 ) has 6 options , ( 6 , 6,2 ) has 3 options , ( 5 , 5,4 ) has 3 options . we have 15 options to get 14 . total : 21 + 15 = 36 / 216 = 1 / 6 . answer a ."
Answer: a
Question (gain): a person purchases 90 clocks and sells 40 clocks at a gain of 10 % and 50 clocks at a gain of 20 % . if he sold all of them at a uniform profit of 15 % , then he would have got rs . 40 less . the cost price of each clock is :
Options: a ) 50 , b ) 90 , c ) 80 , d ) 28 , e ) 93
Rationale: let c . p . of clock be rs . x . then , c . p . of 90 clocks = rs . 90 x . [ ( 110 % of 40 x ) + ( 120 % of 50 x ) ] - ( 115 % of 90 x ) = 40 44 x + 60 x - 103.5 x = 40 0.5 x = 40 = > x = 80 answer : option c
Answer: c
Question (physics): what is the cost of leveling the field in the form of parallelogram at the rate of rs . 60 / 10 sq . metre , whose base & perpendicular distance from the other side being 34 m & 34 m respectively ?
Options: a ) s . 1156 , b ) s . 1300 , c ) s . 1400 , d ) s . 2480 , e ) s . 3600
Rationale: "area of the parallelogram = length of the base * perpendicular height = 34 * 34 = 1156 total cost of levelling = rs . 1156 a"
Answer: a
Question (general): find the remainder of the division ( 3 ^ 33 ) / 7 .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: find the pattern of the remainders after each power : ( 3 ^ 1 ) / 7 remainder 3 ( 3 ^ 2 ) / 7 remainder 2 ( 3 ^ 3 ) / 7 remainder 6 ( 3 ^ 4 ) / 7 remainder 4 ( 3 ^ 5 ) / 7 remainder 5 ( 3 ^ 6 ) / 7 remainder 1 - - > this is where the cycle ends ( 3 ^ 7 ) / 7 remainder 3 - - > this is where the cycle begins again ( 3 ^ 8 ) / 7 remainder 2 continuing the pattern to ( 3 ^ 33 ) / 7 gives us a remainder of 6 final answer : e ) 6
Answer: e
Question (gain): an inspector rejects 0.05 % of the meters as defective . how many will he examine to reject 4 ?
Options: a ) 4000 , b ) 8000 , c ) 5000 , d ) 4500 , e ) 6000
Rationale: "let the number of meters to be examined be x then , 0.05 % of x = 4 ( 5 / 100 ) * ( ( 1 / 100 ) * x = 4 x = 8000 answer is b"
Answer: b
Question (physics): a train passes a platform in 34 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 280 meter , b ) 240 meter , c ) 210 meter , d ) 200 meter , e ) none of these
Rationale: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 34 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 34 = > 300 + l = 15 × 34 = 510 = > l = 510 - 300 = 210 meter answer : option c"
Answer: c
Question (general): the average age of 15 students of a class is 15 years . out of these , the average age of 3 students is 14 years and that of the other 11 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 11 years , c ) 14 years , d ) 7 years , e ) 25 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 3 + 16 x 11 ) ] = ( 225 - 218 ) = 7 years . answer d"
Answer: d
Question (general): a number x is 6 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 83.3 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: say y = 1 and x = 6 . then y = 1 is less than x = 6 by ( 6 - 1 ) / 6 * 100 = 5 / 6 * 100 = 83.3 % . answer : b .
Answer: b
Question (physics): liam is pulled over for speeding just as he is arriving at work . he explains to the police officer that he could not afford to be late today , and has arrived at work only four minutes before he is to start . the officer explains that if liam had driven 5 mph slower for his whole commute , he would have arrived at work exactly on time . if liam ' s commute is 10 miles long , how fast was he actually driving ? ( assume that liam drove at a constant speed for the duration of his commute . )
Options: a ) 50 mph , b ) 45 mph , c ) 48 mph , d ) 30 mph , e ) 60 mph
Rationale: "let t be the number of hours he would need to reach office on time . when he is driving with over speed , he reached office 4 min earlier ! so the equation for this is s ( t - 4 / 60 ) = 30 where s is the speed and 30 is the distance . if he decreases his speed by 5 mph then he would have reached his office on time : ( s - 5 ) t = 30 if you solve above equations , you will arrive at t = 2 / 3 hr and s = 30 mph therefore answer is d"
Answer: d
Question (gain): what is the compound interest paid on a sum of rs . 3000 for the period of 2 years at 10 % per annum .
Options: a ) 630 , b ) 620 , c ) 610 , d ) 600 , e ) none of these
Rationale: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 3000 = 3000 * ( 21 / 100 ) = 630 answer a"
Answer: a
Question (general): what is the least integer greater than – 2 + 0.5 ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: irst , let ' s take care of the arithmetic : ( - 2 ) + ( 0.5 ) = - 1.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from - 2 to - 1.5 ) . next , the question asks for the least integer that is greater than - 1.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of - 1.5 is - 1 . final answer : b
Answer: b
Question (general): if 5 x + y = 15 , 5 y + z = 25 and 2 z + x = 2 , what is the value of x ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 1
Rationale: "explanation : 5 x + y = 15 – - - - - - - - i * 5 5 y + z = 25 – - - - - - - ii 2 z + x = 2 - - - - - - - - iii subtract ( i ) and ( ii ) 25 x + 5 y + 0 = 75 - 0 + 5 y + z = 25 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 25 x + 0 – z = 50 … . . . . . . . . . . iv multiply ( iv ) * 2 , we get 50 x – 2 z = 100 adding ( iii ) and ( iv ) we get , 50 x – 2 z = 100 + x + 2 z = 2 - - - - - - - - - - - - - - - - - - - - - - - - 51 x = 102 x = 2 the value of x = 2 answer : a"
Answer: a
Question (general): a boy perform 5 times a reaction and his reading are 2 , 2.1 , 2 , 2.2 but unfortunately 5 th reading clearly not visible because a drop of chemical fall onto it . but luckily he have mean of all reading which is 2 . please help him in finding 5 th reading .
Options: a ) 2 , b ) 1.7 , c ) 1.9 , d ) 1.8 , e ) 2.1
Rationale: solution let 5 th reading be x ( 2 + 2.1 + 2 + 2.2 + x ) / 5 = 2 8.3 + x = 10 x = 1.7 answer b
Answer: b
Question (gain): thirty percent of the members of a swim club have passed the lifesaving test . among the members who have not passed the test , 12 have taken the preparatory course and 30 have not taken the course . how many members are there in the swim club ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Rationale: 30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 30 + 12 = 42 members have not passed the test , thus 0.7 * total = 42 - - > total = 60 . answer : a .
Answer: a
Question (geometry): a certain rectangular window is ( 1 / 3 ) times as long as it is wide . if its perimeter is 28 feet , what are its dimensions in terms of length by width ?
Options: a ) 12 by 2
b ) 11 by 3
c ) 10.5 by 3.5
d ) 10 by 4
e ) 9 by 3
Rationale: 2 x + 2 y = 28 x + y = 14 x + ( 1 / 3 ) x = 14 4 x = 14 * 3 x = 10.5 answer c
Answer: c
Question (general): there are 8 teams in a certain league and each team plays each of the other teams exactly once . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 56 , e ) 64
Rationale: "number of ways 2 teams can be selected out of 8 teams : c 8 / 2 = 8 ∗ 7 / 2 = 28 ans : ' ' c ' '"
Answer: c
Question (gain): 3 candidates in an election and received 1136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ?
Options: a ) 40 % , b ) 55 % , c ) 57 % , d ) 60 % , e ) 62 %
Rationale: "total number of votes polled = ( 1136 + 7636 + 11628 ) = 20400 so , required percentage = 11628 / 20400 * 100 = 57 % c"
Answer: c
Question (general): if p is the product of the integers from 1 to 36 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "36 ! has 3 , 6 , 9 , . . . . 30 , 33 , 36 as factors , which are 12 multiples of 3 . we need to add 5 more to these 12 because of 9 , 18 , 27 , and 36 . the greatest integer of k is 17 . the answer is c ."
Answer: c
Question (gain): at what rate percent on simple interest will rs . 1750 amount to rs . 2000 in 3 years ?
Options: a ) 4 % , b ) 3 6 / 7 % , c ) 4.76 % , d ) 5 % , e ) 6 %
Rationale: "explanation : 250 = ( 1750 x 3 xr ) / 100 r = 4.76 % answer : option c"
Answer: c
Question (geometry): what is the total surface area in square meters of a rectangular solid whose length is 8 meters , width is 7 meters , and depth is 4 meters ?
Options: a ) 132 m 2 , b ) 145 m 2 , c ) 165 m 2 , d ) 152 m 2 , e ) 120 m 2
Rationale: "surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 8 * 7 + 7 * 4 + 8 * 4 ) = 2 ( 56 + 28 + 32 ) = 2 * 116 = 132 m 2 answer : a"
Answer: a
Question (geometry): the perimeter of a square is equal to the perimeter of a rectangle of length 19 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 ) 22.78 , b ) 23.54 , c ) 23.5 , d ) 24.55 , e ) 25.93
Rationale: "let the side of the square be a cm . perimeter of the rectangle = 2 ( 19 + 14 ) = 66 cm perimeter of the square = 66 cm i . e . 4 a = 66 a = 16.5 diameter of the semicircle = 16.5 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 16.5 ) = 1 / 2 ( 22 / 7 ) ( 16.5 ) = 25.93 cm to two decimal places answer : e"
Answer: e
Question (physics): john and steve are speed walkers in a race . john is 15 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 26 seconds , d ) 34 seconds , e ) 51 seconds
Rationale: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 15 + 2 - - - > 0.5 t = 17 - - - > t = 34 seconds . d is the correct answer ."
Answer: d
Question (other): a ratio between two numbers is 3 : 4 and their l . c . m . is 84 . the first number is
Options: a ) 60 , b ) 45 , c ) 21 , d ) 15 , e ) none
Rationale: "sol . let the required numbers be 3 x and 4 x . then , their l . c . m . is 12 x . ∴ 12 x = 84 ⇔ x = 7 . hence , the first number is 21 . answer c"
Answer: c
Question (gain): the principal that amounts to rs . 4813 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) s . 3096 , b ) s . 4036 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096
Rationale: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4813 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4036 . answer : b"
Answer: b
Question (geometry): the area of a rectangular plot is 18 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 10 metres , b ) 8 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these
Rationale: "l × b = 18 × b ∴ l = 18 m and l – b = 10 ∴ b = 18 – 10 = 8 m answer b"
Answer: b
Question (general): in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 38500 . how many times did he participate in the competition ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: 38500 = 2 * 2 * 5 * 5 * 5 * 7 * 11 john participated 7 times . the answer is b .
Answer: b
Question (gain): the first flight out of phoenix airport had a late departure . if the next 3 flights departed on - time , how many subsequent flights need to depart from phoenix on - time , for the airport ' s on - time departure rate to be higher than 40 % ?
Options: a ) 4 , b ) 6 , c ) 5 , d ) 2 , e ) 8
Rationale: we need on - time departure rate to be higher than 4 / 10 , so it should be at least 5 / 11 , which means that 5 out of 11 flights must depart on time . since for now 3 out of 4 flights departed on time then 5 - 3 = 2 subsequent flights need to depart on - time . answer : d
Answer: d
Question (general): a rainstorm increased the amount of water stored in state j reservoirs from 160 billion gallons to 200 billion gallons . if the storm increased the amount of water in the reservoirs to 40 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 260 , b ) 280 , c ) 325 , d ) 340 , e ) 355
Rationale: "let total capacity be x we know 200 = 0.40 x x = 200 / 0.40 = 500 prior to storm , we had 160 bn gallons 500 - 160 = 340 answer : d"
Answer: d
Question (general): a number when divided by a divisor leaves a remainder of 23 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 12 , b ) 13 , c ) 35 , d ) 36 , e ) 59
Rationale: "let the number is n , the divisor = d , i will make the two equations - n = xd + 23 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 36 as d is also integer and 36 is a prime number , the d should be 36 to satisfy the above equation . hence answer is ' d '"
Answer: d
Question (gain): two years ago , ram put $ 500 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 600 . the next year , his account balance increased by 10 % . at the end of the two years , by what percent has ram ' s account balance increased from his initial deposit of $ 500 ?
Options: a ) 19 % , b ) 28 % , c ) 30 % , d ) 32 % , e ) 25 %
Rationale: investment 500 dollars 1 st year total gained = 100 total amount end of first year = 600 second year account increased by 10 % = 600 * 0.1 = 60 therefore total amount by second year end = 660 so total percentage increase in money = ( 660 - 500 ) * 100 / 500 = 32 % correct answer d = 32 %
Answer: d
Question (gain): population of a city in 20004 was 1000000 . if in 2005 there isan increment of 10 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 976374 , b ) 979923 , c ) 980241 , d ) 1036750 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 10 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1036750 d"
Answer: d
Question (general): if the sum of two numbers is 45 and the h . c . f and l . c . m of these numbers are 3 and 100 respectively , then the sum of the reciprocal of the numbers is equal to :
Options: a ) 103 / 300 , b ) 103 / 200 , c ) 112 / 300 , d ) 154 / 140 , e ) 100 / 300
Rationale: let the numbers be a and b . then , a + b = 45 and ab = 3 * 100 = 300 . required sum = 1 / a + 1 / b = ( a + b ) / ab = 103 / 300 answer : a
Answer: a
Question (general): what is the value of ( 2 ) ^ - 3 ?
Options: a ) 1 / 6 , b ) 1 / 5 , c ) 1 / 8 , d ) 1 / 9 , e ) 1 / 7
Rationale: "2 ^ - 3 = 1 / ( 2 ) ^ 3 = 1 / 8 answer : c"
Answer: c
Question (general): mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 45 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 9 % , b ) 12 % , c ) 15 % , d ) 17 % , e ) 20 %
Rationale: "let me try a simpler one . lets assume that candidate got 45 % votes and total votes is 100 . candidate won = 45 remaining = 55 to get 50 % , candidate requires 5 votes from 100 which is 5 % and 5 votes from 55 . 5 / 55 = 1 / 11 = . 09 = 9 % which is approx 9 % . hence the answer is a ."
Answer: a
Question (physics): pipe a can fill a tank in 6 hours . due to a leak at the bottom , it takes 12 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 13 , b ) 17 , c ) 18 , d ) 19 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 6 - 1 / x = 1 / 12 = > 1 / x = 1 / 6 - 1 / 12 = ( 2 - 1 ) / 12 = 1 / 12 = > x = 12 . answer : e"
Answer: e
Question (gain): w and x start a business with rs . 5000 and rs . 20000 respectively . hoe should they share their profits at the end of one year ?
Options: a ) 4 : 1 , b ) 1 : 3 , c ) 1 : 4 , d ) 1 : 5 , e ) 2 : 1
Rationale: they should share the profits in the ratio of their investments . the ratio of the investments made by w and x = 5000 : 20000 = > 1 : 4 . answer : c
Answer: c
Question (physics): in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 80 questions and secures 130 marks , the no of questions he attempts correctly is :
Options: a ) a ) 35 , b ) b ) 38 , c ) c ) 90 , d ) d ) 88 , e ) e ) 42
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 80 – x ) = 130 = > 5 x = 210 = > x = 42 answer : e"
Answer: e
Question (general): what is the least number should be added to 1056 , so the sum of the number is completely divisible by 29 ?
Options: a ) 17 , b ) 27 , c ) 37 , d ) 47 , e ) 57
Rationale: ( 1056 / 29 ) gives remainder 12 17 + 12 = 29 , so we need to add 17 a
Answer: a
Question (general): an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 1455 , what was the total number of pairs of contact lenses that she sold ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: ( x + 5 ) * 150 + x * 85 = 1455 = > x = 3 total lens = 3 + ( 3 + 5 ) = 11 answer a
Answer: a
Question (gain): if the price of an article went up by 30 % , then by what percent should it be brought down to bring it back to its original price ?
Options: a ) 25 % , b ) 23 1 / 13 % , c ) 16 7 / 3 % , d ) 16 6 / 3 % , e ) 16 2 / 3 %
Rationale: "let the price of the article be rs . 100 . 30 % of 100 = 30 . new price = 100 + 30 = rs . 130 required percentage = ( 130 - 100 ) / 130 * 100 = 30 / 130 * 100 = 23 1 / 13 % answer : b"
Answer: b
Question (general): if n is the product of all the integers from 5 to 20 , inclusive , what is the greatest integer k for which 2 ^ k is a factor of n ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: 20 / 2 = 10 10 / 2 = 5 ans : 10 + 5 = 15 answer : e
Answer: e
Question (geometry): the perimeter of an isosceles right triangle is 14 + 14 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9.899
Rationale: "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 14 + 14 sqrt 2 or , a . ( 2 + sqrt 2 ) = 14 ( 1 + sqrt 2 ) , a = 14 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 14 * 2.414 / 3.414 = then hypotenuse = 9.899 e"
Answer: e
Question (general): sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 180 . if the ratio of his marks in english and maths is 1 : 2 , find his marks in science ?
Options: a ) 19 , b ) 77 , c ) 66 , d ) 55 , e ) 31
Rationale: "s : e = 1 : 3 e : m = 1 : 2 - - - - - - - - - - - - s : e : m = 1 : 3 : 6 1 / 10 * 190 = 19 answer : a"
Answer: a
Question (gain): what is 82 % of 3 / 5 ?
Options: a ) 6.9 , b ) 0.492 , c ) 0.6845 , d ) 0.6859 , e ) 0.69
Rationale: "82 % * ( 3 / 5 ) = 0.82 * 0.6 = 0.492 answer : b"
Answer: b
Question (general): country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 9 % . if ron imported a $ 18000 imported car and ended up paying $ 1950 in taxes , what is the first tier ' s price level ?
Options: a ) $ 11500 , b ) $ 11000 , c ) $ 12000 , d ) $ 12100 , e ) $ 12500
Rationale: let t be the tier price , p be total price = 18000 per the given conditions : 0.12 t + 0.09 ( p - t ) = 1950 0.12 t + 0.09 * 18000 - 0.09 t = 1950 0.03 t + 1620 = 1950 0.03 t = 1950 - 1620 = 330 t = 330 / 0.03 = 11000 answer b
Answer: b
Question (physics): a 90 cm long wire is to be cut into two pieces so that one piece will be 2 / 7 th of the other , how many centimeters will the shorter piece be ?
Options: a ) a ) 73 , b ) b ) 20 , c ) c ) 83 , d ) d ) 21 , e ) e ) 52
Rationale: "explanation : 1 : 2 / 7 = 7 : 2 2 / 9 * 90 = 20 answer : option b"
Answer: b
Question (general): the sum of 3 integers is 33 . the largest integer is 3 times the middle integer , and the smallest integer is 23 less than the largest integer . what is the product of the 3 integers ?
Options: a ) 192 , b ) 203 , c ) 214 , d ) 225 , e ) 236
Rationale: let x be the middle integer . then the largest is 3 x and the smallest is 3 x - 23 . 3 x - 23 + x + 3 x = 33 x = 8 the three integers are 1 , 8 , and 24 . the product is 1 * 8 * 24 = 192 the answer is a .
Answer: a
Question (general): how many integers between 1 and 10 ^ 19 are such that the sum of their digits is 2 ?
Options: a ) 190 , b ) 210 , c ) 211 , d ) 230 , e ) 231
Rationale: "the integers with a sum of 2 are : 2 , 20 , 200 , . . . , 2 * 10 ^ 18 and there are 19 integers in this list . also , these integers have a sum of 2 : 11 101 , 110 1001 , 1010 , 1100 etc . . . the number of integers in this list is 1 + 2 + . . . + 18 thus , the total number of integers is 1 + 2 + . . . + 18 + 19 = 20 * 19 / 2 = 190 the answer is a ."
Answer: a
Question (general): joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 70 . he was allowed to drop his lowest score . after doing so , his average test score improved to 75 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 25 , c ) 55 , d ) 65 , e ) 80
Rationale: "the arithmetic mean of 4 equally weighted tests was 70 . so what we can assume is that we have 4 test scores , each 70 . he dropped his lowest score and the avg went to 75 . this means that the lowest score was not 70 and other three scores had given the lowest score 5 each to make it up to 70 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 70 . so the lowest score = 70 - 15 = 55 answer ( c )"
Answer: c
Question (geometry): an error 2 % in excess is made while measuring the sideofa square . the % of error in the calculated area of the square is ?
Options: a ) 4 % , b ) 4.04 % , c ) 4.15 % , d ) 5 % , e ) 5.24 %
Rationale: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b"
Answer: b
Question (gain): what is the normal price of an article sold at $ 144 after two successive discounts of 10 % and 20 % ?
Options: a ) $ 184 , b ) $ 192 , c ) $ 200 , d ) $ 208 , e ) $ 216
Rationale: "0.8 * 0.9 * cost price = $ 144 cost price = $ 200 the answer is c ."
Answer: c