Cheukting/mathqa huggingface dataset:
Question (general): two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 36 seconds . the length of each train is :
Options: a ) 82 m , b ) 50 m , c ) 72 m , d ) 80 m , e ) none of these
Rationale: "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 36 secs the total distance travelled is 36 x 25 / 9 = 100 m . therefore the length of each train is = 100 / 2 = 50 m . answer b"
Answer: b
Question (general): divide rs . 1400 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) 346 , b ) 368 , c ) 350 , d ) 337 , e ) 639
Rationale: "a + b + c = 1400 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1400 = > 350 answer : c"
Answer: c
Question (geometry): if the sum of a number and its square is 72 , what is the number ?
Options: a ) 15 , b ) 26 , c ) 8 , d ) 91 , e ) none of these
Rationale: "let the number be x . then , x + x 2 = 72 ( x + 9 ) ( x - 8 ) = 0 x = 8 answer : c"
Answer: c
Question (physics): sarah is driving to the airport . after driving at 20 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 50 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 ) 140 , b ) 175 , c ) 210 , d ) 70 , e ) 280
Rationale: "after driving at 20 miles per hourfor one hour , this distance left to cover is d - 20 . say this distance is x miles . now , we know that the difference in time between covering this distance at 20 miles per hour and 50 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 20 - x / 50 = 3 / 2 - - > 5 x / 100 - 2 x / 100 = 3 / 2 - - > 3 x / 100 = 3 / 2 - - > x = 50 . total distance = x + 20 = 70 miles . answer : d"
Answer: d
Question (physics): there are 13 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 288 , b ) 267 , c ) 261 , d ) 211 , e ) 210
Rationale: "the total number of stations = 15 from 15 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 15 p ₂ ways . 15 p ₂ = 15 * 14 = 210 . answer : e"
Answer: e
Question (other): a student committee on academic integrity has 42 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "xc 1 * ( x - 1 ) c 1 = 42 x ^ 2 - x - 42 = 0 ( x - 7 ( x + 6 ) = 0 x = 7 , - 6 - 6 ca n ' t possible . hence 7 should be the answer a"
Answer: a
Question (general): the difference between the local value and the face value of 4 in the numeral 98625147 is
Options: a ) 36 , b ) 63 , c ) 34 , d ) 30 , e ) 33
Rationale: "explanation : ( local value of 4 ) - ( face value of 4 ) = ( 40 - 4 ) = 36 a )"
Answer: a
Question (physics): a boat moves upstream at the rate of 1 km in 30 minutes and down stream 1 km in 12 minutes . then the speed of the current is :
Options: a ) 1.5 kmph , b ) 2 kmph , c ) 3 kmph , d ) 2.5 kmph , e ) 3.5 kmph
Rationale: "rate upstream = ( 1 / 30 * 60 ) = 2 kmph rate down stream = 1 / 12 * 60 = 5 kmph rate of the current = ½ ( 5 - 2 ) = 1.5 kmph answer : a"
Answer: a
Question (physics): if five machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 45 , b ) 60 , c ) 75 , d ) 80 , e ) 100
Rationale: using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 5 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 10 / 3 = 10 / 3 * x x = 1 hour so 60 minutes answer : b
Answer: b
Question (general): a circular racetrack is 3 miles in length and has signs posted to indicate each 1 / 10 mile increment . if a race car starts at a random location on the track and travels exactly one half mile , what is the probability that the car ends within a half mile of the sign indicating 2 1 / 2 miles ?
Options: a ) 1 / 6 , b ) 3 / 10 , c ) 1 / 3 , d ) 1 / 2 , e ) 2 / 3
Rationale: the car ends within a half mile of the sign indicating 2 1 / 2 miles means that the car will end in one mile interval , between the signs indicating 2 and 3 miles . now , it does n ' t matter where the car starts or what distance it travels , the probability will be p = ( favorable outcome ) / ( total # of outcomes ) = 1 / 3 ( as the car starts at random point end travels some distance afterwards we can consider its end point as the point where he randomly appeared , so the probability that the car appeared within 1 mile interval out of total 3 miles will be 1 / 3 ) . answer : c .
Answer: c
Question (gain): the cost price of a radio is rs . 2400 and it was sold for rs . 2100 , find the loss % ?
Options: a ) 12.5 % , b ) 11 % , c ) 13 % , d ) 15 % , e ) 12.8 %
Rationale: "2400 - - - - 300 100 - - - - ? = > 12.5 % answer : a"
Answer: a
Question (general): the ages of two persons differ by 20 years . if 5 years ago , the older one be 5 times as old as the younger one , then their present ages , in years , are
Options: a ) 25 , 5 , b ) 30 , 10 , c ) 35 , 15 , d ) 50 , 30 , e ) none of these
Rationale: "let the ages be ’ x ’ and ’ y ’ years now . then x - y = 20 . . . ( i ) ( x - 5 ) = 5 ( y - 5 ) . . . ( ii ) from ( i ) and ( ii ) , 20 + y - 5 = 5 y - 25 y = 10 and x = 30 . answer : b"
Answer: b
Question (general): the sum of 4 th and 20 th term of a . p . is equal to the sum of 8 th , 15 th and 12 th term . find the term which is 0
Options: a ) 10 , b ) 7 , c ) 11 , d ) 5 , e ) 3
Rationale: t 4 + t 20 = t 8 + t 15 + t 12 = > a + 3 d + a + 19 d = a + 7 d + a + 14 d + a + 11 d = > a + 10 d = 0 = > t 11 = 0 i . e . 11 th term is zero . answer : c
Answer: c
Question (gain): 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 64 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 11 books less ( 75 - 64 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 55 answer e"
Answer: e
Question (general): a 6 - liter solution is 20 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?
Options: a ) 2.4 , b ) 2.7 , c ) 3.0 , d ) 3.3 , e ) 3.6
Rationale: "let x be the amount of pure alcohol required . 0.2 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 1.2 x = 3.6 liters the answer is e ."
Answer: e
Question (general): how many multiples of 2 are there between 1 and 52 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 25 , d ) 26 , e ) 28
Rationale: "25 multiples of 2 between 1 and 52 exclusive . from 2 * 1 upto 2 * 25 , ( 1,2 , 3,4 , . . . , 25 ) . hence , 25 multiples ! correct option is c"
Answer: c
Question (physics): the length of a room is 6 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 25650 , b ) 25750 , c ) 26550 , d ) 26750 , e ) 25725
Rationale: "area = 6 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 6 × 4.75 × 900 = 6 × 4275 = rs . 25650 answer is a ."
Answer: a
Question (general): nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 2 screws and 4 nails ?
Options: a ) a . 4 , b ) b . 5 / 2 , c ) c . 2 , d ) d . 3 / 2 , e ) e . 5 / 4
Rationale: "let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 2 s and 4 n = 2 s + 4 * 2 s = 10 s . . ratio = 15 s / 10 s = 15 / 10 = 3 / 2 d"
Answer: d
Question (general): a box contains 10 tablets of medicine a and 14 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .
Options: a ) 12 , b ) 16 , c ) 17 , d ) 19 , e ) 21
Rationale: the worst case scenario will be if we remove all 14 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 14 + 2 = 16 tablets . answer : b .
Answer: b
Question (physics): a and b together can do a work in 6 days . if a alone can do it in 15 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 99 , c ) 77 , d ) 55 , e ) 21
Rationale: "1 / 6 – 1 / 15 = 1 / 10 = > 10 answer : a"
Answer: a
Question (general): the sum of present age of abe and the age before 7 years is 27 . find the present age of abe . what will be his age after 7 years ?
Options: a ) 25 , b ) 24 , c ) 27 , d ) 28 , e ) 29
Rationale: "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 27 2 x - 7 = 27 2 x = 27 + 7 x = 34 / 2 x = 17 z = x + 7 = 17 + 7 = 24 answer : b"
Answer: b
Question (gain): a , b and c invested rs . 6600 , rs . 4400 and rs . 11000 respectively , in a partnership business . find the share of a in profit of rs . 12100 after a year ?
Options: a ) rs . 3300 , b ) rs . 3100 , c ) rs . 3500 , d ) rs . 4200 , e ) rs . 3400
Rationale: "6600 : 4400 : 11000 3 : 2 : 5 3 / 10 * 11000 = rs . 3300 answera"
Answer: a
Question (physics): a man drive his car to the office at 20 miles / hr . after reaching office , he realize that its a new year holiday so he went back home at a speed of 30 miles / hr . discounting the time spent in the stoppage what was his average speed of his journey ?
Options: a ) 23 miles , b ) 25 miles , c ) 22 miles , d ) 24 miles , e ) 26 miles
Rationale: d 24 miles / hr ( not 25 miles / hr which might be guessed by many ) d : distance traveled t 1 : time of going to office t 2 : time of returning back y : average speed d = 20 * t 1 t 1 = d / 20 d = 30 * t 2 t 2 = d / 30 2 d = y ( t 2 + t 1 ) 2 d = y ( d / 20 + d / 30 ) 2 d = y ( 3 d / 60 + 2 d / 60 ) 2 d = y ( 5 d / 60 ) y = 120 d / 5 d = > y = 24
Answer: d
Question (gain): walking 7 / 6 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 11 , b ) 15 , c ) 16 , d ) 28 , e ) 19
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 4 - - - - - - - - - ? è 28 m answer : d"
Answer: d
Question (general): find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 896 ?
Options: a ) 1000 , b ) 800 , c ) 2889 , d ) 2777 , e ) 2991
Rationale: "896 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 800 answer : b"
Answer: b
Question (other): a number is said to be prime saturated if the product of all the different positive prime factors of g is less than the square root of g . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "g = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."
Answer: d
Question (general): a person saved $ 10 in buying an item on sale . if he spent $ 600 for the item , approximately how much percent he saved in the transaction ?
Options: a ) 8 % , b ) 1.6 % , c ) 2 % , d ) 5 % , e ) 6 %
Rationale: "actual price = 600 + 10 = $ 610 saving = 10 / 610 * 100 = 100 / 61 = 1.6 % approximately answer is b"
Answer: b
Question (gain): an article is bought for rs . 705 and sold for rs . 900 , find the gain percent ?
Options: a ) 27.65 % , b ) 33 1 / 2 % , c ) 33 1 / 3 % , d ) 33 5 / 3 % , e ) 35 1 / 3 %
Rationale: "705 - - - - 195 100 - - - - ? = > 27.65 % answer : a"
Answer: a
Question (geometry): what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 10 % ?
Options: a ) 25 % , b ) 28 % , c ) 21 % , d ) 30 % , e ) 32 %
Rationale: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 10 % increase a surface = 6 * ( ( 1.1 a ) ^ 2 ) = 6 * 1.21 * a ^ 2 the increase in the surface area = ( 6 * 1.21 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.21 - 1 ) ) / ( 6 * a ^ 2 ) = 1.21 - 1 = 0.21 = 21 % answer : c"
Answer: c
Question (probability): how many positive integers less than 500 can be formed using the numbers 1 , 2,3 , and 5 for digits , each digit being used only once .
Options: a ) 34 , b ) 677 , c ) 197 , d ) 177 , e ) 191
Rationale: "single digit numbers = 4 double digit numbers = 4 x 3 = 12 three digit numbers = 3 x 3 x 2 x 1 = 18 total = 34 answer : a"
Answer: a
Question (general): a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 11 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) 34 , b ) 38 , c ) 36 , d ) 40 , e ) 42
Rationale: "at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 11 strikes , there would be 10 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 11 ' o clock , the 11 strikes and 10 intervals will take 2 * ( 11 + 10 ) = 42 secs e"
Answer: e
Question (geometry): the length of a rectangle is 5 more than the width . what are the dimensions of the rectangle if the perimeter is 34 ?
Options: a ) 11
b ) 12
c ) 13
d ) 14
e ) none
Rationale: pretend width = 1 , then length = 6 ( 1 + 5 ) 2 × 1 + 2 × 7 = 2 + 14 = 16 . notice that 16 is far from a perimeter of 34 try much bigger number . how about if we . . . pretend width = 4 , then length = 9 ( 4 + 5 ) 2 × 4 + 2 × 9 = 6 + 18 = 24 . we are getting closer to a perimeter of 34 pretend width = 5 , then length = 10 ( 5 + 5 ) 2 × 5 + 2 × 10 = 10 + 30 = 30 . pretend width = 7 , then length = 12 ( 7 + 5 ) 2 × 7 + 2 × 12 = 14 + 24 = 38 . this is higher than a perimeter of 34 . so width should be higher than 5 and smaller than 7 . may be a width of 6 will work . pretend width = 6 , then length = 11 ( 6 + 5 ) 2 × 6 + 2 × 11 = 12 + 22 = 34 . use of algebra : let width = x let length = x + 5 p = 2 × l + 2 × w 34 = 2 × ( x + 5 ) + 2 × x 34 = 2 x + 10 + 2 x 34 = 4 x + 10 34 - 10 = 4 x + 10 - 10 24 = 4 x 24 / 4 = 4 x / 4 6 = x therefore , width = 6 and length = x + 5 = 6 + 5 = 11 answer a
Answer: a
Question (general): if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 54 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: four wheeler = 13 * 4 = 52 ( max ) 2 wheel = 1 so no of 4 wheeler = 13 answer : c
Answer: c
Question (physics): a train passes a train standing in platform in 30 sec and a man standing on the platform in 12 sec . if the speed of the train is 36 km / hr . what is the length of the platform ?
Options: a ) 250 , b ) 200 , c ) 300 , d ) 240 , e ) 180
Rationale: speed = 36 * 5 / 18 = 10 m / sec . length of the train = 10 * 12 = 120 m . let the length of the platform be x m . then , ( x + 120 ) / 30 = 10 = > x = 180 m . answer : e
Answer: e
Question (general): what is the tenth digit of ( 4 ! * 3 ! + 4 ! * 2 ! ) / 3 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 1 , e ) 0
Rationale: "( 4 ! * 3 ! + 4 ! * 2 ! ) / 2 = 4 ! ( 3 ! + 2 ! ) / 2 = 24 ( 6 + 2 ) / 2 = 96 units digit of the above product will be equal to 9 answer c"
Answer: c
Question (physics): bullock likes to keep a spare tyre in his car every time . on a certain day , he travels 1 , 60,000 km and just to make the most of all the tyres , he changes the tyres between his journey such that each tyre runs the same distance . what is the distance traveled by each tyre ?
Options: a ) 70,000 , b ) 60,000 , c ) 128,000 , d ) 90,000 , e ) 10,000
Rationale: the distance traveled by each tyre : 4 / 5 * 1 , 60 , 000 km = 128,000 km . c
Answer: c
Question (general): what is the remainder when 10 ^ 49 + 2 is divided by 11 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7
Rationale: "with exponent - based problems and huge numbers , it ' s often helpful to try to establish a pattern using small numbers . on this problem , while 1049 + 2 is a massive number that you ' d never want to try to perform calculations with , you can start by using smaller numbers to get a feel for what it would look like : 10 ^ 2 + 2 = 102 , which when divided by 11 produces a remainder of 3 ( as 9 * 11 = 99 , leaving 3 left over ) 10 ^ 3 + 2 = 1002 , which when divided by 11 produces a remainder of 1 ( as 9 * 110 = 990 , and when you add one more 11 to that you get to 1001 , leaving one left ) 10 ^ 4 + 2 = 10002 , which when divided by 11 produces a remainder of 3 ( as you can get to 9999 as a multiple of 11 , which would leave 3 left over ) 10 ^ 5 + 2 = 100002 , which when divided by 11 produces a remainder of 1 ( as you can get to 99990 and then add 11 more , bringing you to 100001 leaving one left over ) . by this point , you should see that the pattern will repeat , meaning that when 10 has an even exponent the remainder is 3 and when it has an odd exponent the remainder is 1 . therefore , since 10 has an odd exponent in the problem , the remainder will be 1 . answer is a"
Answer: a
Question (other): 39 ! is divided by 41 then find the remainder ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: "substituting p = 41 in the wilson ' s theorem , we get 40 ! + 141 = 0 40 × 39 ! + 141 = 0 − 1 × 39 ! 41 = − 1 cancelling - 1 on both sides , 39 ! 41 = 1 a"
Answer: a
Question (general): evaluate : 60 - 9 ÷ 3 × 6 =
Options: a ) 52 , b ) 18 , c ) 42 , d ) 102 , e ) 36
Rationale: "according to order of operations , 9 ÷ 3 × 6 ( division and multiplication ) is done first from left to right 9 ÷ 3 × 6 = 3 × 6 = 18 hence 60 - 9 ÷ 3 × 6 = 60 - 18 = 42 correct answer c ) 42"
Answer: c
Question (gain): a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 20 % , what should be the sale price of the mixed tea ?
Options: a ) 23.75 , b ) 22 , c ) 20 , d ) 19.2 , e ) none of these
Rationale: "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 20 ) / 100 × 16 = 19.2 answer d"
Answer: d
Question (general): the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number w ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: "( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = w answer : b"
Answer: b
Question (gain): uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 12 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 3 , b ) 6 , c ) 7.2 , d ) 7.8 , e ) 9
Rationale: "answer is a . x / x + 36 = 1 / 5 x = 9 12 - 9 = 3"
Answer: a
Question (geometry): approximately how many cubic feet of water are needed to fill a circular swimming pool that is 70 feet across and 9 feet deep ?
Options: a ) 4000
b ) 10000
c ) 20000
d ) 35000
e ) 45000
Rationale: answer should be d . v = \ pir ^ 2 h = \ pi * 35 ^ 2 * 9 = approximately 35000
Answer: d
Question (gain): an empty wooden vessel weighs 14 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled .
Options: a ) 6 / 13 , b ) 5 / 9 , c ) 1 / 24 , d ) 4 / 9 , e ) 2 / 5
Rationale: "an empty wooden vessel weighs 14 % of its total weight when filled with paint : vessel = 0.14 ( vessel + paint ) ; 14 v = v + p ( so the weight of completely filled vessel is 14 v ) p = 13 v ( so the weight of the paint when the vessels is completely filled is 13 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 14 v ; p ' = 6 v ( so the weight of the paint when the vessels is partially filled is 6 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 6 v / 13 v = 6 / 13 . answer : a ."
Answer: a
Question (general): 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , ( . . . )
Options: a ) 53 , b ) 47 , c ) 61 , d ) 59 , e ) 45
Rationale: "explanation : all are prime numbers in their order , starting from 23 hence , next number is 61 answer : c"
Answer: c
Question (general): the arithmetic mean and standard deviation of a certain normal distribution are 12 and 1.2 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 9.6 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "mean = 12 two standard deviations is 1.2 + 1.2 = 2.4 there could be two calues for this . mean + two standard deviations = 14.4 mean - two standard deviations = 9.6 answer choice has 9.6 and so a is the answer ."
Answer: a
Question (general): for what value of â € œ k â €  will the equation ( 2 kx 2 + 4 kx + 2 ) = 0 have equal roots ?
Options: a ) 1 , b ) 9 / 4 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2
Rationale: "for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 4 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 1 answer : a"
Answer: a
Question (general): a is the average ( arithmetic mean ) of the first 7 positive multiples of 7 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 – b ^ 2 is zero , what is the value of n ?
Options: a ) 4 , b ) 12 , c ) 14 , d ) 21 , e ) 28
Rationale: "if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 28 , which also equals b . b is the second positive multiple of n , thus n = 28 / 2 = 14 . the answer is c ."
Answer: c
Question (other): find the highest common factor of 36 and 84 ?
Options: a ) 4 , b ) 6 , c ) 12 , d ) 18 , e ) none of these
Rationale: 36 = 2 ^ 2 * 3 ^ 2 ; 84 = 2 ^ 2 * 3 * 7 h . c . f = 2 ^ 2 * 3 = 12 . correct option : c
Answer: c
Question (geometry): the area of a base of a cone is 30 cm 2 . if the height of the cone is 6 cm , find its volume ?
Options: a ) 87
b ) 16
c ) 17
d ) 60
e ) 18
Rationale: π r 2 = 30 h = 6 1 / 3 * 30 * 6 = 60 answer : d
Answer: d
Question (geometry): an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 3 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ?
Options: a ) 12 : 7 , b ) 15 : 11 , c ) 25 : 16 , d ) 30 : 23 , e ) 32 : 25
Rationale: "let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be 3 y and y . 2 ( 3 x + 2 x ) = 2 ( 3 y + y ) 5 x = 4 y ( 5 / 4 ) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : 3 y * y = 6 x ^ 2 : 3 y ^ 2 = 6 x ^ 2 : 3 * ( 25 / 16 ) * x ^ 2 = 96 : 75 = 32 : 25 the answer is e ."
Answer: e