Cheukting/mathqa huggingface dataset:
Question (general): at deluxe paint store , fuchsia paint is made by mixing 6 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 24 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: in 24 liters , red = 6 / 9 * 24 = 16 and blue = 8 so , 16 / ( 8 + x ) = 4 / 5 or , x = 12 ( answer b )
Answer: b
Question (general): if x is a positive integer with fewer than 3 digits , what is the probability w that x * ( x + 1 ) is a multiple of either 4 or 5 ?
Options: a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99
Rationale: "interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability w that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) ."
Answer: e
Question (gain): because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 2 times as much as mork did , what was their combined tax rate ?
Options: a ) 32.5 % , b ) 34 % , c ) 22.5 % , d ) 33.3 % , e ) 37.5 %
Rationale: "say morks income is - 100 so tax paid will be 40 say mindys income is 2 * 100 = 200 so tax paid is 30 % * 200 = 60 total tax paid = 40 + 60 = 100 . combined tax % will be 100 / 100 + 200 = 33.3 %"
Answer: d
Question (general): two employees m and n are paid a total of rs . 550 per week by their employer . if m is paid 120 percent of the sum paid to n , how much is n paid per week ?
Options: a ) rs . 220 , b ) rs . 250 , c ) rs . 280 , d ) rs . 300 , e ) rs . 320
Rationale: let the amount paid to m per week = x and the amount paid to n per week = y then x + y = 550 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 550 ⇒ y [ 12 / 10 + 1 ] = 550 ⇒ 22 y / 10 = 550 ⇒ 22 y = 5500 ⇒ y = 5500 / 22 = 500 / 2 = rs . 250 b )
Answer: b
Question (general): a certain bag of gemstones is composed of two - thirds diamonds and one - third rubies . if the probability of randomly selecting two diamonds from the bag , without replacement , is 5 / 12 , what is the probability of selecting two rubies from the bag , without replacement ?
Options: a ) 5 / 36 , b ) 5 / 24 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 4
Rationale: 2 / 3 * ( 2 x - 1 ) / ( 3 x - 1 ) = 5 / 12 = > x = 3 so total gems = 9 and probability of ruby = 1 / 3 * 2 / 8 = 1 / 12 answer 1 / 12 c
Answer: c
Question (general): one man adds 5 liters of water to 10 liters of milk and another 4 liters of water to 20 liters of milk . what is the ratio of the strengths of milk in 2 mixtures ?
Options: a ) 4 : 5 , b ) 9 : 11 , c ) 2 : 3 , d ) 4 : 7 , e ) 3 : 7
Rationale: strength of milk in the mixture = quantity of milk / total quantity of mixture strength of milk in the 1 st mixture = 10 / 15 strength of the milk 2 nd mixture = 20 / 24 the ratio of their strengths = 10 / 15 : 20 / 24 = 4 : 5 answer is b
Answer: b
Question (general): the average of 9 observations was 6 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?
Options: a ) 36 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "explanation : 1 to 9 = 9 * 6 = 54 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 54 = 36 option a"
Answer: a
Question (general): in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 60 . what is the total number of students in the school ?
Options: a ) 72 , b ) 80 , c ) 125 , d ) 150 , e ) 100
Rationale: explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 60 + 2 / 3 of 60 80 / 100 x = 100 x = 125 . answer : option c
Answer: c
Question (physics): two pipes a and b can fill a tank in 24 and 48 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 12 , b ) 16 , c ) 19 , d ) 20 , e ) 22
Rationale: "part filled by a in 1 min . = 1 / 24 part filled by b in 1 min . = 1 / 48 part filled by ( a + b ) in 1 min . = 1 / 24 + 1 / 48 = 1 / 16 . both the pipes can fill the tank in 16 minutes . answer : b"
Answer: b
Question (gain): rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 1000 . then his monthly salary is
Options: a ) rs . 5000 , b ) rs . 6000 , c ) rs . 4000 , d ) rs . 3000 , e ) rs . 2000
Rationale: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 1000 â ‡ ” 20 / 100 x = 1000 â ‡ ” x = 1000 ã — 5 = 5000 . answer a"
Answer: a
Question (physics): the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 36 kmph , find the speed of the stream ?
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 36 / 3 = 12 kmph . answer : a"
Answer: a
Question (general): find the average of first 7 multiples of 5 ?
Options: a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 20
Rationale: "average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 ) / 7 = 20 answer is e"
Answer: e
Question (general): robert ' s salary was decreased by 40 % and subsequently increased by 40 % . how much percentage does he lose ?
Options: a ) 16 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 50 %
Rationale: "let original salary be $ 100 salary after decreasing 40 % = 100 - 100 x 40 / 100 = $ 60 salary after increasing 40 % on $ 60 = 60 + 60 x 40 / 100 = $ 84 percentage of loss = 100 - 84 = 16 % answer : a"
Answer: a
Question (general): rs . 1560 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 528 , b ) s . 542 , c ) s . 528 , d ) s . 720 , e ) s . 549
Rationale: "a + b + c = 1560 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1560 = rs . 720 answer : d"
Answer: d
Question (general): the average runs of a cricket player of 12 innings was 48 . how many runs must he make in his next innings so as to increase his average of runs by 10 ?
Options: a ) 12 , b ) 142 , c ) 164 , d ) 178 , e ) 84
Rationale: "explanation : average after 13 innings = 58 required number of runs = ( 58 * 13 ) – ( 48 * 12 ) = 754 – 576 = 178 answer d"
Answer: d
Question (physics): find the area , diameter = 10 m .
Options: a ) 78.24 square meter , b ) 78.57 square meter , c ) 78.26 square meter , d ) 24.24 square meter , e ) 24.43 square meter
Rationale: "diameter = 10 meter . radius = diameter / 2 . = 10 / 2 . = 5 meter . area of a circle = ï € r 2 . here , pi ( ï € ) = 3.14 meter , radius ( r ) = 5 . area of a circle = 3.14 ã — 5 ã — 5 . . = 3.14 ã — 25 . = 78.57 square meter answer : b"
Answer: b
Question (general): tickets numbered from 1 to 22 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 7 / 22
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 , 22 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 ] p ( e ) = n ( e ) / n ( s ) = 7 / 22 the answer is e ."
Answer: e
Question (gain): a present value of a machine is $ 900 . its value depletiation rate is 25 % per annum then find the machine value before 2 years ?
Options: a ) $ 1500 , b ) $ 1200 , c ) $ 1600 , d ) $ 1000 , e ) $ 1350
Rationale: "p = $ 900 r = 25 % t = 2 years machine value before 2 years = p / [ ( 1 - r / 100 ) ^ t ] = 900 * 4 / 3 * 4 / 3 = $ 1600 answer is c"
Answer: c
Question (general): how many positive integers less than 100 are neither multiples of 3 or 5 .
Options: a ) a ) 30 , b ) b ) 31 , c ) c ) 32 , d ) d ) 53 , e ) e ) 34
Rationale: "to answer this q we require to know 1 ) multiples of 5 till 100 = 100 / 5 = 20 2 ) multiples of 3 till 100 = 100 / 3 = 33.33 = 33 add the two 20 + 33 = 53 ; subtract common terms that are multiple of both 5 and 3 . . lcm of 5 and 3 = 15 multiples of 15 till 100 = 100 / 15 = 6 so total multiples of 5 and 3 = 53 - 6 = 47 ans = 100 - 47 = 53 d"
Answer: d
Question (general): 122 * 252 - 12234 = ?
Options: a ) 15310 , b ) 18870 , c ) 24510 , d ) 18510 , e ) 42510
Rationale: "d ? = 122 * 252 - 12234 = 30744 - 12234 = 18510"
Answer: d
Question (gain): a company has two models of computers , model x and model y . operating at a constant rate , a model x computer can complete a certain task in 72 minutes and a model y computer can complete the same task in 36 minutes . if the company used the same number of each model of computer to complete the task in 1 minute , how many model x computers were used ?
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: let ' s say 1 work is processing 72 gb of data . model x : 1 gb per min model y : 2 gb per min working together , 1 x and 1 y = 3 gb per min so , 24 times as many computers would work at 72 gb per min . so no . of x = 24 answer is c
Answer: c
Question (gain): a fruit seller had some oranges . he sells 40 % oranges and still has 360 oranges . how many oranges he had originally ?
Options: a ) 700 , b ) 710 , c ) 600 , d ) 730 , e ) 740
Rationale: "60 % of oranges = 360 100 % of oranges = ( 360 × 100 ) / 6 = 600 total oranges = 700 answer : c"
Answer: c
Question (general): of the goose eggs laid at a certain pond , 1 / 2 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 800 , b ) 840 , c ) 880 , d ) 920 , e ) 960
Rationale: "let x be the number of eggs that were laid . ( 2 / 5 ) ( 3 / 4 ) ( 1 / 2 ) x = 120 ( 6 / 40 ) x = 120 x = 800 the answer is a ."
Answer: a
Question (gain): one fourth of a solution that was 10 % sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 34 % , b ) 24 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "et 100 be the total volume . total salt = 10 salt taken out = 10 / 4 = 2.5 to make solution 16 % , total salt = 16 salt added = 16 - 7.5 = 8.5 solution had = 8.5 / 25 * 100 = 34 % sugar answer : a"
Answer: a
Question (general): if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 420 , what is the least possible value of n ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "420 = 2 * 2 * 3 * 5 * 7 , so n must be at least 7 . the answer is b ."
Answer: b
Question (general): if x = 5 - q and y = 3 q - 1 , then for what value of q , x is three times to y ?
Options: a ) 0 , b ) 1 , c ) - 1 , d ) - 8 , e ) 8
Rationale: "explanation : x = 3 y < = > 5 - q = 3 ( 3 q - 1 ) < = > 5 - q = 9 q - 3 < = > 8 q = 8 < = > q = 1 . answer : b"
Answer: b
Question (physics): express a speed of 16 kmph in meters per second ?
Options: a ) 10 mps , b ) 8 mps , c ) 4 mps , d ) 7 mps , e ) 2 mps
Rationale: "16 * 5 / 18 = 4 mps answer : c"
Answer: c
Question (physics): xavier starts from p towards q at a speed of 90 kmph and after every 12 mins increases his speed by 10 kmph . if the distance between p and q is 51 km , then how much time does he take to cover the distance ?
Options: a ) 30 , b ) 32 , c ) 30 , d ) 36 , e ) 40
Rationale: "first 12 min = 90 * 12 / 60 = 18 km 2 nd 12 min = 100 * 12 / 60 = 20 km 3 rd 12 min = 110 * 12 / 60 = 22 km total time 12 * 3 = 36 min d"
Answer: d
Question (general): a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 63 , what is the total amount ?
Options: a ) 166 , b ) 105 , c ) 178 , d ) 177 , e ) 245
Rationale: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 63 35 - - - ? = > 245 answer : e"
Answer: e
Question (general): how many multiples of 2 are there between 0 and 100 , exclusive ?
Options: a ) 48 , b ) 47 , c ) 46 , d ) 45 , e ) 49
Rationale: "2 * 50 = 100 total multiples = ( 50 - 1 ) + 1 = 50 exclude 0 and 100 = 50 - 1 = 49 answer is e ."
Answer: e
Question (general): the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 68 kg . what is the correct weight ?
Options: a ) 58 kgs , b ) 58.85 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: "actual total weight is ( 20 x 58.4 - 56 + 68 ) = 1180 kgs actual average weight is 1180 / 20 = 59 kgs d"
Answer: d
Question (probability): what is the probability that a two digit number selected at random will be a multiple of ' 3 ' and not a multiple of ' 5 ' ?
Options: a ) 2 / 15 , b ) 4 / 15 , c ) 1 / 15 , d ) 4 / 90 , e ) 5 / 60
Rationale: solution : there are a total of 90 two digit numbers . every third number will be divisible by ' 3 ' . therefore , there are 30 of those numbers that are divisible by ' 3 ' . of these 30 numbers , the numbers that are divisible by ' 5 ' are those that are multiples of ' 15 ' . i . e . numbers that are divisible by both ' 3 ' and ' 5 ' . there are 6 such numbers - - 15 , 30,45 , 60,75 and 90 . we need to find out numbers that are divisible by ' 3 ' and not by ' 5 ' , which will be : 30 â ˆ ’ 6 = 24 24 out of the 90 numbers are divisible by ' 3 ' and not by ' 5 ' . the required probability is therefore , = 24 / 90 = 4 / 15 answer is b
Answer: b
Question (physics): tom , working alone , can paint a room in 12 hours . peter and john , working independently , can paint the same room in 6 hours and 2 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 5 / 3 , b ) 1 / 3 , c ) 7 / 3 , d ) 4 / 9 , e ) 3 / 5
Rationale: let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 12 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 6 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 12 * ( t + 4 ) + 1 / 6 * ( t + 2 ) + 1 / 2 * t = 1 - - > multiply by 12 - - > ( t + 4 ) + ( 2 t + 2 ) + 6 t = 12 - - > t = 2 / 3 ; hence peter has done 1 / 6 * ( 2 / 3 + 2 ) = 1 / 6 * 8 / 3 = 8 / 18 = 4 / 9 answer : d
Answer: d
Question (gain): p and q started a business investing rs 50000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 12 : 5 , b ) 17 : 3 , c ) 10 : 6 , d ) 17 : 7 , e ) 10 : 3
Rationale: "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 50000 : 15000 = 50 : 15 = 10 : 3 option e"
Answer: e
Question (general): there are many numbers that can be expressed as the sum of 3 squares in 3 different ways . can you find out the smallest of such number ?
Options: a ) 87 , b ) 54 , c ) 29 , d ) 30 , e ) 70
Rationale: b 54 7 ^ 2 + 2 ^ 2 + 1 ^ 1 6 ^ 2 + 3 ^ 2 + 3 ^ 2 2 ^ 2 + 5 ^ 2 + 5 ^ 2
Answer: b
Question (physics): the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 100 metres ?
Options: a ) 16 seconds , b ) 20 seconds , c ) 14 seconds , d ) 12 seconds , e ) 15 seconds
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 100 m = 100 / 5 = 20 seconds . answer : b"
Answer: b
Question (general): in a mayoral election , candidate x received 1 / 5 more votes than candidate y , and candidate y received 1 / 2 fewer votes than z . if z received 20,000 votes how many votes did candidate x received ?
Options: a ) 12000 , b ) 22000 , c ) 24000 , d ) 26000 , e ) 32000
Rationale: "z = 20 - - > y received 1 / 2 fewer votes than z - - > y = z - 1 / 2 * z = 10 ; x received 1 / 5 more votes than y - - > x = y + 1 / 5 * y = 12 . answer : a ."
Answer: a
Question (general): ages of two persons differ by 22 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 14,30 , c ) 17,39 , d ) 18,34 , e ) 19,34
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 22 ) = > 3 ( x - 6 ) = ( x + 22 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 16 = > x = 17 . so other person age is x + 22 = 39 answer : option c"
Answer: c
Question (general): a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many w apples did each person get before 45 people joined the feast ?
Options: a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .
Rationale: "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons w = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c"
Answer: c
Question (gain): a watch was sold at a loss of 10 % . if it was sold for rs . 280 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s : 2000 , b ) s : 1067 , c ) s : 1278 , d ) s : 1028 , e ) s : 1027
Rationale: "90 % 104 % - - - - - - - - 14 % - - - - 280 100 % - - - - ? = > rs : 2000 answer : a"
Answer: a
Question (gain): a man can row his boat with the stream at 18 km / h and against the stream in 8 km / h . the man ' s rate is ?
Options: a ) 5 kmph , b ) 2 kmph , c ) 7 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "ds = 18 us = 8 s = ? s = ( 18 - 8 ) / 2 = 5 kmph answer : a"
Answer: a
Question (general): free notebooks were distributed equally among children of a class . the number of notebooks each child got was one - eighth of the number of children . had the number of children been half , each child would have got 16 notebooks . how many notebooks were distributed in all ?
Options: a ) 432 , b ) 640 , c ) 256 , d ) 512 , e ) none of these
Rationale: "in case i : let the no . of children = x . hence , total no . of notebooks distributed 1 ⁄ 8 x . x or x 2 ⁄ 8 . . . . . . . ( i ) in case ii : no . of children = x ⁄ 2 now , the total no . of notebooks = 16 × x ⁄ 2 . . . . . . . ( ii ) comparing ( i ) & ( ii ) , we get x 2 ⁄ 8 = 8 x or , x = 64 hence , total no . of notebooks = 64 × 64 / 8 = 512 answer d"
Answer: d
Question (physics): one pipe can fill a tank 3 times as fast as another pipe . if together the two pipes can fill tank in 40 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 160 , b ) 787 , c ) 144 , d ) 128 , e ) 121
Rationale: let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 40 4 / x = 1 / 40 = > x = 160 min . answer : a
Answer: a
Question (gain): 1500 is increased by 20 % . find the final number .
Options: a ) 1500 , b ) 1800 . , c ) 1900 , d ) 1700 , e ) 1660
Rationale: final number = initial number + 20 % ( original number ) = 1500 + 20 % ( 1500 ) = 1500 + 300 = 1800 . answer b
Answer: b
Question (geometry): the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 50 , then how long is the base of isosceles triangle ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "the base of the isosceles triangle is 50 - 20 - 20 = 10 units the answer is b ."
Answer: b
Question (physics): a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 1 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 120 , c ) 289 , d ) 270 , e ) 927
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 1 = 120 answer : b"
Answer: b
Question (general): ( 0.5 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.5 ) ( power 2 ) + 0.05 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.8 , b ) 0.4 , c ) 0.96 , d ) 0.69 , e ) 0.76
Rationale: "given expression = ( 0.5 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.5 ) ( power 2 ) + ( 0.5 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.5 - 0.1 ) = 0.4 answer is b"
Answer: b
Question (general): if p is a prime number greater than 3 , find the remainder when p ^ 2 + 17 is divided by 12 .
Options: a ) 6 , b ) 1 , c ) 0 , d ) 8 , e ) 7
Rationale: "take any prime number greater than 3 and check - say p = 5 so , p ^ 2 + 17 = 25 + 17 = > 42 42 / 12 will have remainder as 6 say p = 7 so , p ^ 2 + 17 = 49 + 17 = > 66 66 / 12 will have remainder as 6 so answer will be ( a ) 6"
Answer: a
Question (general): 9.8 , 9.8 , 9.9 , 9.9 , 10.0 , 10.0 , 10.1 , 10.5 the mean and the standard deviation of the 8 numbers shown above is 10 and 0.212 respectively . what percent of the 8 numbers are within 1 standard deviation of the mean ?
Options: a ) 90.5 % , b ) 87.5 % , c ) 80.5 % , d ) 77.5 % , e ) 70.5 %
Rationale: within 1 standard deviation of the mean - means in the range { mean - 1 * sd ; mean + 1 * sd } = { 10 - 1 * 0.212 ; 10 + 0.3 } = { 9.788 ; 10.212 } . from the 8 listed numbers , 7 are within this range so 6 / 8 = 87.5 % . answer : b .
Answer: b
Question (physics): at the opening of a trading day at a certain stock exchange , the price per share of stock m was $ 25 . if the price per share of stock m was $ 28 at the closing of the day , what was the percent increase in the price per share of stock m for that day ?
Options: a ) 1.4 % , b ) 5.9 % , c ) 12 % , d ) 12.5 % , e ) 23.6 %
Rationale: "opening = 25 closing = 28 rise in price = 3 so , percent increase = 3 / 25 * 100 = 12 answer : c"
Answer: c
Question (general): the average of 13 numbers is 60 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 43 , b ) 30 , c ) 35 , d ) 45 , e ) 50
Rationale: "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 780 = 46 . answer a"
Answer: a
Question (gain): martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 19.20 , how many discounted tickets did he buy ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 2
Rationale: "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 19.2 0.4 x = 3.2 = > x = 8 discounted tickets = 10 - x = 2 ans : e"
Answer: e
Question (geometry): the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 360 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 75
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 360 , 2 ( 7 / 5 ) w + 2 w = 360 solve the above equation to find : w = 75 m and l = 105 m . correct answer e ) 75"
Answer: e