regisss/math_qa huggingface dataset:
Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 8 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight
Options: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 4 , e ) 4 / 9
Rationale: "good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 1 / 8 of the garden is green , so , since all the flowers must be either green or yellow , we know that 7 / 8 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 7 / 8 * 1 / 2 = 4 / 9 , or e ."
Answer: e
Problem: how many 3 digit positive integers with distinct digits are there , which are not multiples of 10 ?
Options: a ) 576 , b ) 520 , c ) 504 , d ) 432 , e ) 348
Rationale: a number not to be a multiple of 10 should not have the units digit of 0 . xxx 9 options for the first digit ( from 1 to 9 inclusive ) . 8 options for the third digit ( from 1 to 9 inclusive minus the one we used for the first digit ) . 8 options for the second digit ( from 0 to 9 inclusive minus 2 digits we used for the first and the third digits ) 9 * 8 * 8 = 576 . answer : a .
Answer: a
Problem: 3 pounds of 05 grass seed contain 1 percent herbicide . a different type of grass seed , 20 , which contains 20 percent herbicide , will be mixed with 3 pounds of 05 grass seed . how much grass seed of type 20 should be added to the 3 pounds of 05 grass seed so that the mixture contains 15 percent herbicide ?
Options: a ) 3 , b ) 3.75 , c ) 4.5 , d ) 8.4 , e ) 9
Rationale: 05 grass seed contains 5 % herbicide and its amount is 3 pound 20 grass seed contains 20 % herbicide and its amount is x when these two types of grass seeds are mixed , their average becomes 15 % thus we have 3 ( 1 ) + x ( 20 ) / ( x + 3 ) = 15 3 + 20 x = 15 x + 45 5 x = 42 or x = 8.4 d
Answer: d
Problem: if f ( f ( n ) ) + f ( n ) = 2 n + 3 and f ( 0 ) = 1 , what is the value of f ( 2012 ) ?
Options: a ) 222 , b ) 2787 , c ) 2013 , d ) 2778 , e ) 10222
Rationale: "put n = 0 then f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) + 1 = 3 ⇒ ⇒ f ( 1 ) = 2 put n = 1 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) + 2 = 5 ⇒ ⇒ f ( 2 ) = 3 put n = 2 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) + 3 = 7 ⇒ ⇒ f ( 3 ) = 4 . . . . . . f ( 2012 ) = 2013 answer : c"
Answer: c
Problem: a certain barrel , which is a right circular cylinder , is filled to capacity with 60 gallons of oil . the first barrel is poured into a second barrel , also a right circular cylinder , which is empty . the second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel . if all of the oil in the first barrel is poured into the second barrel , how much empty capacity , in gallons , is left in the second barrel ?
Options: a ) there is no empty capacity
b ) 100 gallons
c ) 300 gallons
d ) 420 gallons
e ) 840 gallons
Rationale: radius of first cylinder = r , diameter = 2 r , height = h radius of second cylinder = 2 r , diamter = 2 d and height = 2 h volume of first cylinder = pie ( r ^ 2 ) * h = 60 volume of second cylinder = pie ( 2 r ^ 2 ) 2 h put the value of pie ( r ^ 2 ) * h = 60 in the second cylinder , volume = pie ( r ^ 2 ) * 4 * 2 = 60 * 8 = 480 gallons empty capacity = 420 gallons answer d
Answer: d
Problem: concentrated apples juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches . the tubes are packed into wooden boxes , each with dimensions of 11 inches by 10 inches by 31 inches . how many tubes of concentrated apples juice , at the most , can fit into 3 wooden boxes ?
Options: a ) 24 . , b ) 28 . , c ) 36 . , d ) 42 . , e ) 48 .
Rationale: concentrated apples juice comes inside a cylinder tube since height of a tube is 15 inches , the tubes can fit only in one way now , diameter of each tube = 5 inches therefore , 4 * 2 can be put in each wooden box in 3 boxes 3 * 4 * 2 can be accommodated = 24 = a
Answer: a
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 51.84 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 72 , d ) 87 , e ) 97
Rationale: "explanation : money collected = ( 51.84 x 100 ) paise = 5184 paise . ∴ number of members = √ ( 5184 ) = 72 . answer : c"
Answer: c
Problem: john purchased some shirts and trousers for $ 1550 . he paid $ 250 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "given that the total purchase of two items cost 1550 . so the average purchase of one item will cost 1550 / 2 = 775 . its given as total shirt cost 250 $ less . hence total shirt cost = 775 - 125 and total trouser cost = 775 + 125 5 shirts = 650 $ = = > one shirt = 130 $ one trouser = 130 + 20 = 150 $ total trousers = 900 / 150 = 6 . c"
Answer: c
Problem: a cube has a volume of 125 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?
Options: a ) 24 , b ) 48 , c ) 64 , d ) 80 , e ) 1000
Rationale: "volume = 125 = side ^ 3 i . e . side of cube = 5 new cube has dimensions 10 , 10 , and 10 as all sides are twice of teh side of first cube volume = 10 * 10 * 10 = 1000 square feet answer : option e"
Answer: e
Problem: a car is running at a speed of 110 kmph . what distance will it cover in 9 sec ?
Options: a ) 100 m , b ) 279 m , c ) 180 m , d ) 200 m , e ) 250 m
Rationale: "speed = 110 kmph = 110 * 5 / 18 = 31 m / s distance covered in 9 sec = 31 * 9 = 279 m answer is b"
Answer: b
Problem: in an election , candidate a got 65 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?
Options: a ) 355600 , b ) 355800 , c ) 356500 , d ) 309400 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 65 % therefore , the number of valid votes polled in favour of candidate a = 65 % of 476000 = 65 / 100 × 476000 = 30940000 / 100 = 309400 d )"
Answer: d
Problem: if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly twice in 2 consecutive flips ?
Options: a ) 0.125 , b ) 0.225 , c ) 0.25 , d ) 0.5 , e ) 0.666
Rationale: "total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 = 4 ways for 2 h hh , thus probability is = p ( hh ) = 1 / 4 = . 25 answer : c"
Answer: c
Problem: in a manufacturing plant , it takes 36 machines 4 hours of continuous work to fill 6 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 12 standard orders ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: the choices give away the answer . . 36 machines take 4 hours to fill 8 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 12 / 6 = 4 ans a
Answer: a
Problem: a car is running at a speed of 90 kmph . what distance will it cover in 10 sec ?
Options: a ) 100 m , b ) 150 m , c ) 180 m , d ) 200 m , e ) 250 m
Rationale: "speed = 90 kmph = 90 * 5 / 18 = 25 m / s distance covered in 10 sec = 25 * 10 = 250 m answer is e"
Answer: e
Problem: how many 3 digit number formed by using 23 , 45 , 67 once such that number is divisible by 15 .
Options: a ) 8 , b ) 13 , c ) 12 , d ) 20 , e ) 22
Rationale: 4 * 2 * 1 = 8 at one ' s place only 5 will come and at ten ' s place 4 and 7 can be placed , and at 100 th place rest of the 4 digits can come . . . so the answer is 8 answer : a
Answer: a
Problem: how many 3 digit positive integers t exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: "minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e ."
Answer: e
Problem: in a 100 member association consisting of men and women , exactly 10 % of men and exactly 20 % women are homeowners . what is the maximum number of members who are homeowners ?
Options: a ) 29 , b ) 27 , c ) 25 , d ) 23 , e ) 21
Rationale: "solution simple out of 100 10 % are male i . e 10 and 20 % are female i . e 20 , so total homeowner is 30 . now min number homeowner is 10 and max is 30 so question ask us to find maximum and 29 has maximum value among all option . so ans is 29 . ans : a"
Answer: a
Problem: how many single - digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6 ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: the possible number n can be written as follow : n = multiple of lcm ( 610 ) + 1 st such number n = 30 x + 1 possible values = 1 answer : b
Answer: b
Problem: the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) a ) 17 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24
Rationale: "explanation : 10 * 16 + 36 – 26 = 170 = > 170 / 10 = 17 a )"
Answer: a
Problem: 48 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 16 , c ) 13 , d ) 18 , e ) 19
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 48 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 48 x 5 x 12 x = ( 48 x 5 x 12 ) / ( 30 x 6 ) x = 16 answer b"
Answer: b
Problem: in the coordinate plane , a circle centered on point ( - 3 , 4 ) passes through point ( 1 , 1 ) . what is the area of the circle ?
Options: a ) 9 π , b ) 18 π , c ) 25 π , d ) 37 π , e ) 41 π
Rationale: "r ^ 2 = ( - 3 - 1 ) ^ 2 + ( 4 - 1 ) ^ 2 = 16 + 9 = 25 area of circle = π r ^ 2 = 25 π answer : c"
Answer: c
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 7 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 487 , c ) 481 , d ) 840 , e ) 268
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 7 = 840 answer : d"
Answer: d
Problem: the ratio between x and y is 8 / 3 ; x is multiplied by x and y is multiplied by y , what is the ratio between the new values of x and y ?
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 1 , d ) 64 / 9 , e ) it can not be determined
Rationale: "ratio = 7 k / 9 k = 7 / 9 , 14 / 18 , etc . x is multiplied by x and y is multiplied by y - - > ( 7 k * 7 k ) / ( 9 k * 9 k ) = 49 k ^ 2 / 81 k ^ 2 = 49 / 81 = 7 / 9 answer : a"
Answer: a
Problem: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 100 , the runs scored by a are ?
Options: a ) 11 , b ) 18 , c ) 13 , d ) 16 , e ) 12
Rationale: "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 4 / 25 * 100 = 16 answer : d"
Answer: d
Problem: 1 , 3,5 , 7,9 , . . 50 find term of sequnce
Options: a ) 1230 , b ) 1300 , c ) 1500 , d ) 1679 , e ) 2500
Rationale: "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n − 1 ) l ) sn = 12 n ( 2 a + ( n − 1 ) l ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 98 ) = 25 × ( 2 + 98 ) = 2500 = 2500 . e"
Answer: e
Problem: a palindrome is a number that reads the same forward and backward , such as 120 . how many odd , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 55 , c ) 50 , d ) 90 , e ) 2500
Rationale: "a palindrome is a number that reads the same forward and backward . examples of four digit palindromes are 1221 , 4334 , 2222 etc you basically get to choose the first two digits and you repeat them in opposite order . say , you choose 45 as your first two digits . the next two digits are 54 and the number is 4554 . also , you need only odd palindromes . this means that you need an odd digit at the end i . e . 1 / 3 / 5 / 7 / 9 . this means that you need to start the number with an odd digit . only then will it end with an odd digit . in how many ways can you pick two digits such that the first one is an odd digit ? the first digit can be selected in 5 ways . ( 1 / 3 / 5 / 7 / 9 ) the second digit can be selected in 10 ways . ( 0 / 1 / 2 / 3 . . . 8 / 9 ) total = 5 * 11 = 55 ways b"
Answer: b
Problem: the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if x 20 = 190 , what is the value of x ?
Options: a ) 10 , b ) 12 , c ) 11 , d ) 13 , e ) 14
Rationale: "ab = ( a - 1 ) ( b - 1 ) x 20 = ( x - 1 ) ( 20 - 1 ) = 190 - - > x - 1 = 10 - - > x = 11 answer : c"
Answer: c
Problem: how many 5 digit nos are there if the 2 leftmost digits are odd and the digit 4 ca n ' t appear more than once in the number ? could someone please provide a solution using a approach other than ( 1 - x ( none ) ) approach ?
Options: a ) 24300 , b ) 25700 , c ) 26500 , d ) 24400 , e ) 26300
Rationale: a . 4 is used once : oo * * 4 - - > ( 5 * 5 * 9 * 9 ) * 3 : 5 choices for the first digit as there are 5 odd numbers , 5 choices for the second digit for the same reason , 9 choices for one of the two * ( not - 4 digit ) , 9 choices for another * ( not - 4 digit ) , multiplied by 3 as 4 can take the place of any of the three last digits ( oo * * 4 , oo * 4 * , oo 4 * * ) ; b . 4 is not used : oo * * * - - > 5 * 5 * 9 * 9 * 9 : the same logic as above . 5 * 5 * 9 * 9 * 3 + 5 * 5 * 9 * 9 * 9 = 24300 . answer : a
Answer: a
Problem: the population of a bacteria colony doubles every day . if it was started 8 days ago with 3 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 13122 , d ) 2048 , e ) 4096
Rationale: "3 ^ 8 * ( 2 ) = 13122 the answer is c"
Answer: c
Problem: a cat leaps 6 leaps for every 5 leaps of a dog , but 2 leaps of the dog are equal to 3 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?
Options: a ) 4 : 5 , b ) 2 : 3 , c ) 4 : 1 , d ) 1 : 9 , e ) 3 : 2
Rationale: "given ; 2 dog = 3 cat ; or , dog / cat = 3 / 2 ; let cat ' s 1 leap = 2 meter and dogs 1 leap = 3 meter . then , ratio of speed of cat and dog = 2 * 6 / 3 * 5 = 4 : 5 ' ' answer : 4 : 5 ;"
Answer: a
Problem: a horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 18 m long . over how much area of the field can it graze ?
Options: a ) 154 cm 2 , b ) 308 m 2 , c ) 254 m 2 , d ) 260 m 2 , e ) none of these
Rationale: "area of the shaded portion = 1 ⁄ 4 × π × ( 18 ) 2 = 254 m 2 answer c"
Answer: c
Problem: if the arithmetic mean of seventy 5 numbers is calculated , it is 35 . if each number is increased by 5 , then mean of new number is ?
Options: a ) 87 , b ) 40 , c ) 37 , d ) 28 , e ) 26
Rationale: a . m . of 75 numbers = 35 sum of 75 numbers = 75 * 35 = 2625 total increase = 75 * 5 = 375 increased sum = 2625 + 375 = 3000 increased average = 3000 / 75 = 40 . answer : b
Answer: b
Problem: 8873 + x = 13200 , then x is ?
Options: a ) 3327 , b ) 4327 , c ) 3337 , d ) 2337 , e ) none of these
Rationale: answer x = 13200 - 8873 = 4327 option : b
Answer: b
Problem: a box contains 8 pairs of shoes ( 16 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 15
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 16 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 15 ( as after taking one at random there are 15 shoes left and only one is the pair of the first one ) = 1 / 15 answer : e ."
Answer: e
Problem: sales price is $ 60 , gross profit is 140 % of cost , what is the value of gross profit ?
Options: a ) 32 , b ) 33 , c ) 39 , d ) 35 , e ) 42
Rationale: "cost + profit = sales cost + ( 140 / 100 ) cost = 60 cost = 25 profit = 60 - 25 = 35 answer ( d )"
Answer: d
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts 6 hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4.5 , c ) 4 , d ) d ) 12 , e ) e ) 5
Rationale: the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 6 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 6 + t ) = 40 * t t = 18 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 18 / 60 = 12 hrs time taken by a = 6 + t = 6 + 18 = 24 hrs time taken by k = 12 hrs so k starts 24 - 12 = 12 hrs after a . ( answer d )
Answer: d
Problem: in an exam 80 % of the boys and 40 % of the girls passed . the number of girls who passed is 120 , which is 2 / 3 rd of the number of boys who failed . what is the total number of students who appeared for the exam ?
Options: a ) 1200 , b ) 380 , c ) 3800 , d ) 2180 , e ) 3180
Rationale: let the number of boys = x , number of girls = y 40 y / 100 = 120 y = 300 120 = 2 / 3 * 20 x / 100 = 2 x / 15 x = 900 total = x + y = 300 + 900 = 1200 answer : a
Answer: a
Problem: when 4 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?
Options: a ) 32 , b ) 81 , c ) 60 , d ) 120 , e ) 11
Rationale: "explanation : let the number be 4 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 4 = a / 30 = > a = 120 answer : d"
Answer: d
Problem: a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 15 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 45 , b ) 33 , c ) 26 , d ) 21 , e ) 10
Rationale: "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 15 = > m = 45 answer a"
Answer: a
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 30 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 62.5 % , e ) 75 %
Rationale: "original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.3 c ( 30 % profit ) x = 1.3 / . 8 * c x = 13 / 8 c original selling price is 1.625 c which is 62.5 % profit answer d"
Answer: d
Problem: pipe a fills a tank in 42 minutes . pipe b can fill the same tank 6 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "a ' s rate is 1 / 42 and b ' s rate is 1 / 7 . the combined rate is 1 / 42 + 1 / 7 = 1 / 6 the pipes will fill the tank in 6 minutes . the answer is d ."
Answer: d
Problem: by weight , liquid x makes up 1.5 percent of solution p and 6.5 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 4.5 % , b ) 5.0 % , c ) 5.5 % , d ) 5.8 % , e ) 6.0 %
Rationale: "the number of grams of liquid x is 1.5 ( 200 ) / 100 + 6.5 ( 800 ) / 100 = 3 + 52 = 55 grams . 55 / 1000 = 5.5 % the answer is c ."
Answer: c
Problem: 900 men have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 12.88 , b ) 12.6 , c ) 12.55 , d ) 12.21 , e ) 12.27
Rationale: "900 * 15 = 1100 * x x = 12.27 . answer : e"
Answer: e
Problem: set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 2 ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 8 , e ) e ) 16
Rationale: points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is b
Answer: b
Problem: a snail , climbing a 24 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 12 , b ) 16 , c ) 17 , d ) 20 , e ) 21
Rationale: total transaction in two days = 4 - 2 = 2 feet in 20 days it will climb 20 feet on the 21 st day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 21 e
Answer: e
Problem: a ’ s speed is 25 / 18 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 18 , b ) 7 / 18 , c ) 7 / 25 , d ) 3 / 25 , e ) 1 / 25
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 25 meters , b covers 18 meters in that time . so if the race is 25 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 25 meters ) would be the same as the time required by b ( to cover 18 meters ) to reach the finish line . so b should get a head start of 7 / 25 th of the race . answer ( c )"
Answer: c
Problem: the marked price of a book is 20 % more than the cost price . after the book is sold , the vendor realizes that he had wrongly raised the cost price by a margin of 25 % . if the marked price of the book is rs . 30 , what is the original cost price of the book ?
Options: a ) rs . 30 , b ) rs . 25 , c ) rs . 45 , d ) rs . 20 , e ) rs . 10
Rationale: let the incorrect cost price be c 1 and let the original cost price be c 2 . marked price of book is rs . 30 . it is 20 % more than c 1 . therefore , ( 120 / 100 ) x c 1 = 30 or c 1 = 25 . c 1 is more than c 2 margin of 25 % . or c 1 = ( 125 / 100 ) c 2 therefore , c 2 = ( 100 / 125 ) x 25 = rs 20 answer : d
Answer: d
Problem: the h . c . f . of two numbers is 18 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
Options: a ) 270 , b ) 300 , c ) 299 , d ) 322 , e ) 345
Rationale: "the numbers are ( 18 x 11 ) and ( 18 x 15 ) . larger number = ( 18 x 15 ) = 270 . answer : a"
Answer: a
Problem: the ratio of buses to cars on river road is 1 to 3 . if there are 20 fewer buses than cars on river road , how many cars are on river road ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 30 , e ) 150
Rationale: "b / c = 1 / 3 c - b = 20 . . . . . . . . . > b = c - 20 ( c - 20 ) / c = 1 / 3 testing answers . clearly eliminate abce put c = 30 . . . . . . . . . > ( 30 - 20 ) / 30 = 10 / 30 = 1 / 3 answer : d"
Answer: d
Problem: speed of a boat in standing water is 10 kmph and speed of the stream is 2.5 kmph . a man can rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 23.4 hours , b ) 22.4 hours , c ) 21.4 hours , d ) 20.4 hours , e ) 19.4 hours
Rationale: "speed upstream = 7.5 kmph speed downstream = 12.5 kmph total time taken = 105 / 7.5 + 105 / 12.5 = 22.4 hours answer is b"
Answer: b
Problem: the total of 324 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is
Options: a ) 238 , b ) 277 , c ) 278 , d ) 200 , e ) 288
Rationale: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 324 - x ) . 0.20 * ( x ) + 0.25 ( 324 - x ) = 71 = > x = 200 . . answer : d ) 200"
Answer: d
Problem: if annual decrease in the population of a town is 5 % and the present number of people is 40000 what will the population be in 2 years ?
Options: a ) 24560 , b ) 26450 , c ) 36100 , d ) 38920 , e ) 45200
Rationale: population in 2 years = 40000 ( 1 - 5 / 100 ) ^ 2 = 40000 * 19 * 19 / 20 * 20 = 36100 answer is c
Answer: c
Problem: the price of lunch for 15 people was $ 206.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) $ 11.73 , b ) $ 12.48 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
Rationale: take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 206 is for 115 then we have to calculate for 100 for 115 206 for 100 x so by cross multiplication we get 115 x = 100 * 206 = > x = 100 * 206 / 110 by simplifying we get x as 187.27 which is the price of lunch before gratuity so the gratuity is 18.73 so as the question ask the average price person excluding gratuity is 187.27 / 15 = 12.48 so our answer is b )
Answer: b
Problem: a man can do a piece of work in 5 days , but with the help of his son , he can finish it in 3 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 5 1 / 2 , c ) 7 1 / 2 , d ) 6 , e ) 9 1 / 2
Rationale: "son ' s 1 day work = 1 / 3 - 1 / 5 = 2 / 15 son alone can do the work in 15 / 2 days = 7 1 / 2 days answer is c"
Answer: c
Problem: joe drives 600 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?
Options: a ) 42 , b ) 55 , c ) 50 , d ) 54 , e ) 56
Rationale: "t 1 = 600 / 60 = 10 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 13 hours avg speed = total distance / t = 720 / 13 = 55 mph = b"
Answer: b
Problem: a pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer ’ s suggested retail price . if during a sale , the store discounts an additional 20 percent from the discount price , what would be the lowest possible price of a container of pet food that had a manufacturer ’ s suggested retail price o f $ 20.00 ?
Options: a ) $ 10.00 , b ) $ 11.20 , c ) $ 14.40 , d ) $ 16.00 , e ) $ 18.00
Rationale: "for retail price = $ 20 first maximum discounted price = 20 - 30 % of 20 = 20 - 6 = 14 price after additional discount of 20 % = 14 - 20 % of 14 = 14 - 2.8 = 11.2 answer : option b"
Answer: b
Problem: if 20 liters of chemical x are added to 80 liters of a mixture that is 15 % chemical x and 85 % chemical y , then what percentage of the resulting mixture is chemical x ?
Options: a ) 30 % , b ) 32 % , c ) 35 % , d ) 38 % , e ) 40 %
Rationale: "the amount of chemical x in the solution is 20 + 0.15 ( 80 ) = 32 liters . 32 liters / 100 liters = 32 % the answer is b ."
Answer: b
Problem: a set consists of 12 numbers , all are even or multiple of 5 . if 4 numbers are even and 10 numbers are multiple of 5 , how many numbers is multiple of 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 12 = 4 + 10 - { both } + 0 ; { both } = 2 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : c ."
Answer: c
Problem: two employees x and y are paid a total of rs . 506 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 250 , b ) s . 280 , c ) s . 290 , d ) s . 299 , e ) s . 230
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 506 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 506 ⇒ y [ 12 / 10 + 1 ] = 506 ⇒ 22 y / 10 = 506 ⇒ 22 y = 5060 ⇒ y = 5060 / 22 = 460 / 2 = rs . 230 e"
Answer: e
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . what is the value of 3 * / 4 * ?
Options: a ) 5 , b ) 5 / 4 , c ) 4 / 5 , d ) 1 / 4 , e ) 1 / 5
Rationale: "when dealing with ' symbolism ' questions , it often helps to ' play with ' the symbol for a few moments before you attempt to answer the question that ' s asked . by understanding how the symbol ' works ' , you should be able to do the latter calculations faster . here , we ' re told that k * is the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . based on this definition . . . . if . . . . k = 2 k * = ( 1 / 1 ) ( 1 / 2 ) = 1 / 2 if . . . . k = 3 k * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) = 1 / 6 we ' re asked to find the value of 5 * / 4 * now that we know how the symbol ' works ' , solving this problem should n ' t be too difficult . you can actually choose to do the math in a couple of different ways . . . . 5 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) do n ' t calculate this just yet though . . . . since we ' re dividing by 4 * , many of those fractions will ' cancel out . ' 4 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) we ' re looking for the value of : ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) / ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) since the first four fraction in the numerator and denominator cancel out , we ' re left with just one fraction : 5 / 4 b"
Answer: b
Problem: find the missing figures : ? % of 25 = 20125
Options: a ) 4.5 , b ) 6.5 , c ) 2.5 , d ) 7.5 , e ) 8.5
Rationale: "let x % of 25 = 2.125 . then , ( x / 100 ) * 25 = 2.125 x = ( 2.125 * 4 ) = 8.5 . answer is e ."
Answer: e
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 10 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 11 years , c ) 14 years , d ) 21 years , e ) 9 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 4 + 16 x 10 ) ] = ( 225 - 216 ) = 9 years . answer e"
Answer: e
Problem: a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 40 , find the sum of money ?
Options: a ) 288 , b ) 262 , c ) 72 , d ) 205 , e ) 267
Rationale: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 40 41 - - - - ? = > rs . 205 answer : d"
Answer: d
Problem: two trains leave the train station at the same time . one train , on the blue line , heads east - while the other , on the red line , heads west . if the train on the blue line averages 40 km / hr and the other train averages 40 km / hr - how long will it take for the trains to be 100 km apart ?
Options: a ) 2 hours , b ) 2.25 hours , c ) 1 hour , d ) 1.25 hours , e ) not enough information
Rationale: each train is averaging 40 km / hour in an opposite direction . after 1 hour , they will be 80 km apart , and after 1.25 hours , they will be 100 km apart . ( 80 * 1.25 = 100 ) answer is d
Answer: d
Problem: a certain college ' s enrollment at the beginning of 1992 was 30 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 10 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options: a ) 43 % , b ) 45 % , c ) 50 % , d ) 35 % , e ) 38 %
Rationale: "suppose enrollment in 1991 was 100 then enrollment in 1992 will be 130 and enrollment in 1993 will be 130 * 1.1 = 143 increase in 1993 from 1991 = 143 - 100 = 43 answer : a"
Answer: a
Problem: what is the greatest possible length which can be used to measure exactly the lengths 10 m 50 cm , 14 m 55 cm and 50 cm ?
Options: a ) 20 cm , b ) 24 cm , c ) 30 cm , d ) 10 cm , e ) 5 cm
Rationale: "required length = hcf of 1050 cm , 1455 cm , 50 cm = 5 cm answer is e"
Answer: e
Problem: for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 9 + 3 and * 9 + 9 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "generally * p or p ! will be divisible by all numbers from 1 to p . therefore , * 9 would be divisible by all numbers from 1 to 9 . = > * 9 + 3 would give me a number which is a multiple of 3 and therefore divisible ( since * 9 is divisible by 3 ) in fact adding anyprimenumber between 1 to 9 to * 9 will definitely be divisible . so the answer is none ( a ) ! supposing if the question had asked for prime numbers between * 9 + 3 and * 9 + 11 then the answer would be 1 . for * 9 + 3 and * 9 + 13 , it is 2 and so on . . . a"
Answer: a
Problem: a can give b 120 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 90.09 meters , b ) 111.12 meters , c ) 112.12 meters , d ) 113.12 meters , e ) none of these
Rationale: "explanation : a runs 1000 meters while b runs 880 meters and c runs 800 meters . therefore , b runs 880 meters while c runs 800 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 800 ) / 880 = 909.09 meters thus , b can give c ( 1000 - 909.09 ) = 90.09 meters start answer : a"
Answer: a
Problem: convert 40 miles into yards ?
Options: a ) 25630 yards , b ) 35200 yards , c ) 39520 yards , d ) 42560 yards , e ) 70400 yards
Rationale: "1 mile = 1760 yards 40 miles = 40 * 1760 = 70400 yards answer is e"
Answer: e
Problem: a merchant marks his goods up by 30 % and then offers a discount of 20 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 8 % , b ) 10 % , c ) 21 % , d ) 15 % , e ) 4 %
Rationale: "let the price be 100 . the price becomes 130 after a 30 % markup . now a discount of 20 % on 130 . profit = 104 - 100 4 % answer e"
Answer: e
Problem: the owner of a furniture shop charges his customer 42 % more than the cost price . if a customer paid rs . 8300 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 5725 , b ) rs . 5845 , c ) rs . 6275 , d ) rs . 6725 , e ) none of these
Rationale: cp = sp * ( 100 / ( 100 + profit % ) ) = 8300 ( 100 / 142 ) = rs . 5845 . answer : b
Answer: b
Problem: an article with cost price of 320 is sold at 18 % profit . what is the selling price ?
Options: a ) 198 , b ) 200 , c ) 204 , d ) 378 , e ) 347
Rationale: "sp = 1.18 * 320 = 378 answer : d"
Answer: d
Problem: if it takes a tub 5 minutes to drain 5 / 7 of its content , how much more time will it take for the tub to be empty ?
Options: a ) 48 seconds , b ) 1 minute , 12 seconds , c ) 1 minute , 50 seconds , d ) 2 minutes , 00 seconds , e ) 4 minutes , 12 seconds
Rationale: "if 5 / 7 of tub ' s content is drained 2 / 7 th of tub still needs to be drained . if it takes 5 minutes to drain 5 / 7 th of tub it takes 5 * ( 7 / 5 ) minutes to drain the entire tub and 5 * ( 7 / 5 ) * ( 2 / 7 ) min to drain 2 / 7 th of the tub which is 2 minutes so answer is d"
Answer: d
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 3.25 each . if none of the 20 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 130 , b ) $ 185 , c ) $ 175 , d ) $ 165 , e ) $ 155
Rationale: "if 20 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 40 books amount received for sold books = 40 * 3.25 = $ 130 answer : a"
Answer: a
Problem: there are two cars . one is 160 miles north of the other . simultaneously , the car to the north is driven westward at 10 miles per hour and the other car is driven eastward at 30 miles per hour . how many miles apart are the cars after 3 hours ?
Options: a ) 180 , b ) 200 , c ) 220 , d ) 240 , e ) 250
Rationale: "here , drawing a quick sketch of the ' actions ' described will end in a diagonal line that you canbuilda right triangle around : the right triangle will have a base of 120 and a height of 160 . the hidden pattern here is a 3 / 4 / 5 right triangle ( the 120 lines up with the ' 3 ' and the 160 lines up with the ' 4 ' ) . in this way , you can deduce that each side is ' 40 times ' bigger than it ' s corresponding side : 3 / 4 / 5 becomes 120 / 160 / 200 thus the distance between the two cars is the length of the hypotenuse of this larger right triangle . . . final answer : b"
Answer: b
Problem: a batsman scored 120 runs which included 5 boundaries and 8 sixes . what % of his total score did he make by running between the wickets
Options: a ) 43.33 % , b ) 50 % , c ) 65 % , d ) 70 % , e ) 75 %
Rationale: "number of runs made by running = 120 - ( 5 x 4 + 8 x 6 ) = 120 - ( 68 ) = 52 now , we need to calculate 60 is what percent of 120 . = > 52 / 120 * 100 = 43.33 % a"
Answer: a
Problem: given that 100.48 = x , 100.70 = y and xz = y 2 , then the value of z is close to :
Options: a ) 2.2 , b ) 8.2 , c ) 2.9 , d ) 2.1 , e ) 2.6
Rationale: "xz = y 2 10 ( 0.48 z ) = 10 ( 2 x 0.70 ) = 101.40 0.48 z = 1.40 z = 140 = 35 = 2.9 ( approx . ) 48 12 answer : c"
Answer: c
Problem: how many digits are required to number a book containing 250 pages ?
Options: a ) 756 , b ) 642 , c ) 492 , d ) 372 , e ) 250
Rationale: "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 250 - ( 90 + 9 ) = 151 pages will require 151 * 3 = 453 digits . the total number of digits is 9 + 180 + 453 = 642 . the answer is b ."
Answer: b
Problem: at scratch and dents rent - a - car , it costs $ 34.95 a day plus $ 0.23 per mile to rent a car . at rent - a - lemon , the charge is $ 25.00 a day plus $ 1.31 per mile . if you need to rent a car for 3 days , how many miles ( to nearest tenth ) must you drive for a car from both agencies to cost the same amount ?
Options: a ) 25.7 miles , b ) 26.2 miles , c ) 27.6 miles , d ) 27.9 miles , e ) 29.9 miles
Rationale: for sad : saddaily = $ 34.95 / day sadmile = $ 0.23 / mile for ral : raldaily = $ 25.00 / day ralmile = $ 1.31 / mile we want the raltotal = sadtotal , so we get ( raldaily * days ) + ( ralmile * miles ) = ( saddaily * days ) + ( sadmile * miles ) = > miles = ( ( saddaily * days ) - ( raldaily * days ) ) / ( ralmiles - sadmiles ) = ( ( saddaily - raldaily ) * days ) / ( ralmiles - sadmiles ) miles = ( ( $ 34.95 * 3 ) - ( $ 25.00 * 3 ) ) / ( $ 1.31 - $ 0.23 ) = 27.6 miles c . 27.6 miles
Answer: c
Problem: pipe a can fill a tank in 9 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 ) 36 , b ) 88 , c ) 18 , d ) 26 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 9 - 1 / x = 1 / 12 = > 1 / x = 1 / 9 - 1 / 12 = 1 / 12 = > x = 36 . answer : a"
Answer: a
Problem: if p is a prime number greater than 3 , find the remainder when p ^ 2 + 16 is divided by 12 .
Options: a ) 5 , b ) 1 , c ) 0 , d ) 8 , e ) 7
Rationale: every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 16 = 36 n ^ 2 + 12 n + 1 + 16 = 36 n ^ 2 + 12 n + 12 + 5 if p = 6 n - 1 , then p ^ 2 + 16 = 36 n ^ 2 - 12 n + 1 + 16 = 36 n ^ 2 - 12 n + 12 + 5 when divided by 12 , it must leave a remainder of 5 . the answer is a .
Answer: a
Problem: a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked at 7 miles per hour for 2 hours . how many miles in total did she walk ?
Options: a ) 24 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 7 miles per hour and 2 hours - 14 miles total 18 + 20 + 14 = 52 answer : option b ."
Answer: b
Problem: if f ( x ) = 3 x ^ 4 - 4 x ^ 3 - 2 x ^ 2 + 5 x , then f ( - 1 ) =
Options: a ) - 4 , b ) - 2 , c ) 0 , d ) 2 , e ) 4
Rationale: "f ( - 1 ) = 3 ( - 1 ) ^ 4 - 4 ( - 1 ) ^ 3 - 2 ( - 1 ) ^ 2 + 5 ( - 1 ) = 3 + 4 - 2 - 5 = 0 the answer is c ."
Answer: c
Problem: carol spends 1 / 4 of her savings on a stereo and 1 / 5 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 9 / 20 , e ) 7 / 12
Rationale: "total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 1 / 5 ) ( 1 / 4 ) s = ( 4 / 5 ) * ( 1 / 4 ) * s = ( 1 / 5 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 5 ) / s = 9 / 20 answer : d"
Answer: d
Problem: if x is 20 percent greater than 55 , then x =
Options: a ) 68 , b ) 70.4 , c ) 86 , d ) 66 , e ) 108
Rationale: x is 20 % greater than 55 means x is 1.2 times 55 ( in other words 55 + 20 / 100 * 55 = 1.2 * 55 ) therefore , x = 1.2 * 55 = 66 answer : d
Answer: d
Problem: find the value of 72519 x 9999 = y ?
Options: a ) 354517481 , b ) 457687783 , c ) 246567689 , d ) 725117481 , e ) 565776879
Rationale: "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d"
Answer: d
Problem: a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 49 / 64 . how many marbles are in the bag ?
Options: a ) 24 , b ) 48 , c ) 60 , d ) 96 , e ) 84
Rationale: "ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 49 / 64 - - > ( x - 12 ) ^ 2 = 49 / 64 x ^ 2 square rooting u have x - 12 / x = 7 / 8 or x = 96 d"
Answer: d
Problem: average of 15 results is 43 . if the average of first 7 results is 41 and average of last 7 results is 45 then find the eighth result ?
Options: a ) 41 , b ) 39 , c ) 43 , d ) 45 , e ) 47
Rationale: option ' c '
Answer: c
Problem: the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 432 . find the principal ?
Options: a ) 2277 , b ) 2667 , c ) 3600 , d ) 9766 , e ) 10800
Rationale: p = 432 ( 100 / 5 ) ^ 2 = > p = 10800 answer : e
Answer: e
Problem: a sprinter starts running on a circular path of radius r metres . her average speed ( in metres / minute ) is π r during the first 30 seconds , π r / 2 during next one minute , π r / 4 during next 2 minutes , π r / 8 during next 4 minutes , and so on . what is the ratio of the time taken for the nth round to that for the previous round ?
Options: a ) 4 , b ) 8 , c ) 16 , d ) 32 , e ) 36
Rationale: explanation : there is more than 1 way to approach the solution ; however , i will detail the easiest way to go about it here . we want to find the ratio of time taken for nth round : time taken for ( n - 1 ) th round it will be same as finding the ratio of time taken for 2 nd round : time taken for 1 st round . 1 round = circumference of the circle = 2 π r 1 st round : speed = π r for 30 seconds . so , total distance travelled = π r / 2 . speed = π r / 2 for 1 minute . so , total distance travelled = π r / 2 . speed = π r / 4 for 2 minutes . so , total distance travelled = π r / 2 . speed = π r / 8 for 4 minutes . so , total distance travelled = π r / 2 . so , for a distance of 2 π r , time taken is 7.5 minutes . 2 nd round : speed = π r / 16 for 8 minutes . so , total distance travelled = π r / 2 . speed = π r / 32 for 16 minutes . so , total distance travelled = π r / 2 . speed = π r / 64 for 32 minutes . so , total distance travelled = π r / 2 . speed = π r / 128 for 64 minutes . so , total distance travelled = π r / 2 . so , for a distance of 2 π r , time taken is 120 minutes . ratio is 120 : 7.5 = 16 : 1 . answer : c
Answer: c
Problem: . a car covers a distance of 1028 km in 4 hours . find its speed ?
Options: a ) 104 , b ) 255 , c ) 266 , d ) 257 , e ) 276
Rationale: "1028 / 4 = 257 kmph answer : d"
Answer: d
Problem: the cost price of a radio is rs . 2550 and it was sold for rs . 2130 , find the loss % ?
Options: a ) 18 , b ) 10 , c ) 15 , d ) 66 , e ) 41
Rationale: "2550 - - - - 400 100 - - - - ? = > 15 % answer : c"
Answer: c
Problem: if x * y = xy – 2 ( x + y ) for all integers x and y , then 4 * ( – 3 ) =
Options: a ) – 14 , b ) – 11 , c ) – 4 , d ) 4 , e ) 16
Rationale: "4 * ( - 3 ) = 4 * ( - 3 ) - 2 ( 4 + ( - 3 ) ) = - 12 - 2 = - 14 option ( a )"
Answer: a
Problem: the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams t ?
Options: a ) t = 16 , b ) t = 32 , c ) t = 64 , d ) 128 , e ) 512
Rationale: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"
Answer: b
Problem: an enterprising businessman earns an income of re 5 on the first day of his business . on every subsequent day , he earns an income which is just thrice of that made on the previous day . on the 10 th day of business , he earns an income of :
Options: a ) 21 , b ) 22 , c ) 20 , d ) 45 , e ) 30
Rationale: 2 nd day he earns = 3 ( 2 – 5 ) 3 rd day he earns = 3 ( 3 – 5 ) on 20 th day he earns 3 ( 20 - 5 ) = 45 rupees answer : d
Answer: d
Problem: a student chose a number , multiplied it by 3 , then subtracted 138 from the result and got 102 . what was the number he chose ?
Options: a ) 80 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "solution : let xx be the number he chose , then 3 ⋅ x − 138 = 102 3 x = 240 x = 80 answer a"
Answer: a