Cheukting/mathqa huggingface dataset:
Question (other): present ages of abi and suji are in the ratio of 5 : 4 respectively . 3 years hence , the ratio of their ages will become 11 : 9 respectively . what is suji ' s present age in years ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: present ages = 5 x : 4 x three hence = 5 x + 3 : 4 x + 3 5 x + 3 : 4 x + 3 = 11 : 9 weget x = 6 suji age is = 4 x = 4 * 6 = 24 answer : e
Answer: e
Question (physics): a can do a work in 15 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is ?
Options: a ) 8 , b ) 8 / 11 , c ) 8 / 13 , d ) 8 / 15 , e ) none
Rationale: a ' s 1 day ' s work = 1 ; 15 b ' s 1 day ' s work = 1 ; 20 ( a + b ) ' s 1 day ' s work = ( 1 + 1 ) = 7 . 15 20 60 ( a + b ) ' s 4 day ' s work = ( 7 x 4 ) = 7 . 60 15 therefore , remaining work = ( 1 - 7 ) = 8 . 15 15 option d
Answer: d
Question (general): let f ( x ) = x ^ 2 + bx + c . if f ( 1 ) = 0 and f ( - 7 ) = 0 , then f ( x ) crosses the y - axis at what y - coordinate ?
Options: a ) - 7 , b ) - 1 , c ) 0 , d ) 1 , e ) 7
Rationale: "when x = 1 and when x = - 7 , the expression f ( x ) = x ² + bx + c equals 0 . then f ( x ) = ( x - 1 ) ( x + 7 ) f ( 0 ) = - 7 the answer is a ."
Answer: a
Question (other): the ratio of flour to water to sugar in a recipe is 8 : 4 : 3 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "the ratio of flour to water is 16 : 4 = 4 : 1 . the ratio of flour to sugar is 4 : 3 . the new ratio of flour to water to sugar is 4 : 1 : 3 if we need 2 cups of water , then we need 6 cups of sugar . the answer is a ."
Answer: a
Question (physics): a train 165 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 8 , e ) 5
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 165 * 3 / 55 ] sec = 9 sec answer : c"
Answer: c
Question (general): joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 12100 , how many months will it take joan to pay back her mortgage ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 5 , e ) 13
Rationale: "joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 12100 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 121 so we have 1 , 3 , 9 , 27 . . . . . 12100 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r 121 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 121 x - 2 = 1 - 3 ^ n - 242 = 1 - 3 ^ n - 243 = - 3 ^ n 243 = 3 ^ n ( negatives cancel out ) 243 can also be re written as 3 ^ 5 therefore ; 3 ^ 5 = 3 ^ n thus n = 5 ( d )"
Answer: d
Question (geometry): the diagonals of two squares are in the ratio of 2 : 5 . find the ratio of their areas .
Options: a ) 4 : 25
b ) 4 : 15
c ) 3 : 25
d ) 3 : 15
e ) none of these
Rationale: explanation : let the diagonals of the squares be 2 x and 5 x . then ratio of their areas will be area of square = 1 / 2 ∗ diagonal 2 1 / 2 ∗ 2 x 2 : 1 / 2 ∗ 5 x 2 4 x 2 : 25 x 2 = 4 : 25 option a
Answer: a
Question (general): s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits q are in s ( 99 ) ?
Options: a ) q = 350 , b ) q = 353 , c ) q = 354 , d ) q = 356 , e ) 357
Rationale: focus on the points where the number of digits q in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b
Answer: b
Question (gain): bhanu spends 30 % of his income on petrol on scooter 30 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?
Options: a ) 2287 , b ) 140 , c ) 128 , d ) 210 , e ) 123
Rationale: "given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 30 % ( 700 ) = rs . 210 answer : d"
Answer: d
Question (geometry): the slant height of a right circular cone is 10 m and its height is 8 m . find the area of its curved surface .
Options: a ) 30 pi m ^ 2
b ) 40 pi m ^ 2
c ) 60 pi m ^ 2
d ) 80 pi m ^ 2
e ) 100 pi m ^ 2
Rationale: l = 10 m h = 8 m r = root ( i ^ 2 - h ^ 2 ) = root ( 10 ^ 2 - 8 ^ 2 ) = 6 m curved surface area = pi ri = 60 pi m ^ 2 answer c
Answer: c
Question (general): at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 150 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "250 employees : 90 male , 160 female 40 managers , 210 associates 150 male associates implies 60 female associates which means the remaining 30 females must be managers d . 30"
Answer: d
Question (general): the average height of 35 boys in a class was calculated as 183 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
Options: a ) 178.27 cm , b ) 181.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
Rationale: "calculated average height of 35 boys = 183 cm . wrong total height of 35 boys = 183 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm - 106 cm ) / 35 = 183 cm - 60 / 35 cm = 183 cm - 1.71 cm = 181.29 cm . answer : b"
Answer: b
Question (general): 65 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 22 , b ) 77 , c ) 29 , d ) 66 , e ) 21
Rationale: "65 + 5 * 12 / ( 180 / 3 ) = 65 + 5 * 12 / ( 60 ) = 65 + ( 5 * 12 ) / 60 = 65 + 1 = 66 . answer : d"
Answer: d
Question (geometry): what is the ratio between perimeters of two squares one having 1.5 times the diagonal then the other ?
Options: a ) 3 : 6 , b ) 1.5 : 1 , c ) 3 : 1.5 , d ) 2 : 1 , e ) 3 : 2
Rationale: "d = 1.5 d d = d a √ 2 = 1.5 d a √ 2 = d a = 1.5 d / √ 2 a = d / √ 2 = > 1.5 : 1 answer : b"
Answer: b
Question (geometry): a circular garden is surrounded by a fence of negligible width along the boundary . if the length of the fence is 1 / 6 of th area of the garden . what is the radius of the circular garden ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 8 , e ) 12
Rationale: "as per the question - - width is negligible now , let l be the length of the fence = 2 pir l = 1 / 6 ( pir ^ 2 ) pir ^ 2 = 12 pir r = 12 answer : e"
Answer: e
Question (general): what is the 28 th digit to the right of the decimal point in the decimal form of 4 / 11 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "4 / 11 = 0.363636 . . . the even numbered positions in the decimal expansion are all 6 . the answer is d ."
Answer: d
Question (physics): the radius of the wheel of a bus is 140 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 125 , b ) 250 , c ) 300 , d ) 330 , e ) none of these
Rationale: "radius of the wheel of bus = 140 cm . then , circumference of wheel = 2 ï € r = 280 ï € = 880 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 880 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 880 = 125 answer a"
Answer: a
Question (physics): a can finish a work in 15 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 5 , b ) 5 1 / 2 , c ) 6 , d ) 8 , e ) none of these
Rationale: "b ' s 10 day ' s work = ( 1 / 15 * 10 ) = 2 / 3 remaining work = ( 1 - 2 / 3 ) = 1 / 3 now , 1 / 18 work is done by a in 1 day 1 / 3 work is done by a in ( 15 * 1 / 3 ) = 5 days . correct option : a"
Answer: a
Question (general): in the county of veenapaniville , there are a total of 50 high schools , of 3 kinds : 25 public schools , 16 parochial schools , and 9 private independent schools . these 50 schools are divided between 3 districts : a , b , and c . district a has 18 high schools total . district b has 17 high schools total , and only two of those are private independent schools . if district c has an equal number of each of the 3 kinds of schools , how many private independent schools are there in district a ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: “ in the county of veenapaniville , there are a total of 50 high schools , of three kinds : 25 public schools , 16 parochial schools , and 9 private independent schools . ” “ district a has 18 high schools total . ” “ district b has 17 high schools total , and only two of those are private independent schools . ” “ district c has an equal number of each of the three kinds of schools . ” hmm . that ’ s not a simple number . let ’ s put that on hold for a moment . so far , from the matrix it looks like we could figure out the missing number in the “ totals ” row . that number must be 15 , because 18 + 17 + 15 = 50 . now , go back to that last fact : “ district c has an equal number of each of the three kinds of schools . ” now that makes sense . district c has 15 schools , so it must have 5 of each kind : the question is asking : “ how many private independent schools are there in district a ? ” well , now that ’ s just a matter of adding across the “ private independent ” row . we know 2 + 2 + 5 = 9 , so the missing number must be 2 . there ’ s still a good deal of information we can ’ t figure out from the information given in the question , but we are able to answer the specific question asked here . there are 2 private independent schools in district a , so the answer = ( a ) .
Answer: a
Question (physics): a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 12 seconds . what is the length of the train in meters ?
Options: a ) 400 meters , b ) 120 meters , c ) 1777 meters , d ) 60 meters , e ) none of these
Rationale: "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 12 seconds distance = speed * time 36000 * 12 / 3600 = 120 meters . b is the answer ."
Answer: b
Question (general): how many positive integers less than 22 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?
Options: a ) 17 , b ) 13 , c ) 12 , d ) 11 , e ) 10
Rationale: "the number = 2 a + 3 b < 20 when a = 1 , b = 1 , 2 , 3 , 4 , 5 , 6 - > 2 a = 2 ; 3 b = 3 , 6 , 9 , 12 , 15 , 18 - > the number = 5 , 8 , 11 , 14 , 17 , 20 - - > 6 numbers when a = 2 , b = 1 , 2,3 , 4,5 , 6 - > . . . . - - > 6 numbers when a = 3 , b = 1,2 , 3,4 , 5 - - > . . . . - - > 5 numbers total number is already 17 . look at the answer there is no number greater than 17 - - > we dont need to try any more answer must be a"
Answer: a
Question (general): the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.4 kg . the weight of the new student is ?
Options: a ) 10.6 kg , b ) 3 kg , c ) 11 kg , d ) 14.9 kg , e ) none
Rationale: "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.4 - 19 x 15 ) kg = 3 kg . correct option : b"
Answer: b
Question (physics): a , b , c can complete a piece of work in 21 , 6,12 days . working together , they complete the same work in how many days ?
Options: a ) 2 , b ) 4 / 5 , c ) 7 / 9 , d ) 10 , e ) 84 / 25
Rationale: "a + b + c 1 day work = 1 / 21 + 1 / 6 + 1 / 12 = 25 / 84 a , b , c together will complete the job in 84 / 25 days answer is e"
Answer: e
Question (other): ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age
Options: a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 23
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 answer : option b"
Answer: b
Question (general): a new model car was not selling as expected and the base retail price was lowered by 5 % to increase sales . a customer haggled on the price and negotiated a final agreed price of 90 % of the retail price . how much did the customer save off the retail price ?
Options: a ) 10.5 % , b ) 11.5 % , c ) 12.5 % , d ) 13.5 % , e ) 14.5 %
Rationale: quantity x rate = price 1 x 1 = 1 0.9 x 0.95 = 0.855 decrease in price = ( 0.145 / 1 ) ã — 100 = 14.5 % answer = option e
Answer: e
Question (physics): a machine , working at a constant rate , manufactures 40 pencils in 30 minutes . how many pencils does it make in 1 hr 30 min ?
Options: a ) 120 , b ) 125 , c ) 110 , d ) 115 , e ) 121
Rationale: "change 1 hr 30 min to 90 min . for this , we need to set up a simple proportion of pensils per time 40 / 30 = s / 90 the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . instead , cancel before you multiply . for what we can and can ’ t cancel in a proportion , seethis post . we can cancel the factor of 10 in the 40 and 30 . 4 / 3 = s / 90 we can cancel the common factor of 3 in the two denominators . 4 / 1 = s / 30 . now that the fraction is entirely simplified , we can cross - multiply . s = 4 * 30 = 120 the machine would be 120 pencils in 1 hr 30 min . answer : a"
Answer: a
Question (gain): sandy buys an old scooter for $ 900 and spends $ 300 on its repairs . if sandy sells the scooter for $ 1320 , what is the gain percent ?
Options: a ) 2 % , b ) 4 % , c ) 6 % , d ) 8 % , e ) 10 %
Rationale: "selling price / total cost = 1320 / 1200 = 1.1 the gain percent is 10 % . the answer is e ."
Answer: e
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 8 m wide at the top and 2 m wide at the bottom and the area of cross - section is 770 sq m , the depth of cannel is ?
Options: a ) 150 , b ) 152 , c ) 154 , d ) 156 , e ) 158
Rationale: "1 / 2 * d ( 8 + 2 ) = 770 d = 154 answer : c"
Answer: c
Question (physics): a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 80 seconds . what is the length of the train in meters ?
Options: a ) 400 meters , b ) 1111 meters , c ) 800 meters , d ) 1822 meters , e ) none of these
Rationale: "train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 80 seconds distance = speed * time 36000 * 80 / 3600 = 800 meters . c is the answer ."
Answer: c
Question (physics): if 8 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
Options: a ) 127 , b ) 237 , c ) 287 , d ) 450 , e ) 281
Rationale: "explanation : let the required no of hectares be x . then more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) men \ : 8 : 36 \ \ days \ : 24 : 30 \ end { matrix } \ right \ } : 80 : x \ inline \ fn _ jvn \ therefore \ inline \ fn _ jvn 8 \ times 24 \ times x = 36 \ times 30 \ times 80 \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 30 \ times 80 } { 8 \ times 24 } \ inline \ fn _ jvn \ leftrightarrow x = 450 answer : d"
Answer: d
Question (general): 1 / 4 of all married couples have more than one child . 1 / 5 of all married couples have more than 3 children . what fraction of all married couples have 2 or 3 children ?
Options: a ) 1 / 5 , b ) b . 1 / 4 , c ) 1 / 20 , d ) 3 / 5 , e ) it can not be determined from the given information .
Rationale: "plug in simple numbers . take 100 couples for example . 1 / 4 of 100 couples have more than one child = 25 couples . 1 / 5 of 100 couples have more than 3 kids = 20 couples . this implies that 20 couples are a subset of 25 couples and the complement of 25 couples within those 100 couples , which equals 75 couples have either one or no kids at all . we need to find couples that have 2 or 3 kids , so essentially , it is 25 - 20 = 5 . fraction will be 5 / 100 = 1 / 20 . option c"
Answer: c
Question (general): a welder received an order to make a 1 million liter cube - shaped tank . if he has only 4 x 2 meter sheets of metal that can be cut , how many metal sheets will be required for this order r ? ( 1 cubic meter = 1000 liters )
Options: a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 75
Rationale: i get 75 . a cube with 1 million liters cube would be a cube with the dimensions of 100 * 100 * 100 . 4 * 2 covers 8 sq liters so 100 / 8 = 12.5 . r = 12.5 * 6 = 75 . e
Answer: e
Question (gain): a man can row downstream at the rate of 26 kmph and upstream at 12 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 8.5 , b ) 8.0 , c ) 9.5 , d ) 7.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 26 + 12 ) = 19 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 26 - 12 ) = 1 / 2 ( 14 ) = 7 kmph answer is d ."
Answer: d
Question (geometry): the perimeter of a rectangle is equal to the perimeter of aright - angled triangle of height 12 cm . if the base of the triangle is equal to the breadth of the rectangle , what is the length of the rectangle ”
Options: a ) 18 cm
b ) 24 cm
c ) 22 cm
d ) data inadequate
e ) none of these
Rationale: p = 2 ( l + b ) = l + b + h = l + b + 12 . data inadequate . answer d
Answer: d
Question (general): in a renowned city , the average birth rate is 7 people every two seconds and the death rate is 1 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 32,300 , b ) 172,800 , c ) 468,830 , d ) 338,200 , e ) 259,200
Rationale: "every 2 seconds , 6 persons are added ( 7 - 1 ) . every second 3 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 3 = 259200 option e"
Answer: e
Question (general): each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 45 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 43 , e ) 39
Rationale: "james worked for 41 hours hence he earned 40 * x + 5 * 2 x = 50 x dollars ; we know that harry also earned the same 50 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 20 x additional dollars . since for each additional hour he gets 1.5 x dollars then he worked for 20 x / 1.5 x = 13 additional hours , so harry worked for total of 30 + 13 = 43 hours . answer : d ."
Answer: d
Question (geometry): a certain cube floating in a bucket of water has between 60 and 85 percent of its volume below the surface of the water . if between 9 and 26 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: "if sides are 7 , vol = 7 ^ 3 = 343 60 % = 205.8 , 85 % = 291.55 so vol above water , between 137.2 and 51.45 - - > too big if side are 4 , vol = 64 60 % = 38.4 , 85 % = 54.4 vol above water between 25.6 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 60 % = 75 , . 85 % = 106.25 vol above water between 18.75 - 50 ( sides are 4 cubic centimeters ) a"
Answer: a
Question (physics): how long does a train 150 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length ?
Options: a ) 14.1 sec , b ) 12.1 sec , c ) 16.1 sec , d ) 13.1 sec , e ) 12.15 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 150 + 132 = 282 m . required time = 282 / 20 = 14.1 sec . answer : a"
Answer: a
Question (other): the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 900 gm and 800 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.84 , b ) 1.75 , c ) 3.44 , d ) 2.72 , e ) none of these
Rationale: "here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 800 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 800 * 2 * ( 4 / 5 ) = 1280 2160 + 1280 = 3440 solving for units gives us 3.44 so the answer is c"
Answer: c
Question (general): what is the unit ’ s digit of 7 ^ 7
Options: a ) 9 , b ) 5 , c ) 3 , d ) 7 , e ) 1
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) 7 ^ 5 = 7 ( last digit ) and the cycle repeats after every 4 powers therefore , last digit of 7 ^ 7 = 3 answer c"
Answer: c
Question (gain): the list price of an article is rs . 70 . a customer pays rs . 61.11 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 8 % , b ) 7 % , c ) 10 % , d ) 3 % , e ) 4 %
Rationale: "explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 61.11 x = 3 % d"
Answer: d
Question (physics): a train is 300 meter long is running at a speed of 35 km / hour . in what time will it pass a bridge of 115 meter length ?
Options: a ) 29 , b ) 23 , c ) 47.119 , d ) 44.586 , e ) 42.686
Rationale: "speed = 35 km / hr = 35 * ( 5 / 18 ) m / sec = 175 / 18 m / sec total distance = 300 + 115 = 415 meter time = distance / speed = 415 * ( 18 / 175 ) = 42.686 seconds . answer : e"
Answer: e
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 70 , then how long is the base of isosceles triangle ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "the base of the isosceles triangle is 70 - 20 - 20 = 30 units the answer is d ."
Answer: d