Cheukting/mathqa huggingface dataset:
Question (gain): a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 7.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 10 % , c ) 35 % , d ) 55 % , e ) 65 %
Rationale: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.075 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 75 f - - > s = 9 f - - > f / s = 1 / 9 - - > f / ( s + f ) = 1 / ( 1 + 9 ) = 1 / 10 = 0.1 . answer : b ."
Answer: b
Question (physics): excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 42 kmph . of how many minutes does the train stop per hour ?
Options: a ) 16 , b ) 4 , c ) 15 , d ) 18 , e ) 12
Rationale: "t = 3 / 45 * 60 = 4 answer : b"
Answer: b
Question (general): . 008 / ? = . 01
Options: a ) . 8 , b ) . 09 , c ) . 009 , d ) . 0009 , e ) none of them
Rationale: "let . 008 / x = . 01 ; then x = . 008 / . 01 = . 8 / 1 = . 8 answer is a"
Answer: a
Question (general): a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 17000 left with him . find salary . .
Options: a ) $ 10700 , b ) $ 17000 , c ) $ 180000 , d ) $ 1700 , e ) $ 170000
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 17000 , = [ 1 - 9 / 10 ] * total salary = $ 17000 , total salary = $ 17000 * 10 = $ 180000 , correct answer ( e )"
Answer: e
Question (general): what is the lowest positive integer that is divisible by 8 through 11 , inclusive ?
Options: a ) 999 , b ) 7811 , c ) 6555 , d ) 9200 , e ) 7920
Rationale: "the integer should be divisible by : 8 , 9 , 10 and 11 . the least common multiple of these integers is lcm = 8 * 9 * 10 * 11 = 7920 answer : e"
Answer: e
Question (physics): the sector of a circle has radius of 20 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 , b ) 87.1 , c ) 91.7 , d ) 91.3 , e ) 91.1
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 20 ) + 2 ( 20 ) = 47.1 + 40 = 87.1 cm answer : b"
Answer: b
Question (general): tara bought 19 cartons of ice cream and 4 cartons of yoghurt . each carton of ice cream cost $ 7 and each carton of yoghurt cost $ 1 . how much more did tara spend on ice cream than on yoghurt ?
Options: a ) $ 144 , b ) $ 130 , c ) $ 80 , d ) $ 110 , e ) $ 129
Rationale: step 1 : find the cost of the ice cream . 19 × $ 7 = $ 133 step 2 : find the cost of the yoghurt . 4 × $ 1 = $ 4 step 3 : find how much more the ice cream cost than the yoghurt . $ 133 – $ 4 = $ 129 tara spent $ 129 more on ice cream . answer is e .
Answer: e
Question (general): if 9 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 41 , b ) 42 , c ) 36 , d ) 44 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 9 * 8 / 2 = 36 answer : c"
Answer: c
Question (physics): car a runs at the speed of 50 km / hr and reaches its destination in 8 hours . car b runs at the speed of 65 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
Options: a ) 3 : 7 , b ) 4 : 9 , c ) 20 : 13 , d ) 5 : 7 , e ) 6 : 11
Rationale: "car a travels 50 × 8 = 400 km car b travels 65 × 4 = 260 km the ratio is 400 : 260 = 40 : 26 = 20 : 13 the answer is c ."
Answer: c
Question (general): a grocer is storing soap boxes in cartons that measure 25 inches by 48 inches by 60 inches . if the measurement of each soap box is 8 inches by 6 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
Options: a ) 210 , b ) 252 , c ) 280 , d ) 320 , e ) 300
Rationale: "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 48 * 60 dimensions of the soap = 5 * 6 * 8 we get = 5 x 6 x 10 = 300 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( e )"
Answer: e
Question (general): what is the greatest 5 - digit number when divided by 6 , 7 , 8 , 9 , and 10 leaves a remainder of 4 , 5 , 6 , 7 , and 9 respectively ?
Options: a ) 56780 , b ) 78910 , c ) 97479 , d ) 97918 , e ) 97920
Rationale: when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 9 when we divide by 10 , so c is the only possible answer .
Answer: c
Question (general): a collection of books went on sale , and 2 / 3 of them were sold for $ 5 each . if none of the 50 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 550 , b ) $ 600 , c ) $ 500 , d ) $ 400 , e ) $ 450
Rationale: "if 50 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 100 books amount received for sold books = 100 * 5 = $ 500 answer : c"
Answer: c
Question (physics): a rower can row 6 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?
Options: a ) 2.21 , b ) 2.45 , c ) 2.67 , d ) 2.83 , e ) 2.95
Rationale: "let x be the distance to big rock . time = x / 4 + x / 8 = 1 x = 32 / 12 = 2.67 km the answer is c ."
Answer: c
Question (general): 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 75 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 7 rs , c ) 8 rs , d ) 5 rs , e ) 1 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 75 rs . 5 m + 5 m + 5 m - - - - - 75 rs . 15 m - - - - - - 75 rs . = > 1 m = 5 rs . answer : d"
Answer: d
Question (geometry): the radius of a cylindrical vessel is 7 cm and height is 6 cm . find the whole surface of the cylinder ?
Options: a ) 281 , b ) 771 , c ) 440 , d ) 767 , e ) 572
Rationale: "r = 7 h = 6 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 13 ) = 572 answer : e"
Answer: e
Question (general): the value of ( 34.31 * 0.473 * 1.5 ) / ( 0.0673 * 23.25 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.01 , d ) 2.06 , e ) 2.35
Rationale: "( 34.31 * 0.473 * 1.5 ) / ( 0.0673 * 23.25 * 7.57 ) = 24.343 / 11.845 = 2.06 answer : d"
Answer: d
Question (general): elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 40 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 4 , e ) $ 28
Rationale: bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 40 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 40 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 40 i . e . x = 36 i . e . fixed monthly charge , y = 4 answer : option d
Answer: d
Question (physics): how many seconds does puja take to cover a distance of 500 m , if she runs at a speed of 30 km / hr ?
Options: a ) 60 sec , b ) 82 sec , c ) 95 sec , d ) 100 sec , e ) 120 sec
Rationale: hint : time = distance / speed we see that the distance is given in metres while the speed is given in km / hr and the answer is asked in seconds . so , convert km / hr into m / s by multiplying 5 / 18 m / s to the given value of speed . 30 km / hr = 30 x 5 / 18 = 75 / 9 m / sec i . e . place these values in the formula : time = 500 x 9 / 75 = 60 sec answer is a
Answer: a
Question (other): the l . c . m . of 2 numbers is 40 . the numbers are in the ratio 4 : 5 . find their sum ?
Options: a ) 18 , b ) 40 , c ) 48 , d ) 32 , e ) 56
Rationale: "let the numbers be 4 x and 5 x l . c . m . = 20 x 20 x = 40 x = 2 the numbers are = 8 and 10 required sum = 8 + 10 = 18 answer is a"
Answer: a
Question (general): the sum of the ages 4 members of a family 5 years ago was 94 . today , when the daughter has been married off and replaced by a daughter - in - law , the sum of their ages is 100 . assuming that there has been no other change in the family structure and all members are alive , what is the difference in the ages of daughter and daughter - in - law ?
Options: a ) 22 , b ) 11 , c ) 25 , d ) 14 , e ) 16
Rationale: solution : sum of ages of 4 members 5 years ago = 94 = > sum of present ages of 4 members = 94 + 4 * 5 = 114 difference in the sum of the ages = difference in the ages of daughter and daughter - in - law difference in the sum of the ages = 114 - 100 = 14 = > difference in the ages of daughter and daughter - in - law = 14 answer d
Answer: d
Question (physics): 35 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 87 , b ) 18 , c ) 42 , d ) 16 , e ) 10
Rationale: "binders books days 35 1400 21 x 1600 20 x / 35 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 42 answer : c"
Answer: c
Question (general): for each month of a given year except december , a worker earned the same monthly salary and donated one - tenth of that salary to charity . in december , the worker earned n times his usual monthly salary and donated one - fifth of his earnings to charity . if the worker ' s charitable contributions totaled one - sixth of his earnings for the entire year , what is the value of n ?
Options: a ) 8 / 5 , b ) 22 , c ) 3 , d ) 11 / 3 , e ) 4
Rationale: "let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 5 = 1 / 6 ( 11 x + nx ) ; 11 / 10 + n / 5 = 1 / 6 ( 11 + n ) 11 + 2 n / 10 = 11 + n / 6 = > 66 + 12 n = 110 + 10 n = > 2 n = 44 n = 22 answer : b"
Answer: b
Question (probability): what is the probability of getting exactly 4 heads in a single throw of five fair coins ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 32 , e ) 7 / 32
Rationale: "one possible case is hhhht . p ( hhhht ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 there are 5 c 4 = 5 possible cases . p ( 4 heads ) = 5 * 1 / 32 = 5 / 32 the answer is d ."
Answer: d
Question (general): 40 × ? + ( 12 + 8 ) × 3 / 5 = 1212
Options: a ) a ) 7 , b ) b ) 5 , c ) c ) 4 , d ) d ) 18 , e ) e ) 30
Rationale: "explanation : = > 40 × ? + ( 12 + 8 ) × 3 / 5 = 1212 = > 40 × ? = 1212 - ( 12 + 8 ) × 3 / 5 = > 40 × ? = 1212 - 20 × 3 / 5 = > 40 × ? = 1212 - 20 × 3 / 5 = 1200 = > ? = 1200 / 40 = 30 answer : option e"
Answer: e
Question (probability): in how many ways 4 boys and 5 girls can be seated in a row so that they are alternate .
Options: a ) 144 , b ) 288 , c ) 12 , d ) 256 , e ) 2880
Rationale: "solution : let the arrangement be , g b g b g b g b g 4 boys can be seated in 4 ! ways . girl can be seated in 3 ! ways . required number of ways , = 4 ! * 5 ! = 2880 . answer : option e"
Answer: e
Question (physics): in a manufacturing plant , it takes 48 machines 4 hours of continuous work to fill 8 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 12 standard orders ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: "the choices give away the answer . . 48 machines take 4 hours to fill 8 standard orders . . in next eq we are doubling the machines from 48 to 72 , but the work is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 12 / 8 = 4 ans a"
Answer: a
Question (general): f ( x ) is a function such that f ( x ) + 3 f ( 8 - x ) = x for all real numbers x . find the value of f ( 2 )
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "f ( x ) + 3 f ( 8 - x ) = f ( 2 ) + 3 f ( 6 ) = 2 : x = 2 above f ( 6 ) + 3 f ( 2 ) = 6 : x = 6 above f ( 6 ) = 6 - 3 f ( 2 ) : solve equation c for f ( 6 ) f ( 2 ) + 3 ( 6 - 3 f ( 2 ) ) = 2 : substitute f ( 2 ) = 2 : solve above equation correct answer c"
Answer: c
Question (geometry): two cubes of their volumes in the ratio 64 : 1331 . the ratio of their surface area is :
Options: a ) 1.5 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 4 : 11 , e ) 4 : 5
Rationale: "the ratio of their surface area is 64 : 1331 4 : 11 answer is d ."
Answer: d
Question (gain): at joel ’ s bookstore , the current inventory is 30 % historical fiction . of the historical fiction books , 30 % are new releases , while 40 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
Options: a ) 4 / 25 , b ) 9 / 37 , c ) 2 / 5 , d ) 8 / 15 , e ) 2 / 3
Rationale: "let there be 100 books in all historic fiction books = 30 % of total = 30 other books = 70 new historic fiction = 30 % of 30 = 9 other new books = 40 % of 70 = 28 total new books = 37 fraction = 9 / 37 ans : b"
Answer: b
Question (general): a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student b answers each of the 100 questions on her test and receives a score of 73 , how many questions did student b answer correctly ?
Options: a ) 55 , b ) 60 , c ) 73 , d ) 82 , e ) 91
Rationale: "a score of 73 brings to mind that it is an odd number even though you are subtracting an even number ( twice the incorrect responses ) out of the correct responses score . so the correct responses score must be an odd number too ( odd - even = odd ) . since the overall score is 73 , the number of correct responses must be more than 73 since the student answered all questions . only 91 satisfies both these conditions . answer ( e )"
Answer: e
Question (geometry): a box measuring 30 inches long by 48 inches wide by 12 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 78 , b ) 80 , c ) 85 , d ) 88 , e ) 90
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 6 is the biggest number that could divide all three , 30 , 48 and 12 . thus side of cube must be 6 , and total number of cubes = 30 / 6 * 48 / 6 * 12 / 6 = 80 ans b ."
Answer: b
Question (gain): on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 30 %
Rationale: "say there are 100 motorists . { # of motorists who exceed speed & receive tickets } + { # of motorists who exceed speed & do n ' t receive tickets } = { total # of motorist who exceed speed } ; given : { # of motorists who exceed speed & receive tickets } = 10 ; also , if { total # of motorist who exceed speed } = x , then 0.2 x = { # of motorists who exceed speed & do n ' t receive tickets } ; 10 + 0.2 x = x - - > x = 12.5 answer : b ."
Answer: b
Question (gain): a man can row downstream at the rate of 24 kmph and upstream at 7 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 8.5 , b ) 8.0 , c ) 9.5 , d ) 9.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 24 + 7 ) = 15.5 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 24 - 7 ) = 1 / 2 ( 17 ) = 8.5 kmph answer is a ."
Answer: a
Question (general): the average weight of 5 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 76 kg , b ) 77 kg , c ) 72.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 5 × 1.5 = 7.5 kg so the weight of new person = 65 + 7.5 = 72.5 kg answer c"
Answer: c
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 4 hours and 16 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 5 , b ) 4 : 2 , c ) 4 : 4 , d ) 4 : 8 , e ) 4 : 1
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 16 : √ 4 = 4 : 2 answer : b"
Answer: b
Question (general): on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent e of thatbeforejuly 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: "the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before e = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % = b"
Answer: b
Question (general): when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 70 .
Options: a ) 3 , b ) 4 , c ) 12 , d ) 32 , e ) 35
Rationale: "first , let us say i have a number n which is divisible by 5 and by 7 . we all agree that it will be divisible by 35 , the lcm of 5 and 7 . now , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1 , we can say the number is of the form n = 5 a + 1 e . g . 5 + 1 , 10 + 1 , 15 + 1 , 20 + 1 , 25 + 1 , 30 + 1 , 35 + 1 etc and n = 7 b + 1 e . g . 7 + 1 , 14 + 1 , 21 + 1 , 28 + 1 , 35 + 1 etc so when it is divided by the lcm , 35 , it will give 1 as remainder ( as is apparent above ) next , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3 , we can say the number is of the form n = 5 a + 1 and n = 7 b + 3 now , the only thing you should try to understand here is that when n is divided by 5 and if i say the remainder is 1 , it is the same as saying the remainder is - 4 . e . g . when 6 is divided by 5 , remainder is 1 because it is 1 more than a multiple of 5 . i can also say it is 4 less than the next multiple of 5 , ca n ' t i ? 6 is one more than 5 , but 4 less than 10 . therefore , we can say n = 5 x - 4 and n = 7 y - 4 ( a remainder of 3 when divided by 7 is the same as getting a remainder of - 4 ) now this question is exactly like the question above . so when you divide n by 70 , remainder will be - 4 i . e . n will be 4 less than a multiple of 70 . so you must add 4 to n to make it a multiple of 70 d"
Answer: d
Question (general): the difference between the place values of 6 and 5 in the number 826533 is
Options: a ) 5500 , b ) 4500 , c ) 2500 , d ) 6970 , e ) none
Rationale: sol . = ( place value of 6 ) – ( place value of 5 ) = ( 6000 - 500 ) = 5500 answer a
Answer: a
Question (physics): a works twice as fast as b . if b can complete a work in 12 days independently , the number of days in which a and b can together finish the work in :
Options: a ) 4 days , b ) 6 days , c ) 8 days , d ) 18 days , e ) 28 days
Rationale: "explanation : ratio of rates of working of a and b = 2 : 1 . so , ratio of times taken = 1 : 2 . b ' s 1 day ' s work = 1 / 12 a ' s 1 day ' s work = 1 / 6 ; ( 2 times of b ' s work ) ( a + b ) ' s 1 day ' s work = ( 1 / 6 + 1 / 12 ) = 3 / 12 = 1 / 4 so , a and b together can finish the work in 4 days . answer is a"
Answer: a
Question (other): if a student loses 5 kilograms , he will weigh twice as much as his sister . together they now weigh 104 kilograms . what is the student ' s present weight in kilograms ?
Options: a ) 70 , b ) 71 , c ) 72 , d ) 73 , e ) 74
Rationale: "let x be the weight of the sister . then the student ' s weight is 2 x + 5 . x + ( 2 x + 5 ) = 104 3 x = 99 x = 33 kg then the student ' s weight is 71 kg . the answer is b ."
Answer: b
Question (gain): a football team lost 5 yards and then gained 13 . what is the team ' s progress ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "for lost , use negative . for gain , use positive . progress = - 5 + 13 = 8 yards e"
Answer: e
Question (general): find the last digit of 322 ^ 369
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: for calculating the unit place of these type of question ( exponent ) as the power of 2 repeats after 4 , so we will divide the exponent by 4 e . g , 2 ^ 1 = 2 and 2 ^ ( 4 + 1 ) = 32 , both have same unit place 369 / 4 gives the remainder as 1 so we can write 322 ^ 369 = 2 ^ 1 = 2 so , the unit place will be 2 answer : b
Answer: b
Question (general): find the value of x from logx 100 = 2
Options: a ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "solution : logb 1000 = 3 we can write it as , b 3 = 1000 b 3 = 103 so from the above equation b = 10 answer is a"
Answer: a
Question (other): x starts a business with rs . 52000 . y joins in the business after 6 months with rs . 26000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 1 : 3 , d ) 4 : 1 , e ) none of these
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 52000 * 12 : 26000 * 6 = 52 * 12 : 26 * 6 = 24 : 6 = 4 : 1 . answer : option d"
Answer: d
Question (general): if x is equal to the sum of the even integers from 40 to 60 inclusive , and y is the number of even integers from 40 to 60 inclusive , what is the value of x + y ?
Options: a ) 550 , b ) 551 , c ) 560 , d ) 561 , e ) 572
Rationale: this is a perfect example of why you should not use formulas without understanding them properly . if you understand them , you will not make a mistake and will save time . the formula quoted by the original poster : n ( n + 1 ) is absolutely fine . but one needs to understand that n is the number of even terms starting from the first even term . ( i discuss why this is so here : sum of even numbers from 40 to 60 using this formula will be : 30 * 31 - 19 * 20 = 10 ( 3 * 31 - 19 * 2 ) = 550 since number of terms is 11 , required sum is 561 but , i would not use this formula for this question and would do it the way many of you have done : average = 50 ( it is the middle number ) , number of terms = 11 ( no formula again . any 10 consecutive integers have 5 even and 5 odd numbers . 41 to 60 will have 10 even integers and 40 is the 11 th one ) sum = 50 * 11 + 11 = 561 answer is d
Answer: d
Question (physics): a monkey start climbing up a tree 17 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 19 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 14 hrs it wil be 14 ft . bt since the height of the tree is 17 ft , so if the monkey hops up the tree in the next hr i . e 15 th hr then it reaches at the top of the tree . hence it takes 15 hrs for monkey to reach at the top answer : a"
Answer: a