euclaise/mathqa_programs huggingface dataset:
Problem: what is the difference between the c . i . on rs . 8000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?
Options: a ) s . 3.26 , b ) s . 2.08 , c ) s . 2.02 , d ) s . 2.83 , e ) s . 2.42
Rationale: "c . i . when interest is compounded yearly = [ 8000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 8000 * 26 / 25 * 51 / 50 = rs . 8486.4 c . i . when interest is compounded half - yearly = [ 8000 * ( 1 + 2 / 100 ) 2 ] = ( 8000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 8489.66 difference = ( 8489.66 - 8486.4 = rs . 3.26 . answer : a"
Answer: a
Python program:
a = 2 / 100
b = 1 + a 
c = 2 / 100
d = 1 + c 
e = b * d
f = 2 / 100
g = 1 + f 
h = e * g
i = 8000 * h
j = 2 / 100
k = 1 + j 
l = 4 / 100
m = 1 + l 
n = k * m
o = 8000 * n
p = i - o
Problem: the number of timeshare condos available at sunset beach is 2 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 210 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 240
Rationale: "let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 2 / 5 x = 210 hence , x = 150 . so , number of timeshare condos available at playa del mar = 150 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 2 / 5 x = 2 / 5 x = 3 / 5 ( 150 ) = 90 the correct answer is b"
Answer: b
Python program:
a = 210 * 2
b = a / 5
c = 2 * 5
d = b + c
Problem: a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 3840 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) s . 380 , b ) s . 600 , c ) s . 420 , d ) s . 400 , e ) s . 480
Rationale: "explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3840 × ( 1 / 8 ) = 480 answer : option e"
Answer: e
Python program:
a = 1 / 3
b = 1 / 6
c = 1 / 8
d = b + c 
e = a - d
f = 3 * e
g = f * 3840
Problem: on dividing 13698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
Options: a ) 743 , b ) 154 , c ) 852 , d ) 741 , e ) 785
Rationale: divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 13698 - 14 ) / 89 = 154 answer ( b )
Answer: b
Python program:
a = 13698 - 14
b = a / 89
Problem: a store owner estimates that the average price of type a products will increase by 30 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,980 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.30 * 4500 = 5850 cost of type b products next year = 1.1 * 8300 = 9130 total 5850 + 9130 = 14980 option a"
Answer: a
Python program:
a = 3 / 4
b = a * 1000
Problem: a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 38 now , the son age 5 years back was
Options: a ) 14 , b ) 17 , c ) 11 , d ) 19 , e ) 99
Rationale: "let the son ' s present age be x years . then , ( 38 - x ) = x x = 19 . son ' s age 5 years back = ( 19 - 5 ) = 14 years answer : a"
Answer: a
Python program:
a = 38 / 2
b = a - 5
Problem: the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people x who purchased only book a ?
Options: a ) 250 , b ) 500 , c ) 750 , d ) 1000 , e ) 1500
Rationale: "this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , x = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000"
Answer: d
Python program:
a = 500 / 2
b = 500 + a 
c = b * 2
d = c - 500
Problem: a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 854 in 4 years . the sum is ?
Options: a ) rs . 738 , b ) rs . 638 , c ) rs . 650 , d ) rs . 730 , e ) rs . 735
Rationale: "s . i . for 1 year = ( 854 - 825 ) = rs . 29 s . i . for 3 years = 29 * 3 = rs . 87 principal = ( 825 - 87 ) = rs . 738 . answer : a"
Answer: a
Python program:
a = 854 - 825
b = a * 3
c = b / 4
d = 825 - c
Problem: in how many seconds will a train 150 meters long pass an oak tree , if the speed of the train is 54 km / hr ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "speed = 54 * 5 / 18 = 15 m / s time = 150 / 15 = 10 seconds the answer is c ."
Answer: c
Python program:
a = const_0_2778 * 54
b = 150 / a
Problem: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 3 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3
Rationale: "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 4 - 3 ) / ( 10 - 4 ) = 1 / 6 so they should be mixed in the ratio 1 : 6 answer - c"
Answer: c
Python program:
a = 4 - 3
b = 10 - 4
c = a / b
Problem: in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive e difference between n and m ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result e will be 8 - 5 = 3 and answer b
Answer: b
Python program:
a = 5 - 2
Problem: 4 years ago , paula was 4 times as old as karl . in 4 years , paula will be twice as old as karl . what is the sum of their ages now ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "p - 4 = 4 ( k - 4 ) and so p = 4 k - 12 p + 4 = 2 ( k + 4 ) ( 4 k - 12 ) + 4 = 2 k + 8 k = 8 p = 20 p + k = 28 the answer is d ."
Answer: d
Python program:
a = 4 * 2
b = 4 - a
c = negate + ( 
d = 4 * 3
e = d - 4
f = c * e
g = f - 3
h = 4 * 4
i = h - 4
j = g + i
Problem: a palindrome is a word or a number that reads the same forward and backward . for example , 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits 1 , 2 , 3 , 4 , and 5 , how many palindromes are possible ?
Options: a ) 25 , b ) 75 , c ) 125 , d ) 225 , e ) 625
Rationale: there are 5 choices for each of the first three digits . the number of possible palindromes is 5 ^ 3 = 125 . the answer is c .
Answer: c
Python program:
a = 5 ** 3
Problem: if the personal income tax rate is lowered from 40 % to 33 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 45000 ?
Options: a ) $ 3500 , b ) $ 5000 , c ) $ 3150 , d ) $ 7000 , e ) $ 10000
Rationale: "saving = ( 40 - 33 ) % of 45000 = 3150 . answer : c"
Answer: c
Python program:
a = 45000 / 100
b = 40 - 33
c = a * b
Problem: the length of minute hand of a clock is 5.4 cm . what is the area covered by this in 10 minutes
Options: a ) 15.27 , b ) 16.27 , c ) 17.27 , d ) 18.27 , e ) 19.27
Rationale: "area of circle is pi * r ^ 2 but in 10 minutes area covered is ( 10 / 60 ) * 360 = 60 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.4 ^ 2 ) * ( 60 / 360 ) = 15.27 cm ^ 2 answer : a"
Answer: a
Python program:
a = 2 * 10
b = a + 2 
c = 3 + 4 
d = b / c
e = 5 * 4
f = 1 * const_60
g = 100 * const_3_6
h = f / g
i = e * h
j = d * i
Problem: a pipe takes a hours to fill the tank . but because of a leakage it took 4 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 70 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 240 x = 80 min answer : d"
Answer: d
Python program:
a = 1 * 4
b = 10 * a
Problem: the compound interest on $ 30,000 at 7 % per annum is $ 4347 . the period ( in years ) is :
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "amount = $ ( 30000 + 4347 ) = $ . 34347 . let the time be n years . then , 30000 1 + 7 n = 34347 100 107 n = 34347 = 11449 = 107 2 100 30000 10000 100 n = 2 years . answer a - 2"
Answer: a
Python program:
a = 30 / 0
Problem: jonathan can type a 50 page document in 40 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?
Options: a ) 5 minutes , b ) 10 minutes , c ) 15 minutes , d ) 18 minutes , e ) 20 minutes
Rationale: "you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 50 / 40 + 50 / 30 + 50 / 24 = 50 / x if you solve this equation , you get the same answer b ( 10 )"
Answer: b
Python program:
a = 50 / 24
b = 50 / 40
c = 50 / 30
d = b + c 
e = a + d 
f = 50 / e
Problem: find the annual income derived by investing $ 6800 in 30 % stock at 136 .
Options: a ) 550 , b ) 1500 , c ) 250 , d ) 1300 , e ) 400
Rationale: by investing $ 136 , income obtained = $ 30 . by investing $ 6800 , income obtained = $ [ ( 30 / 136 ) * 6800 ] = $ 1500 . answer b .
Answer: b
Python program:
a = 6800 * 30
b = a / 136
Problem: joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 90 . he was allowed to drop his lowest score . after doing so , his average test score improved to 85 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 25 , c ) 55 , d ) 75 , e ) 80
Rationale: "the arithmetic mean of 4 equally weighted tests was 90 . so what we can assume is that we have 4 test scores , each 90 . he dropped his lowest score and the avg went to 95 . this means that the lowest score was not 90 and other three scores had given the lowest score 5 each to make it up to 90 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 90 . so the lowest score = 90 - 15 = 75 answer ( d )"
Answer: d
Python program:
a = 90 * 4
b = 85 * 3
c = a - b
Problem: the average age of 6 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years . find the average age of the women ?
Options: a ) 87 , b ) 12 , c ) 30 , d ) 28 , e ) 17
Rationale: "10 + 12 + 6 * 2 = 34 / 2 = 17 answer : e"
Answer: e
Python program:
a = 10 + 12 
b = 6 * 2
c = a + b 
d = c / 2
Problem: it takes 35 identical printing presses 15 hours to print 500,000 papers . how many hours would it take 25 of these printing presses to print 500,000 papers ?
Options: a ) 18 , b ) 20 , c ) 21 , d ) 24 , e ) 25
Rationale: "35 printing presses can do 1 / 15 of the job each hour . 25 printing presses can do 5 / 7 * 1 / 15 = 1 / 21 of the job each hour . the answer is c ."
Answer: c
Python program:
a = 1000 / 2
b = a * 1000
c = 1000 / 2
d = c * 1000
e = d / 35
f = e / 15
g = f * 25
h = b / g
Problem: 3639 + 11.95 - x = 3054 . find the value of x .
Options: a ) 407.09 , b ) 479.75 , c ) 523.93 , d ) 596.95 , e ) none of these
Rationale: "explanation : let 3639 + 11.95 – x = 3054 then , x = ( 3639 + 11.95 ) – 3054 = 3650.95 – 3054 = 596.95 answer : d"
Answer: d
Python program:
a = 3639 + 11 
b = a - 3054
Problem: a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 104 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 42 % , e ) 56 %
Rationale: "( 9 / 104 ) / ( 3 / 20 ) = 30 / 54 = 57,6 % it means that 9 / 108 represents only 57,6 % . therefore a decrease of 42 % . answer d"
Answer: d
Python program:
a = 3 / 20
b = a * 100
Problem: the cost per pound of milk powder and coffee were the same in june . in july , the price of coffee shot up by 300 % and that of milk powder dropped by 80 % . if in july , a mixture containing equal quantities of milk powder and coffee costs $ 6.30 for 3 lbs , how much did a pound of milk powder cost in july ?
Options: a ) $ 4 , b ) $ 0.2 , c ) $ 1 , d ) $ 3 , e ) $ 1.65
Rationale: lets assume price of coffee in june = 100 x price of milk powder in june = 100 x price of coffee in july = 400 x ( because of 300 % increase in price ) price of milk powder in july = 20 x ( because of 80 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of milk powder in july will be = 600 x + 30 x = 630 x as per question 630 x = 6.30 $ x = 0.01 s so the price of milk powder in july = 20 x = 20 x 0.01 = 0.2 $ / pound answer b
Answer: b
Python program:
a = 80 / 100
b = 1 - a
Problem: a certain class of students is being divided into teams . the class can either be divided into 18 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
Options: a ) 6 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: prime factorization of 18 = 2 * 3 ^ 2 prime factorization of 24 = 2 ^ 3 * 3 lcm of the given numbers = 2 ^ 3 * 3 ^ 2 = 72 answer e
Answer: e
Python program:
a = math.lcm(18, 24)
Problem: a bus started its journey from mumbai and reached pune in 44 min with its average speed of 50 km / hr . if the average speed of the bus is increased by 5 km / hr , how much time will it take to cover the same distance ?
Options: a ) 38 min , b ) 36 min , c ) 31 min , d ) 40 min , e ) 49 min
Rationale: "sol . distance between ramgarh and devgarh = ( 50 * 44 ) / 60 = 110 / 3 average speed of the bus is increased by 5 km / hr then the speed of the bus = 55 km / hr required time = 110 / 3 * 60 / 55 = 40 min d"
Answer: d
Python program:
a = 44 / 50
b = 50 * a
c = 50 + 5 
d = b / c
Problem: daniel went to a shop and bought things worth rs . 25 , out of which 30 paise went on sales tax on taxable purchases . if the tax rate was 10 % , then what was the cost of the tax free items ?
Options: a ) a ) 19.7 , b ) b ) 20 , c ) c ) 21.3 , d ) d ) 21.7 , e ) e ) 22
Rationale: "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 paise is given as tax = > total tax incurred = 30 paise = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 10 % ∴ ( 25 − 30 / 100 − x ) 10 / 100 = 30 / 100 ⇒ 10 ( 25 − 0.3 − x ) = 30 ⇒ ( 25 − 0.3 − x ) = 3 ⇒ x = 25 − 0.3 − 3 = 21.7 d"
Answer: d
Python program:
a = 30 / 100
b = 25 - a
c = 30 / 10
d = b - c
Problem: how many positive integers less than 250 are there such that they are multiples of 15 or multiples of 16 ?
Options: a ) 28 . , b ) 29 . , c ) 30 . , d ) 31 . , e ) 32 .
Rationale: "250 / 15 = 16 ( plus remainder ) so there are 16 multiples of 15 250 / 16 = 15 ( plus remainder ) so there are 15 multiples of 16 we need to subtract 1 because 15 * 16 is a multiple of both so it was counted twice . the total is 16 + 15 - 1 = 30 the answer is c ."
Answer: c
Python program:
a = 4 + 15 
b = a - 1
c = math.factorial(b)
d = math.factorial(15)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: if ( 5 - x ) / ( 5 + x ) = x , what is the value of x ^ 2 + 6 x - 5 ?
Options: a ) - 6 , b ) - 4 , c ) - 2 , d ) 0 , e ) 3
Rationale: "( 5 - x ) = x * ( 5 + x ) ( 5 - x ) = 5 x + x ^ 2 0 = x ^ 2 + 6 x - 5 the answer is d ."
Answer: d
Python program:
a = 5 * 2
b = a - 5
Problem: 1 / 2 - [ ( 2 / 7 * 7 / 32 ) + 1 ] + 9 / 16 =
Options: a ) 29 / 16 , b ) 19 / 16 , c ) 15 / 16 , d ) 9 / 13 , e ) 0
Rationale: 1 / 2 - [ ( 2 / 7 * 7 / 32 ) + 1 ] + 9 / 16 = 1 / 2 - [ ( 1 / 16 ) + 1 ] + 9 / 16 = 1 / 2 - [ 17 / 16 ] + 9 / 16 = 8 / 16 - 17 / 16 + 9 / 16 = 0 the answer is e .
Answer: e
Python program:
a = 9 / 16
Problem: if a person buy radio worth rs 2468 and pay 7 % sales . how much price of radio should reduce to pay only rs 2468 .
Options: a ) 162 , b ) 158 , c ) 159 , d ) 130 , e ) 160
Rationale: ( x + . 07 x ) = 2468 1.07 x = 2468 x = 2306 reduce = 2468 - 2306 = 162 answer : a
Answer: a
Python program:
a = 7 / 100
b = 1 + a 
c = 2468 / b
d = 2468 - c
Problem: 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 48 days . if 60 more cows and 30 more buffaloes are brought in , how many days will the fodder last ?
Options: a ) 15 days , b ) 18 days , c ) 21 days , d ) 24 days , e ) 27 days
Rationale: 2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 48 days . 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen the new total is equal to 80 oxen instead of 30 oxen . 30 * 48 / 80 oxen = 18 days the answer is b .
Answer: b
Python program:
a = 24 / 4
b = a * 3
c = 15 + b 
d = 8 / 2
e = d * 3
f = c + e 
g = 48 * f
h = 15 + 30 
i = 24 + 60 
j = i / 4
k = j * 3
l = h + k 
m = 8 / 2
n = m * 3
o = l + n 
p = g / o
Problem: the difference between a number and its three - fifth is 50 . what is the number ?
Options: a ) 185 , b ) 190 , c ) 160 , d ) 120 , e ) 125
Rationale: "let the number be x . then , x - 3 / 5 x = 50 = > 2 / 5 x = 50 x = ( 50 * 5 ) / 2 = 125 . answer : e"
Answer: e
Python program:
a = 50 + 4 
b = a ** 4
Problem: two thirds of the roads from a to b are at least 5 miles long , and 3 / 4 of the roads from b to c are at least 5 miles long . if you randomly pick a road from a to b and then randomly pick a road from b to c , what is the probability that at least one of the roads you pick is at least 5 miles long ?
Options: a ) 1 / 6 , b ) 1 / 4 , c ) 2 / 3 , d ) 3 / 4 , e ) 11 / 12
Rationale: so please : find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long : p = 1 - 1 / 3 * 1 / 4 = 11 / 12 . answer : e .
Answer: e
Python program:
a = 2 / 3
b = 1 - a
c = 3 / 4
d = 1 - c
e = b * d
f = 1 - e
Problem: if x = 6 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.01 , c ) 0.25 , d ) 4 , e ) 8
Rationale: "( x − 2 y ) ^ y = ( 6 − 2 ( − 2 ) ) ^ − 2 = 1 / ( 6 + 4 ) ^ 2 = 1 / 100 = 0.01 answer : b"
Answer: b
Python program:
a = 2 / 2
b = a / 1000
Problem: a 270 m long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 320 m , e ) 350 m
Rationale: "speed of first train = ( 120 * 5 / 18 ) m / sec = 100 / 3 m / sec speed of other train = ( 80 * 5 / 18 ) m / sec = 200 / 9 m / sec time to cross each other = 9 sec let x be the length of 2 nd train therefore 9 = ( 270 + x ) / ( 100 / 3 + 200 / 9 ) 500 = 270 + x 230 m = x answer : a"
Answer: a
Python program:
a = 120 + 80 
b = a / const_3_6
c = b * 9
d = c - 270
Problem: a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money t did bob receive ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 52
Rationale: "notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ t = 20 answer : b"
Answer: b
Python program:
a = 32 * 2
b = a / 3
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 40 kilometers , maxwell ' s walking speed is 3 km / h , and brad ' s running speed is 5 km / h . what is the distance traveled by maxwell when they meet in the middle ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 15 , e ) 14
Rationale: "consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 3 xt = 40 - 5 xt ( i . e distance = speed x time ) = > 8 t = 40 hence t = 5 oa = 3 x 5 = 15 km answer : d"
Answer: d
Python program:
a = 3 + 5 
b = 40 / a
c = 3 * b
Problem: in a urban village of india named ` ` owlna ' ' , 70 % people have refrigerator , 75 % people have television , 65 % people got computers and 95 % got air - conditionor . how many people ( minimum ) got all these luxury .
Options: a ) 5 % , b ) 7 % , c ) 3 % , d ) 9 % , e ) 15 %
Rationale: a 10 % 100 - [ ( 100 - 65 ) + ( 100 - 95 ) + ( 100 - 75 ) + ( 100 - 70 ) ] = 100 - ( 30 + 25 + 35 + 5 ) = 100 - 95
Answer: a
Python program:
a = 100 - 70
b = 100 - 75
c = a + b 
d = 100 - 65
e = c + d 
f = 100 - 95
g = e + f 
h = 100 - g
Problem: in a group of 12 engineers , 4 engineers have a phd degree ; the others have only an ms or bs degree . a team of 4 engineers is to be chosen which must have at least 1 engineer with a phd , how many different teams can be chosen ?
Options: a ) 495 , b ) 70 , c ) 245 , d ) 425 , e ) 555
Rationale: "the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 12 r = 4 so , total teams is 12 c 4 = 12 ! / ( 4 ! ( 12 - 4 ) ! ) = 495 , and n = 12 - 4 = 8 r = 4 for teams without a phd is 8 c 4 = 8 ! / ( 4 ! ( 8 - 4 ) ! ) = 70 , so , teams with at least 1 phd = 495 - 70 = 425 answer : d"
Answer: d
Python program:
a = 12 - 4
b = a * 4
c = b * 4
d = 1 + c