euclaise/mathqa_programs huggingface dataset:
Problem: a certain lab experiments with white and brown mice only . in one experiment , 2 / 4 of the mice are white . if there are 16 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 32 , b ) 36 , c ) 34 , d ) 39 , e ) 42
Rationale: "let total number of mice = m number of white mice = 2 / 4 m number of brown mice = 2 / 4 m = 16 = > m = 32 answer a"
Answer: a
Python program:
a = 2 / 4
b = 16 / a
c = b - 16
Problem: if x is divided by 7 , the remainder is 5 . what is the remainder if 4 x is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: x = 7 q + 5 4 x = 7 * 4 q + 20 4 x = 7 * 4 q + 7 * 2 + 6 4 x = 7 ( 4 q + 2 ) + 6 4 x = 7 k + 6 ( k = 4 q + 2 ) answer d
Answer: d
Python program:
a = 4 * 7
b = a + 10 
c = b + 10 
d = c / 4
e = d / 2
Problem: the speed of a boat in still water is 21 km / hr and the rate of current is 8 km / hr . the distance travelled downstream in 13 minutes is
Options: a ) 1.6 km , b ) 2 km , c ) 6.3 km , d ) 4 km , e ) none of these
Rationale: "explanation : speed downstreams = ( 21 + 8 ) kmph = 18 kmph . distance travelled = ( 29 x 13 / 60 ) km = 6.3 km option c"
Answer: c
Python program:
a = 13 / const_60
b = 21 + 8 
c = a * b
Problem: jolene entered an 16 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 12 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
Options: a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24
Rationale: "if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 920.24 answer : d ."
Answer: d
Python program:
a = 3 / 100
b = 2 / 100
c = 100 ** 2
d = b * c
e = 100 ** 2
f = d + e 
g = a * f
h = 2 / 100
i = 100 ** 2
j = h * i
k = 100 ** 2
l = j + k 
m = g + l 
n = 4 / 100
o = m * n
p = 3 / 100
q = 2 / 100
r = 100 ** 2
s = q * r
t = 100 ** 2
u = s + t 
v = p * u
w = o + v
Problem: divide $ 600 among a , b in the ratio 1 : 3 . how many $ that a get ?
Options: a ) $ 50 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600
Rationale: "sum of ratio terms = 1 + 3 = 4 a = 600 * 1 / 4 = $ 150 answer is c"
Answer: c
Python program:
a = 600 / 1
Problem: 3 candidates in an election and received 3000 , 5000 and 20000 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 45.12 % , b ) 50 % , c ) 57 % , d ) 71.42 % , e ) 65 %
Rationale: "total number of votes polled = ( 3000 + 5000 + 20000 ) = 28000 so , required percentage = 11628 / 20400 * 100 = 71.42 % d"
Answer: d
Python program:
a = 3000 + 5000 
b = a + 20000 
c = 20000 / b
d = c * 100
Problem: what number times ( 1 ⁄ 5 ) ^ 2 will give the value of 5 ^ 3 ?
Options: a ) 5 , b ) 25 , c ) 125 , d ) 625 , e ) 3125
Rationale: "x * ( 1 / 5 ) ^ 2 = 5 ^ 3 x = 5 ^ 2 * 5 ^ 3 = 5 ^ 5 = 3125 the answer is e ."
Answer: e
Python program:
a = 5 ** 5
b = 5 ** 3
c = a * b
Problem: a clock shows the time as 9 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 4 p . m . ?
Options: a ) 30 min , b ) 35 min , c ) 45 min , d ) 50 min , e ) 55 min
Rationale: there are 7 hours in between 9 a . m . to 4 p . m . 7 * 5 = 35 minutes . answer : b
Answer: b
Python program:
a = 3 + 4 
b = a * 5
Problem: the average weight of 4 person ' s increases by 3 kg when a new person comes in place of one of them weighing 70 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 82 kg , c ) 86 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increased = ( 4 x 3 ) kg = 12 kg . weight of new person = ( 70 + 12 ) kg = 82 kg . answer : option b"
Answer: b
Python program:
a = 4 * 3
b = a + 70
Problem: the no . of girls in a class are 7 times the no . of boys , which value cannever be the of total students ?
Options: a ) 20 , b ) 35 , c ) 30 , d ) 40 , e ) 42
Rationale: let the boys are x , then girls are 7 x , total = x + 7 x = 8 x so it should be multiple of 8 , 30 is not a multiple of 8 . c
Answer: c
Python program:
a = 7 + 1 
b = a * 4
c = b - 2
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 650 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 85 , d ) 88 , e ) none
Rationale: "explanation we have : l = 20 ft and lb = 650 sq . ft . so , b = 32.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 65 ) ft = 85 ft . answer c"
Answer: c
Python program:
a = 650 / 20
b = a * 2
c = b + 20
Problem: john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 50 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 50 % , d ) 70 % , e ) 80 %
Rationale: "the is always the difference between our starting and ending points . in this case , it ’ s 100 – 50 = 50 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 50 / 100 ) * 100 = ( 0.5 ) * 100 = 50 % . c"
Answer: c
Python program:
a = 100 - 50
Problem: 10 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 288 , b ) 3200 , c ) 800 , d ) 267 , e ) 121
Rationale: "( 10 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 10 x = 320 x = 3200 answer : b"
Answer: b
Python program:
a = 650 * 20
b = a / 100
c = b + 190 
d = c * 100
e = d / 10
Problem: a clock store sold a certain clock to a collector for 25 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 55 percent of what the collector had paid . the shop then sold the clock again at a profit of 70 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 125 , for how much did the shop sell the clock the second time ?
Options: a ) $ 500 , b ) $ 467.5 , c ) $ 935 , d ) $ 525.5 , e ) $ 465.5
Rationale: "now , in the question above , lets say the original cost of the clock to store was c $ and then it sold the same to the collector at 25 % profit . this means the clocks ' selling price was c ( 1.25 ) and this becomes cost price for the collector . now , when the collector tries to sell the same clock to the store , the store buys it for 55 % the price at which the collector bought it . thus , you get = 1.25 * 0.55 * c = 0.6875 c furthermore , the store sells the clock for the second time for 70 % profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy - back * 1.7 = 1.7 * 0.6875 c finally given that c - 0.6875 c = 125 - - - - > c = 400 $ thus , the cost of the clock the second time around = 1.7 * 0.6875 c = 1.7 * 0.6875 * 400 = 467.5 $ . hence b is the correct answer ."
Answer: b
Python program:
a = 100 + 0 
b = 100 + 0 
c = b / 2
d = a * c
e = d / 125
f = 125 * e
g = 125 + 25 
h = g / 2
i = h - 25
j = f / i
Problem: the ratio of spinsters to cats is 2 to 9 . if there are 63 more cats than spinsters , how many spinsters are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "let 2 x be the number of spinsters . then 9 x is the number of cats . 9 x - 2 x = 63 x = 9 and the number of spinsters is 2 ( 9 ) = 18 . the answer is e ."
Answer: e
Python program:
a = 9 - 2
b = 63 / a
c = b * 2
Problem: 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 8.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 9 % , 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 + 0.085 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 85 f - - > s = 10 f - - > f / s = 1 / 10 - - > f / ( s + f ) = 1 / ( 1 + 10 ) = 1 / 11 = 0.09 . answer : b ."
Answer: b
Python program:
a = 3 - 5
b = 8 - 5
c = a / b
d = c * 100
Problem: the time it took car p to travel 600 miles was 2 hours less than the time it took car r to travel the same distance . if car p ’ s average speed was 10 miles per hour greater than that of car r , what was car r ’ s average speed , in miles per hour ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let speed of car r be = x then speed of car p = x + 10 a / q , ( 600 / x ) - ( 600 / ( x + 10 ) ) = 2 solving for x = 50 miles \ hr answer : b"
Answer: b
Python program:
a = negate + ( 
b = negate ** (
c = b - 2
d = 600 * 10
e = d / 2
f = 4 * negate
g = math.sqrt(c)
h = a / g
Problem: the h . c . f . of two numbers is 60 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
Options: a ) 276 , b ) 300 , c ) 500 , d ) 700 , e ) 900
Rationale: "the numbers are ( 60 x 11 ) and ( 60 x 15 ) . larger number = ( 60 x 15 ) = 900 . answer : e"
Answer: e
Python program:
a = 60 * 15
Problem: the number of even factors of 21600 is
Options: a ) 32 , b ) 42 , c ) 60 , d ) 25 , e ) 52
Rationale: make a prime factorization of the number : 21,600 = 25 ∗ 33 ∗ 52 according to the above the number of factors is ( 5 + 1 ) ( 3 + 1 ) ( 2 + 1 ) = 72 now , get rid of powers of 2 as they give even factors - - > you ' ll have 33 ∗ 52 which has ( 3 + 1 ) ( 2 + 1 ) = 12 factors . all the remaining factors will be odd , therefore 21,600 has 72 - 12 = 60 even factors . answer : c .
Answer: c
Python program:
a = 2 + 3 
b = a + 1 
c = 3 + 1 
d = b * c
e = 2 + 1 
f = d * e
g = 3 + 1 
h = 2 + 1 
i = g * h
j = f - i
Problem: at a speed of 50 miles per hour , a certain car uses 1 gallon of gasoline every 30 miles . if the car starts with a full 10 gallon tank of gasoline and travels for 5 hours at 50 miles per hour , the amount of gasoline used would be what fraction of a full tank ?
Options: a ) 3 / 25 , b ) 5 / 6 , c ) 7 / 12 , d ) 2 / 3 , e ) 25 / 36
Rationale: "gas used = ( 5 hours ) * ( 50 miles / hour ) * ( 1 gallon / 30 miles ) = 8 + 1 / 3 gallons portion used = ( 8 + 1 / 3 ) / 10 = 5 / 6 ans b"
Answer: b
Python program:
a = 50 * 5
b = a / 30
c = b / 10
Problem: what least number should be subtracted from 2590 so that the remainder when divided by 9 , 11 , and 13 will leave in each case the same remainder 6 ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 10 , e ) 11
Rationale: "the lcm of 9 , 11 , and 13 is 1,287 . the next multiple is 2 * 1,287 = 2,574 . 2,574 + { remainder } = 2,574 + 6 = 2,580 , which is 10 less than 2,590 . answer : d ."
Answer: d
Python program:
a = 9 * 11
b = a * 13
c = b * 2
d = c + 6 
e = 2590 - d
Problem: the second angle of a triangle is double the first ( 110 ) . the third angle is 40 less than the first ( 15 ) . find the first angle .
Options: a ) 35 , b ) 45 , c ) 55 , d ) 65 , e ) 75
Rationale: first x with nothing given about the firstwemake that x second 2 x the second is double the first , third x − 40 the third is 40 less than the first f + s + t = 180 all three angles add to 180 ( x ) + ( 2 x ) + ( x − 40 ) = 180 replace f , s , and t with the labeled values . x + 2 x + x − 40 = 180 here the parenthesis are not needed . 4 x − 40 = 180 combine like terms , x + 2 x + x + 40 + 40 add 40 to both sides 4 x = 220 the variable ismultiplied by 4 4 4 divide both sides by 4 x = 55 our solution for x first 55 replace xwith 55 in the original list of angles second 2 ( 55 ) = 110 our angles are 55 , 110 , and 15 third ( 55 ) − 40 = 15 correct answer c
Answer: c
Python program:
a = 40 + 15
Problem: find the compound interest on $ 36,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532.6 , b ) 2552.2 , c ) 2524.1 , d ) 5674.5 , e ) 2512.9
Rationale: "principal = $ 36000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 36000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 41674.5 ci . = $ ( 41674.5 - 36000 ) = $ 5674.5 answer d ."
Answer: d
Python program:
a = 9 / 100
b = 1 + a 
c = b ** 20
d = 36 * 0
e = d - 36
Problem: for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 25 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 % , c ) 25 % , d ) 27 % , e ) 28 %
Rationale: "total sales = 800 comission = ( 20 / 100 ) * 500 + ( 25 / 100 ) * 300 = 100 + 75 = 175 % comission = ( 175 / 800 ) * 100 = 21.8 ~ 22 % answer is a"
Answer: a
Python program:
a = 20 / 100
b = a * 500
c = 25 / 100
d = 800 - 500
e = c * d
f = b + e 
g = f / 800
h = g * 100
Problem: mike took a bus from home to market , that travels at 30 kmph . while walking back at 6 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 20 kmph . find the average speed .
Options: a ) 21.2 kmph , b ) 12.1 kmph , c ) 23.4 kmph , d ) 20.4 kmph , e ) none of these
Rationale: let the distance be 2 x ( one way ) time taken by bus = 2 x / 30 , by walking = x / 6 , by cycling = x / 20 hours : . average speed = total distance / total time = 6 x / x / 15 + x / 6 + x / 20 = 6 * 60 / 4 + 10 + 3 = 21.2 answer : a
Answer: a
Python program:
a = 6 + 20 
b = a / 2
c = b + 30 
d = c / 2
Problem: circular gears l and r start to rotate at the same time at the same rate . gear l makes 10 complete revolutions per minute and gear r makes 30 revolutions per minute . how many seconds after the gears start to rotate will gear r have made exactly 6 more revolutions than gear l ?
Options: a ) a ) 6 , b ) b ) 8 , c ) c ) 10 , d ) d ) 12 , e ) e ) 18
Rationale: "gear l - - 10 rotations per 60 seconds - - 1 rotation per 6 seconds . gear r - - 40 rotations per 60 seconds - - 3 rotations per 6 seconds . first 6 seconds - - gear l makes 1 rotation . - - gear r makes 4 rotations - - net difference - - 2 rotations hence every 6 seconds the difference between the number of rotations of r and l gear is 2 units . required net difference should be 6 rotations = > 3 ( 6 seconds later ) = = > 18 seconds . answer : e"
Answer: e
Python program:
a = 30 / const_60
b = 10 / const_60
c = a - b
d = 6 / c
e = d / 3
Problem: in the youth summer village there are 100 people , 50 of them are not working , 25 of them have families and 75 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
Options: a ) 100 , b ) 75 , c ) 25 , d ) 50 , e ) 125
Rationale: "total = 100 not working = 50 having family = 25 like to sing in shower = 75 working = 100 - 50 = 50 not having family = 100 - 25 = 75 like to sing in shower = 75 largest possible number is the lowest possible among the above thus 50 d"
Answer: d
Python program:
a = 50 + 25 
b = a + 75 
c = b - 100
Problem: what is the smallest no . which must be added to 3245613 so as to obtain a sum which is divisible by 11 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 9 , e ) 3
Rationale: "for divisibility by 11 , the difference of sums of digits at even and odd places must be either zero or divisible by 11 . for 3245613 , difference = ( 3 + 4 + 6 + 3 ) - ( 2 + 5 + 1 ) = 16 - 8 = 8 . the units digit is at odd place . so we add 3 to the number = > 3245613 + 3 = 3245616 now , ( 3 + 4 + 6 + 6 ) - ( 2 + 5 + 1 ) = 19 - 8 = 11 = > 11 is a multiple of 11 and hence 3245616 is also divisible by 11 e"
Answer: e
Python program:
a = 3245613 * 11
b = a / 3245613
Problem: a train 130 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 ) 4 , b ) 7 , c ) 5 , d ) 9 , e ) 8
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 = [ 130 * 3 / 55 ] sec = 7 sec answer : b"
Answer: b
Python program:
a = 130 / 1000
b = 60 + 6 
c = a / b
d = 3600 * c
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent j of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , j = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d . d"
Answer: d
Python program:
a = 100 - 68
b = a / 2
c = 100 - b
Problem: in a 4 person race , medals are awarded to the fastest 3 runners . the first - place runner receives a gold medal , the second - place runner receives a silver medal , and the third - place runner receives a bronze medal . in the event of a tie , the tied runners receive the same color medal . ( for example , if there is a two - way tie for first - place , the top two runners receive gold medals , the next - fastest runner receives a silver medal , and no bronze medal is awarded ) . assuming that exactly 3 medals are awarded , and that the 3 medal winners stand together with their medals to form a victory circle , how many z different victory circles are possible ?
Options: a ) 24 , b ) 52 , c ) 96 , d ) 144 , e ) 648
Rationale: possible scenarios are : 1 . gold / silver / bronze / no medal ( no ties ) - 4 ! = 24 ; 2 . gold / gold / silver / no medal - 4 ! / 2 ! = 12 ; 3 . gold / silver / silver / no medal - 4 ! / 2 ! = 12 ; 4 . gold / gold / gold / no medal - 4 ! / 3 ! = 4 . total z : 24 + 12 + 12 + 4 = 52 answer : b .
Answer: b
Python program:
a = math.factorial(4)
b = math.factorial(4)
c = math.factorial(2)
d = b / c
e = a + d 
f = math.factorial(4)
g = math.factorial(2)
h = f / g
i = e + h 
j = math.factorial(4)
k = math.factorial(3)
l = j / k
m = i + l
Problem: an air - conditioning unit costs $ 470 . on december there was a discount for christmas of 16 % . 6 months later , the holiday season was over so the company raised the price of the air - conditioning by 12 % . how much will an air - conditioning unit cost in november ?
Options: a ) $ 442 , b ) $ 470 , c ) $ 472 , d ) $ 484 , e ) $ 491
Rationale: if its previous november ( before discount ) then price is $ 470 . but if its november of next year then 16 % discount on $ 470 = 470 ( 1 - 16 / 100 ) = $ 394.8 again a corrected raised price of 12 % over $ 394.8 = 394.8 ( 1 + 12 / 100 ) = 442.176 ~ $ 4442 ans a
Answer: a
Python program:
a = 12 / 100
b = a + 1 
c = 16 / 100
d = 1 - c
e = d * 470
f = b * e
Problem: in the hillside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?
Options: a ) 50 , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .
Rationale: "given there are 50 students , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . answer : option a is correct ."
Answer: a
Python program:
a = 100 - 5
b = a / 100
c = b * 50
d = 5 / 100
e = d * 50
f = c + e
Problem: the average of first five multiples of 5 is
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "solution average = 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 75 / 5 . = 15 answer e"
Answer: e
Python program:
a = 5 + 1
Problem: maths , physics and chemistry books are stored on a library shelf that can accommodate 25 books . currently , 20 % of the shelf spots remain empty . there are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books . among all the books , 12 books are soft cover and the remaining are hard - cover . if there are a total of 7 hard - cover books among the maths and physics books . what is the probability e , that a book selected at random is either a hard cover book or a chemistry book ?
Options: a ) 1 / 10 , b ) 3 / 20 , c ) 1 / 5 , d ) 1 / 4 , e ) 9 / 20
Rationale: "first phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf . to do so , you have the equations : m + p + c = 20 ( since 4 / 5 of the 25 spots are full of books ) m = 2 p p = 4 + c from that , you can use substitution to get everything down to one variable . c = p - 4 m = 2 p p = p then ( p - 4 ) + 2 p + p = 20 , so 4 p = 24 and p = 6 . that means that there are 12 math , 6 physics , and 2 chemistry books on the shelf . with those numbers , you also know that there are 8 total hardcovers , 1 of which is chemistry . so if your goal is to get either a hardcover or a chemistry , there are 9 ways towin - either one of the 7 hardcovers that are n ' t chemistry or the two chemistry books . so out of the 20 total , e = 9 provide the desired outcome , making the answer e ."
Answer: e
Python program:
a = 2 + 4 
b = 2 + a 
c = b + 12 
d = 2 / c
e = 2 + 4 
f = 2 + e 
g = 2 + 4 
h = 2 + g 
i = h + 12 
j = f / i
k = d + j 
l = 2 + 4 
m = 2 + l 
n = m + 12 
o = 2 / n
p = 2 + 4 
q = 2 + p 
r = 2 + 4 
s = 2 + r 
t = s + 12 
u = q / t
v = o * u
w = k - v
Problem: how many diagonals does a polygon with 17 sides have , if one of its vertices does not connect to any diagonal ?
Options: a ) 102 , b ) 104 , c ) 110 , d ) 90 , e ) 84
Rationale: "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 17 - 1 then 16 * ( 16 - 3 ) / 2 = 104 correct option : b"
Answer: b
Python program:
a = 17 - 1
b = 17 - 1
c = b - 3
d = a * c
e = d / 2
Problem: the sum of 3 consecutive multiples of 3 is 72 . what is the larget number ?
Options: a ) 26 , b ) 27 , c ) 46 , d ) 57 , e ) none
Rationale: sol . let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 72 ⇔ 9 x = 63 ⇔ x = 7 . ∴ largest number = 3 x + 6 = 27 . answer b
Answer: b
Python program:
a = 72 / 3
b = a + 3
Problem: find the value of sin 75 ° + sin 15 ° = ?
Options: a ) 0 , b ) 1 / 2 , c ) 1 , d ) 3 / 2 , e ) 2
Rationale: "sin a + sin b = 2 sin [ ( a + b ) / 2 ] cos [ ( a - b ) / 2 ] = 2 sin [ ( 75 + 15 ) / 2 ] cos [ ( 75 - 15 ) / 2 ] = 2 sin 90 cos 60 = 2 * 1 * ( 1 / 2 ) = 1 answer : c"
Answer: c
Python program:
a = 75 * 15