euclaise/mathqa_programs huggingface dataset:
Problem: a man ' s speed with the current is 15 km / hr and the speed of the current is 2.8 km / hr . the man ' s speed against the current is ?
Options: a ) 9.4 , b ) 20 , c ) 50 , d ) 30 , e ) 40
Rationale: "man ' s speed with the current = 15 km / hr = > speed of the man + speed of the current = 15 km / hr speed of the current is 2.8 km / hr hence , speed of the man = 15 - 2.8 = 12.2 km / hr man ' s speed against the current = speed of the man - speed of the current = 12.2 - 2.8 = 9.4 km / hr answer is a ."
Answer: a
Python program:
a = 15 - 2
b = a - 2
Problem: 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 - 2 / 15 =
Options: a ) 0 , b ) 2 / 15 , c ) 2 / 5 , d ) 9 / 20 , e ) 5 / 6
Rationale: "we need to determine the result of 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 let ’ s add the given fractions in two groups . in the group of the first three fractions , notice that 1 / 3 and 1 / 2 share a common denominator of 6 with 5 / 6 . 1 / 2 + 1 / 3 = 3 / 6 + 2 / 6 = 5 / 6 thus , 5 / 6 – 5 / 6 = 0 looking at the 2 nd group of the fractions ( 1 / 5 , 1 / 4 , and 9 / 20 ) , notice that 1 / 5 and 1 / 4 share a common denominator of 20 with 9 / 20 . 1 / 5 + 1 / 4 = 4 / 20 + 5 / 20 = 9 / 20 thus , 9 / 20 – 9 / 20 = 0 . thus , the result of 1 / 3 + 1 / 2 – 5 / 6 + 1 / 5 + 1 / 4 – 9 / 20 is 2 / 15 . answer : b"
Answer: b
Python program:
a = 2 / 15
Problem: a river 2 m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 , b ) 2678 , c ) 2689 , d ) 2761 , e ) 2882
Rationale: "( 3000 * 2 * 5 ) / 60 = 4500 m 3 answer : a"
Answer: a
Python program:
a = 2 * 45
b = 3 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: in a coconut grove , ( x + 2 ) trees yield 60 nuts per year , x trees yield 120 nuts per year and ( x – 2 ) trees yield 180 nuts per year . if the average yield per year per tree be 100 , find x .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "( x + 2 ) × 60 + x × 120 + ( x − 2 ) × 180 / ( x + 2 ) + x + ( x − 2 ) = 100 ⇒ 360 x − 240 / 3 x = 100 ⇒ 60 x = 240 ⇒ x = 4 answer e"
Answer: e
Python program:
a = 180 * 2
b = 60 * 2
c = a - b
d = 60 + 120 
e = d + 180 
f = 100 * 3
g = e - f
h = c / g
Problem: tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 70 ?
Options: a ) 4 , b ) 12 , c ) 15 , d ) 20 , e ) 24
Rationale: "you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 12 * 50 600 1800 - 600 1200 18 66.67 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is c"
Answer: c
Python program:
a = 70 * 30
b = a - 1800
c = 70 - 50
d = b / c
Problem: in a graduating class , 40 percent of the students are male . in this class , 50 percent of the male students and 40 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) 0.44 , b ) 0.5 , c ) 0.56 , d ) 0.62 , e ) 0.68
Rationale: "let x be the total number of students . the number students who are younger than 25 is 0.5 * 0.4 x + 0.6 * 0.6 x = 0.56 x the answer is c ."
Answer: c
Python program:
a = 40 / 100
b = 50 / 100
c = a * b
d = 40 / 100
e = 40 / 100
f = 1 - e
g = d * f
h = c + g 
i = 1 - h
Problem: up to 20 , how many no . are odd and prime both ?
Options: a ) 9 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: we have to calculate it manually . odd 1,3 , 5,7 , 9,11 , 13,15 , 17,19 prime 2,3 , 5,7 , 11,13 , 17,19 common 3 , 5,7 , 11,13 , 17,19 total no . 7 answer d
Answer: d
Python program:
a = 20 / 4
b = a + 2
Problem: the area of sector of a circle whose radius is 15 metro and whose angle at the center is 42 â ° is ?
Options: a ) 52.6 , b ) 52.9 , c ) 52.8 , d ) 52.1 , e ) 82.5
Rationale: "42 / 360 * 22 / 7 * 15 * 15 = 82.5 m 2 answer : e"
Answer: e
Python program:
a = 15 ** 2
b = 2 * 10
c = b + 2 
d = 4 + 3 
e = c / d
f = a * e
g = 3600 / 10
h = 42 / g
i = f * h
Problem: 9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 42 miles per hour faster than the first runner ' s rate . how far apart , to the nearest mile , will they be after 1 / 2 hour ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 8 m / h - - > 4 m in 1 / 2 hr side 2 = 10 m / h - - > 5 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 5 ^ 2 d ^ 2 = 41 = ~ 6 answer option a"
Answer: a
Python program:
a = 1 / 42
b = 8 * a
c = b ** 42
d = 8 - 42
e = 1 / 42
f = d * e
g = f ** 42
h = c + g 
i = math.sqrt(h)
Problem: if x , y , and z are positive integers and 2 x = 4 y = 5 z , then the least possible value of x + y + z is
Options: a ) 40 , b ) 50 , c ) 55 , d ) 60 , e ) 19
Rationale: "given 2 x = 4 y = 5 z x + y + z in terms of x = x + ( 2 x / 4 ) + ( 2 x / 5 ) = 38 x / 20 = 19 x / 10 now checking with each of the answers and see which value gives a minimum integer value . a x = 10 / 19 * 40 , not an integer b , c , e can be ruled out similarly . d is minimum value as x = 19 * 10 / 19 = 10 answer is e"
Answer: e
Python program:
a = 2 * 4
b = a * 5
c = b / 2
d = 2 * 4
e = d * 5
f = e / 4
g = c - f
h = 2 * 4
i = h * 5
j = i / 5
k = g + j
Problem: a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 68 km downstream .
Options: a ) 2 , b ) 4 , c ) 6 , d ) 5 , e ) 3
Rationale: "speed downstream = ( 13 + 4 ) km / hr = 17 km / hr . time taken to travel 68 km downstream = 68 / 17 = 4 hrs ans - b"
Answer: b
Python program:
a = 13 + 4 
b = 68 / a
Problem: the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 5 times the probability that both events a and b occur . what is the probability that event a occurs ?
Options: a ) 1 / 45 , b ) 1 / 2 , c ) 1 / 8 , d ) 2 / 3 , e ) 2 / 11
Rationale: let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 5 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 5 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 5 * 2 b * b 3 b - 2 b ^ 2 = 110 b ^ 2 3 b = 12 b ^ 2 b = 3 / 12 = 1 / 4 so , a = 2 b = 1 / 2
Answer: b
Python program:
a = 2 + 1 
b = 5 * 2
c = b + 2 
d = a / c
e = d * 2
Problem: a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 7.5 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?
Options: a ) 3 / 8 , b ) 1 / 2 , c ) 11 / 16 , d ) 23 / 32 , e ) 3 / 4
Rationale: "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 7.5 / 8 * c : ( b + c ) / 2 = ( 7.5 / 8 ) * c b = ( 7 / 8 ) * c for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 7 / 8 * c ) / 2 = ( 7 / 16 ) * c median = ( a + c ) / 2 = ( 7 / 16 * c + c ) / 2 = ( 23 / 16 ) * c / 2 = ( 23 / 32 ) * c ( answer d )"
Answer: d
Python program:
a = 7 / 5
b = a * 2
c = b - 1
d = 3 / 4
e = d * 2
f = e - 1
g = 1 / f
h = c / g
i = 1 + h 
j = i / 2
Problem: barbata invests $ 1400 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 700 , b ) 300 , c ) 1000 , d ) 360 , e ) 2400
Rationale: let the additional invested amount for 8 % interest be x ; equation will be ; 1400 + 0.05 * 2400 + x + 0.08 x = 1400 + x + 0.06 ( 2400 + x ) 0.05 * 1400 + 0.08 x = 0.06 x + 0.06 * 1400 0.02 x = 1400 ( 0.06 - 0.05 ) x = 1400 * 0.01 / 0.02 = 700 ans : a
Answer: a
Python program:
a = 6 / 100
b = a * 1400
c = 5 / 100
d = 1400 * c
e = b - d
f = 8 / 100
g = 6 / 100
h = f - g
i = e / h
Problem: a person has 12004 coins of silver . how much would he need to add so that he can distribute equally among his 7 children in whole numbers ?
Options: a ) 1 coin , b ) 2 coins , c ) 3 coins , d ) 4 coins , e ) coins
Rationale: he would need to add one coin more so 12005 is fully divisible by 7 and each would get 1715 coins . so the correct answer is a
Answer: a
Python program:
a = 12004 / 7
b = math.floor(a)
c = b + 1 
d = c * 7
e = d - 12004
Problem: a cistern 7 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 53.5 m 2 , d ) 55.5 m 2 , e ) 57 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 7 x 1.25 ) + 7 x 4 ] m 2 = 55.5 m 2 . answer : option d"
Answer: d
Python program:
a = 25 / 100
b = a + 1 
c = b * 4
d = 25 / 100
e = d + 1 
f = e * 7
g = c + f 
h = 2 * g
i = 4 * 7
j = h + i
Problem: a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 162 . find the unknown rate of two blankets ?
Options: a ) 420 , b ) 550 , c ) 490 , d ) 570 , e ) 457
Rationale: "10 * 162 = 1620 3 * 100 + 5 * 150 = 1050 1620 – 1050 = 570 answer : d"
Answer: d
Python program:
a = 10 * 162
b = 3 * 100
c = 5 * 150
d = b + c 
e = a - d
Problem: a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 12 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 10 , b ) 25 , c ) 60 , d ) 16 , e ) 20
Rationale: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 12 days whole work will be done by a in 12 * 4 / 3 = 16 days answer is d"
Answer: d
Python program:
a = 12 * 40
b = 40 - 10
c = a / b
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 20 % , then the cost price of the article is :
Options: a ) 500 , b ) 277 , c ) 466.7 , d ) 297 , e ) 111
Rationale: "explanation : 110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 100 * 560 ) / 120 = rs . 466.7 answer : c"
Answer: c
Python program:
a = 616 * 100
b = 100 + 10 
c = a / b
d = 100 + 10 
e = c * d
f = 100 + 20 
g = e / f
Problem: the l . c . m of two numbers is 48 . the numbers are in the ratio 1 : 4 . the sum of numbers is :
Options: a ) 28 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 1 x and 4 x . then , their l . c . m = 4 x . so , 4 x = 48 or x = 12 . the numbers are 12 and 48 . hence , required sum = ( 12 + 48 ) = 60 . answer : e"
Answer: e
Python program:
a = 1 * 48
b = a / 4
Problem: the effective annual rate of interest corresponding to a nominal rate of 6 % per annum payable half yearly is
Options: a ) 6.06 % , b ) 6.07 % , c ) 6.08 % , d ) 6.09 % , e ) none
Rationale: "solution amount of rs . 100 for 1 year when compounded half yearly = rs . [ 100 x ( 1 + 3 / 100 ) 2 ] = rs . 106.09 % . effective rate = ( 106.09 - 100 ) % = rs . 6.09 % . answer d"
Answer: d
Python program:
a = 6 / 2
b = 6 / 2
c = a + b 
d = 6 / 2
e = 6 / 2
f = d * e
g = f / 100
h = c + g
Problem: on a certain day , tim invested $ 500 at 10 percent annual interest , compounded annually , and lana invested 1,000 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 2.5 , b ) $ 15 , c ) $ 50 , d ) $ 100 , e ) $ 105
Rationale: "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 500 ( 1.10 ) ^ 2 = 500 ( 1.21 ) = 605 and lana would have 1,000 ( 1.05 ) ^ 2 = 1,000 ( 1.1025 ) = 1102.5 thus , tim earned 105 dollars , while lana earned 102.5 dollars the difference is $ 2.5 and the answer is a ."
Answer: a
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 500 * c
e = d - 500
f = 5 / 100
g = 1 + f 
h = g ** 2
i = h * 1
j = i - 1
k = e - j
Problem: two trains of equal are running on parallel lines in the same direction at 49 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 50 , b ) 88 , c ) 65 , d ) 55 , e ) 22
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 49 - 36 = 13 km / hr . = 13 * 5 / 18 = 65 / 18 m / sec . 2 x / 36 = 65 / 18 = > x = 65 . answer : c"
Answer: c
Python program:
a = 49 - 36
b = a * 1000
c = b / 3600
d = 36 * c
e = d / 2
Problem: evaluate : 1222343 - 12 * 3 * 2 = ?
Options: a ) 122336 , b ) 145456 , c ) 122347 , d ) 126666 , e ) 383838
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 1222343 - 12 * 3 * 2 = 122343 - 8 = 122336 correct answer a"
Answer: a
Python program:
a = 12 * 3
b = a * 2
c = 1222343 - b
Problem: the ratio of boarders to day students at a school was originally 2 to 5 . however , after a number of new boarders join the initial 60 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 30
Rationale: "let x be the number of new boarders . the ratio changed from 2 : 5 = 4 : 10 up to 1 : 2 = 5 : 10 . 60 / ( 60 + x ) = 4 / 5 x = 15 the answer is b ."
Answer: b
Python program:
a = 60 / 2
b = a * 5
c = b / 2
d = c - 60
Problem: a candidate got 33 % of the votes polled and he lost to his rival by 833 votes . how many votes were cast ?
Options: a ) 2250 , b ) 2450 , c ) 2650 , d ) 2850 , e ) 3050
Rationale: "let x be the total number of votes . 0.33 x + 833 = 0.67 x 0.34 x = 833 x = 833 / 0.34 = 2450 the answer is b ."
Answer: b
Python program:
a = 33 / 100
b = 1 - a
c = 33 / 100
d = b - c
e = 833 / d
Problem: calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 18 % and its breadth is decreased by 16 % ?
Options: a ) 5.88 % decrease , b ) 0.88 % decrease , c ) 0.88 % increase , d ) 1.88 % decrease , e ) 2.88 % decrease
Rationale: "let l and b be 100 each 100 * 100 = 10000 l increase by 18 % = 118 b decrease by 16 % = 84 118 * 84 = 9912 0.88 % decrease answer : b"
Answer: b
Python program:
a = 100 + 18 
b = 100 - 16
c = a * b
d = 100 * 100
e = c - d
f = 100 * 100
g = e / f
h = g * 100
Problem: a boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . how long will it take to go 6 km in stationary water ?
Options: a ) 40 minutes , b ) 1 hour , c ) 1 hour 15 min , d ) 1 hour 30 min , e ) 1 hour 10 min
Rationale: "speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 10 / 60 ) = 6 kmhr speed in still water = 1 / 2 ( 2 + 6 ) = 4 kmhr time taken in stationary = 6 / 4 = 1 hrs 30 min answer : d"
Answer: d
Python program:
a = 1 / 10
b = a * const_60
c = 2 / 2
d = b + c 
e = d / 2
f = 6 / e
Problem: jane makes toy bears . when she works with an assistant , she makes 71 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 90 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 68.4 bears per 36 hours a week or 1.9 bears / hr ( [ 40 bears * 1.71 ] / [ 40 hrs * . 90 ] ) . [ ( 1.9 - 1 ) / 1 ] * 100 % = 90 % answer : c"
Answer: c
Python program:
a = 100 - 71
b = a - 10
c = 10 / b
d = c * 100
Problem: 34 . the side surface of a cylinder can is rolled with a rectangular plate . if the height of a cylinder tank is 8 feet and the perimeter of the circular base is 6 feet , what is the diagonal of the rectangular plate ?
Options: a ) 10
b ) 12
c ) 8
d ) 14
e ) 9
Rationale: think of a can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the hypothenuse , 10 . ( correct answer : a )
Answer: a
Python program:
a = 8 ** 2
b = 6 ** 2
c = a + b 
d = math.sqrt(c)
Problem: a train 120 meters long completely crosses a 480 meters long bridge in 55 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 545 , c ) 39 , d ) 40 , e ) 09
Rationale: s = ( 120 + 480 ) / 45 = 600 / 55 * 18 / 5 = 39 answer : c
Answer: c
Python program:
a = 120 + 480 
b = a / 1000
c = 55 / 3600
d = b / c
Problem: employees of a certain company are each to receive a unique 6 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , and 5 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
Options: a ) 48 , b ) 56 , c ) 64 , d ) 72 , e ) 80
Rationale: "there are 4 ! ways to make codes starting with 12 . there are 4 ! ways to make codes starting with 24 . the number of codes is 2 * 4 ! = 48 . the answer is a ."
Answer: a
Python program:
a = 2 * 3
b = a * 2
Problem: in an examination , a pupil ’ s average marks were 63 per paper . if he had obtained 20 more marks for his geography paper and 2 more marks for his history paper , his average per paper would have been 65 . how many papers were there in the examination ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: solution let the number pf papers be x . then , 63 x + 20 + 2 = 65 x 65 x - 63 x = 22 2 x = 22 x = 11 . answer d
Answer: d
Python program:
a = 20 + 2 
b = 65 - 63
c = a / b
Problem: if 15 % of 40 is greater than 25 % of a number by 2 , then find the number is ?
Options: a ) 20 , b ) 15 , c ) 16 , d ) 25 , e ) 30
Rationale: "15 / 100 * 40 - 25 / 100 * x = 2 or x / 4 = 4 so x = 16 answer c"
Answer: c
Python program:
a = 15 / 100
b = a * 40
c = b - 2
d = 25 / 100
e = c / d
Problem: what is the rate percent when the simple interest on rs . 800 amount to rs . 144 in 4 years ?
Options: a ) 5 % , b ) 8 % , c ) 3 % , d ) 4.5 % , e ) 1 %
Rationale: "144 = ( 800 * 4 * r ) / 100 r = 4.5 % answer : d"
Answer: d
Python program:
a = 100 * 144
b = 800 * 4
c = a / b
Problem: if p / q = 2 / 7 , then 2 p + q = ?
Options: a ) 11 , b ) 14 , c ) 13 , d ) 15 , e ) 16
Rationale: "let p = 2 , q = 7 then 2 * 2 + 7 = 11 so 2 p + q = 11 . answer : a"
Answer: a
Python program:
a = 2 * 2
b = a + 7
Problem: martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 17.60 , how many discounted tickets did he buy ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 17.6 0.4 x = 1.6 = > x = 4 discounted tickets = 10 - x = 6 ans : d"
Answer: d
Python program:
a = 10 * 2
b = 1 * 60
c = a - b
Problem: the sum of the non - prime numbers between 50 and 60 , non - inclusive , is
Options: a ) 263 , b ) 293 , c ) 323 , d ) 353 , e ) 383
Rationale: sum of consecutive integers from 51 to 59 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 51 + 59 ) / 2 * 9 = 55 * 9 = 495 sum of non - prime numbers b / w 50 and 60 , non inclusive = = = > 495 - 112 ( i . e . , 53 + 59 , being the prime # s in the range ) = 383 answer : e
Answer: e
Python program:
a = 50 + 1 
b = 50 + 1 
c = b + 1 
d = a + c 
e = 50 + 1 
f = e + 1 
g = f + 2 
h = d + g 
i = 50 + 1 
j = i + 1 
k = j + 2 
l = k + 1 
m = h + l 
n = 50 + 1 
o = n + 1 
p = o + 2 
q = p + 1 
r = q + 1 
s = m + r 
t = 50 + 1 
u = t + 1 
v = u + 2 
w = v + 1 
x = w + 1 
y = x + 1 
z = s + y 
A = 50 + 1 
B = A + 1 
C = B + 2 
D = C + 1 
E = D + 1 
F = E + 1 
G = F + 1 
H = z + G
Problem: frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 500 square feet . how many feet offence does frank use ?
Options: a ) 14 , b ) 47 , c ) 70 , d ) 180 , e ) 240
Rationale: "area = length x breadth 500 = 40 x breadth so , breadth = 15 units fencing required is - breadth + breadth + length 15 + 15 + 40 = > 70 feet answer must be ( c ) 70"
Answer: c
Python program:
a = 500 / 40
b = 500 / 40
c = a + b 
d = c + 40
Problem: the class mean score on a test was 80 , and the standard deviation was 15 . if jack ' s score was within 2 standard deviations of the mean , what is the lowest score he could have received ?
Options: a ) 30 , b ) 31 , c ) 50 , d ) 90 , e ) 89
Rationale: "1 sd from the mean is adding and subtrating the amount if standard deviation from the mean one time . 2 sd from the mean is adding and subtracting twice . 1 sd from the mean ranges from 95 to 65 , where 95 is within sd above the mean and 65 within 1 sd below the mean 2 sd = 15 twice = 30 from the the mean , which is 95 to 50 , where 90 is within 2 sd above the mean and 50 is within 2 sd below the mean . answer = c"
Answer: c
Python program:
a = 2 * 15
Problem: there are 3 red chips and 3 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 24 , d ) d ) 60 , e ) e ) 200
Rationale: "using anagram method : @nl 6 _ 5 _ 4 _ 3 _ 2 _ 1 r _ r _ r _ b _ b _ b so . . 6 ! / number of repeated letters ( 3 ! ) ( 3 ! ) = 20 ans : e"
Answer: e
Python program:
a = math.factorial(4)
b = math.factorial(3)
c = a * b
Problem: the average age of applicants for a new job is 32 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 77 , c ) 7 , d ) 18 , e ) 34
Rationale: "minimum age = average - 1 standard deviation = 32 - 8 = 24 maximum age = average + 1 standard deviation = 32 + 8 = 40 maximum number of different ages of the applicants = 30 - 24 + 1 = 7 answer c"
Answer: c
Python program:
a = 32 + 8 
b = 32 - 8
c = a - b
d = c + 1
Problem: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 9 : 17 . the first number is :
Options: a ) 36 , b ) 77 , c ) 88 , d ) 55 , e ) 221
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 9 : 17 x = 12 = > 3 x = 36 answer : a"
Answer: a
Python program:
a = 3 * 5
b = 9 / a
c = 3 * b
d = 3 * 5
e = 9 / d
f = 5 * e
g = c + f