euclaise/mathqa_programs huggingface dataset:
Problem: the length of minute hand of a clock is 5.2 cm . what is the area covered by this in 10 minutes
Options: a ) 15.27 , b ) 14.15 , 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 * ( 5.2 ^ 2 ) * ( 60 / 360 ) = 14.15 cm ^ 2 answer : b"
Answer: b
Python program:
a = 2 * 10
b = a + 2 
c = 3 + 4 
d = b / c
e = 5 * 2
f = 1 * const_60
g = 100 * const_3_6
h = f / g
i = e * h
j = d * i
Problem: the lcm of two numbers is 2310 and hcf is 26 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 715 , b ) 825 , c ) 286 , d ) 582 , e ) 465
Rationale: "first number * second number = lcm * hcf other number = 2310 * 26 / 210 = 11 * 26 = 286 answer : c"
Answer: c
Python program:
a = 2310 * 26
b = a / 210
Problem: find the compound interest accrued on an amount of rs . 14,800 at 13.5 % p . a at the end of two years . ( round off your answer to nearest integer )
Options: a ) 3337 , b ) 2782 , c ) 2788 , d ) 4266 , e ) 2321
Rationale: ci = 14800 { [ 1 + 13.5 / 100 ] 2 - 1 } = 14800 { [ 1 + 27 / 200 ] 2 - 1 = 14800 { 2 + 27 / 200 } { 27 / 200 } = ( 74 ) [ 2 + 27 / 200 ] ( 27 ) = 1998 [ 2 + 27 / 200 ] = 3996 + 269.73 = rs . 4266 answer : d
Answer: d
Python program:
a = 3 + 4 
b = a * 2
c = 2 + 3 
d = c * 2
e = 100 * d
f = b * e
g = 2 + 3 
h = g * 2
i = h - 2
j = i * 100
k = f + j 
l = 13 / 5
m = 1 + l 
n = m ** 2
o = n - 1
p = k * o
Problem: if all of the telephone extensions in a certain company must be even numbers , and if each of the extensions uses all 4 of the digits 1 , 2 , 3 , and 8 , what is the greatest number of 4 - digit extensions that the company can have ?
Options: a ) 4 , b ) 6 , c ) 12 , d ) 16 , e ) 24
Rationale: since the phone number must be even , the unit ' s digit can be either 2 or 8 . when the unit ' s digit is 2 - - > number of possibilities is 3 ! = 6 when the unit ' s digit is 8 - - > number of possibilities is 3 ! = 6 largest number of extensions = 6 + 6 = 12 answer : c
Answer: c
Python program:
a = 4 * 3
Problem: a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 7 per sq m ?
Options: a ) 4350 , b ) 4725 , c ) 4328 , d ) 4329 , e ) 4829
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 7 = rs . 4725 answer : b"
Answer: b
Python program:
a = 2 * 5
b = 75 + a 
c = 2 * 5
d = 55 + c 
e = rectangle_area - (
f = e * rectangle_area
Problem: of 40 applicants for a job , 24 had at least 4 years ' experience , 15 had degrees , and 4 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 3 , c ) 9 , d ) 7 , e ) 5
Rationale: "set a : people with more than 4 years exp set b : people with degree aub = total - ( less than 4 exp and no degree ) aub = 40 - 4 = 36 aub = a + b - aib aib = 15 + 24 - 36 = 3 answer b"
Answer: b
Python program:
a = 24 + 15 
b = 40 - 4
c = a - b
d = 15 - 24
e = c + d
Problem: what is the sum of all the multiples of 3 between 30 and 80 ?
Options: a ) 2103 , b ) 2106 , c ) 1053 , d ) 1252 , e ) 1535
Rationale: "you first have to know all the multiples of 3 between 30 and 80 . they are 3 , 6,9 , 12,15 , 18,21 , 24,27 , 30,33 , 36,39 , 42,45 , 48,51 , 54,57 , 60,63 , 66,69 , 72,75 , and 78 . if you add all these numbers together , you get 1053 . final answer : c"
Answer: c
Python program:
a = 12 + 2 
b = a + 1 
c = 12 + 2 
d = 2 + 4 
e = d + 4 
f = 10 - 1
g = e + f 
h = 2 + 4 
i = h + 4 
j = g + i 
k = 10 + 2 
l = j + k 
m = c + l 
n = b + m 
o = 12 + 2 
p = o + 1 
q = p + 1 
r = n + q 
s = r + 3 
t = 2 + 4 
u = s + t
Problem: the first half of the 20 th century , the population of a particular country increased by 200 percent . in the second half of the century , the population increased by 300 percent . what was the percent increase for the 20 th century as a whole ?
Options: a ) 500 % , b ) 600 % , c ) 800 % , d ) 1100 % , e ) 1200 %
Rationale: say initially population was 100 . what is 200 % of 100 ? it is 200 / 100 * 100 = 200 . an increase of 200 % means the new population became 100 + 200 = 300 what is 300 % of 300 ? it is 300 / 100 * 300 = 900 an increase of 300 % means the new population now is 300 + 900 = 1200 so from 100 , the population increased to 1200 i . e . an increase of 1100 . 1100 is what percent of 100 ? 1100 = x / 100 * 100 i . e . it is 1100 % d
Answer: d
Python program:
a = 300 / 100
b = 100 * a
c = 300 / 100
d = b * c
e = 300 / 100
f = 100 * e
g = d + f 
h = g - 100
Problem: at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 60 . if the restaurant serves 120 customers today , raising the average to 70 customers per day , what is the value of x ?
Options: a ) 2 , b ) 5 , c ) 9 , d ) 15 , e ) 30
Rationale: "withoutusing the formula , we can see that today the restaurant served 50 customers above the average . the total amount above the average must equal total amount below the average . this additional 50 customers must offset the “ deficit ” below the average of 70 created on the x days the restaurant served only 60 customers per day . 50 / 10 = 5 days . choice ( a ) . withthe formula , we can set up the following : 70 = ( 60 x + 120 ) / ( x + 1 ) 70 x + 70 = 60 x + 120 10 x = 50 x = 5 answer choice ( b )"
Answer: b
Python program:
a = 120 - 70
b = 70 - 60
c = a / b
d = 120 - 100
e = d / 100
f = c - e
Problem: 100 students appeared in 2 tests . 60 students passed 1 st test . 40 students passed in the 2 nd test . 20 students passed in both 1 and 2 tests . what is the probability of the students who failed in both tests ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: 20 student passed both two test 40 student passed only 1 st test 20 student passed only 2 nd test so 100 - ( 20 + 40 + 20 ) = 20 student failed in both sub so ans is 20 % answer : c
Answer: c
Python program:
a = 60 + 40 
b = a - 20
c = 100 - b
Problem: how many 3 - digit even numbers are possible such that if one of the digits is 5 , the next / succeeding digit to it should be 6
Options: a ) 5 , b ) 305 , c ) 365 , d ) 405 , e ) 495
Rationale: 560 , 562 , 564 , 566 , and 568 , so total 5 . hence option a .
Answer: a
Python program:
a = 3 + 6 
b = a + 6
Problem: there has been successive increases of 30 % and then 20 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 20 % , b ) 24 % , c ) 28 % , d ) 32 % , e ) 36 %
Rationale: "let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.2 * 1.3 * p = x * p y = x / ( 1.2 * 1.3 ) which is about 0.64 x which is a decrease of about 36 % . the answer is e ."
Answer: e
Python program:
a = 100 + 30 
b = 100 + 30 
c = b * 20
d = c / 100
e = a + d 
f = 100 / e
g = 1 - f
h = g * 100
Problem: a train speeds past a pole in 50 seconds and a platform 500 m long in 100 seconds . its length is :
Options: a ) 550 m . , b ) 300 m . , c ) 600 m . , d ) 400 m . , e ) 500 m .
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 50 = > y = x / 50 x + 500 / 100 = x / 50 x = 500 m . answer : option e"
Answer: e
Python program:
a = 2 - 1
b = 500 * a
Problem: if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 24 - m ) then m = ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "2 m = 24 - m 3 m = 24 m = 8 the answer is b ."
Answer: b
Python program:
a = 2 + 1 
b = 24 / a
Problem: a seller of used cars has 16 cars to sell and each of his clients selected 2 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 24
Rationale: ifno caris selected more than once then the number of clients = 16 / 2 = 8 but since every car is being selected three times so no . of clients must be thrice as well = 8 * 3 = 24 answer : option e
Answer: e
Python program:
a = 16 / 2
b = a * 3
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 ) 76 , c ) 98 , d ) 27 , e ) 24
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
Problem: the smallest fraction , which each of 6 / 7 , 5 / 14 , 10 / 21 will divide exactly is ?
Options: a ) 30 / 7 , b ) 30 / 9 , c ) 30 / 2 , d ) 30 / 3 , e ) 30 / 6
Rationale: "required fraction = l . c . m of 6 / 7 , 5 / 14 , 10 / 21 = ( l . c . m of 6 , 5 , 10 ) / ( h . c . f of 7 , 14 , 21 ) = 30 / 7 answer : a"
Answer: a
Python program:
a = 6 * 5
b = a / 7
Problem: a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 40 % lemonade syrup ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.14 , d ) 2.34 , e ) 2.64
Rationale: "let the total solution is 150 l with 80 l water & 70 l syrup . to make 40 % syrup solution , the result solution must have 90 l syrup and 60 l syrup . therefore we are taking 10 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 10 l syrup in 21.4 l solution we started by multiplying 10 now to get to the result we need to divide by 10 = > amount of solution to be replaced with water = ( 21.4 / 10 ) = 2.14 . correct option : c"
Answer: c
Python program:
a = 8 + 7 
b = 7 / a
c = 2 + 3 
d = 2 / c
e = b - d
f = 8 + 7 
g = 7 / f
h = e / g
i = 8 + 7 
j = h * i
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 640 is required to paint the floor at the rate of rs . 5 per sq m , then what would be the length of the floor ?
Options: a ) 19.6 m . , b ) 20.0 m . , c ) 19.3 m . , d ) 18.5 m . , e ) 18.9 m .
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 3 b = 3 b area of the floor = 640 / 5 = 128 sq m l b = 128 i . e . , l * l / 3 = 128 l 2 = 384 = > l = 19.6 m . answer : a"
Answer: a
Python program:
a = 640 / 5
b = a / 3
c = math.sqrt(b)
d = c * 3
Problem: a reduction of 15 % in the price of wheat enables a house wife to obtain 3 kgs more for rs . 500 , what is the reduced price for kg ?
Options: a ) rs . 10 , b ) rs . 15 , c ) rs . 20 , d ) rs . 25 , e ) rs . 30
Rationale: explanation : 500 * ( 15 / 100 ) = 75 - - - - 3 ? - - - - 1 = > rs . 25 answer : d
Answer: d
Python program:
a = 100 - 15
b = a / 100
c = b * 500
d = 500 - c
e = d / 3
Problem: in a certain corporation , there are 300 male employees and 150 female employees . it is known that 20 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 7 / 15 , b ) 3 / 10 , c ) 3 / 5 , d ) 2 / 5 , e ) 3 / 4
Rationale: "p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.2 * 300 / 450 = 60 / 450 = 2 / 15 the sum of the probabilities is 7 / 15 the answer is a ."
Answer: a
Python program:
a = 20 * 20
b = 40 / a
c = 1 - b
d = c * 150
e = d / 450
f = 20 * 20
g = 20 / f
h = g * 300
i = 20 * 20
j = 40 / i
k = j * 150
l = h + k 
m = l / 450
n = e + m
Problem: the ration of the father ’ s age to his son ’ s age is 7 : 3 . the product of their ages is 756 . the ratio of their ages after 6 years will be :
Options: a ) 5 : 2 , b ) 2 : 1 , c ) 11 : 7 , d ) 13 : 9 , e ) none of these
Rationale: solution let the present ages of the father and son be 7 x and 3 x years respectively . then , 7 x 3 x = 756 ⇔ 21 x 2 = 756 ⇔ x 2 = 36 ⇔ x = 6 . ∴ required ratio = ( 7 x + 6 ) : ( 3 x + 6 ) = 48 : 24 = 2 : 1 . answer b
Answer: b
Python program:
a = 7 * 3
b = 756 / a
c = math.sqrt(b)
d = 7 * c
e = d + 6 
f = 7 * 3
g = 756 / f
h = math.sqrt(g)
i = 3 * h
j = i + 6 
k = e / j
Problem: at a certain university , 68 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?
Options: a ) 25 , b ) 37.5 , c ) 55 , d ) 62.5 , e ) 75
Rationale: total women = 68 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 22 % but question wants to know the percent of men that are tenured 22 % / 40 % = 55 % c
Answer: c
Python program:
a = 100 - 68
b = 90 - 68
c = a + b
Problem: how many times are the hands of a clock at right angles in a day ?
Options: a ) 42 , b ) 44 , c ) 49 , d ) 41 , e ) 47
Rationale: in 12 hours , they are at right angles 22 times . = = > in 24 hours , they are at right angles 44 times . answer is b .
Answer: b
Python program:
a = 12 - 1
b = a * 2
c = b * 2
Problem: a cyclist traveled for two days . on the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day . if during the two days she traveled a total of 240 miles and spent a total of 12 hours traveling , what was her average speed on the second day ?
Options: a ) 5 mph , b ) 10 mph , c ) 20 mph , d ) 30 mph , e ) 40 mph
Rationale: solution : d = 280 mi t = 12 hrs đ â y 1 time = t 1 d â y 2 time = t 2 t 2 - t 1 = 4 hrs - - - - - ( i ) t 1 + t 2 = 12 hrs - - - - - ( ii ) adding i and ii , t 2 = 8 hrs and t 1 = 4 hrs d à y 1 rate = r 1 d â y 2 rate = r 2 r 1 - r 2 = 10 mph í . ẹ . r 1 = 10 + r 2 280 = 8 r 2 + 4 r 1 í . ẹ . 280 = 8 r 2 + 4 ( 10 + r 2 ) í . ẹ . r 2 = 20 mph answer : b
Answer: b
Python program:
a = 12 - 4
b = a / 2
c = b * 10
d = 240 - c
e = 12 - 4
f = e / 2
g = 12 - 4
h = g / 2
i = h + 4 
j = f + i 
k = d / j
Problem: a is twice as good as workman as b and together they finish a piece of work in 18 days . in how many days will b alone finish the work .
Options: a ) 27 days , b ) 54 days , c ) 56 days , d ) 68 days , e ) none of these
Rationale: explanation : as per question , a do twice the work as done by b . so a : b = 2 : 1 also ( a + b ) one day work = 1 / 18 to get days in which b will finish the work , lets calculate work done by b in 1 day = = ( 118 ∗ 13 ) = 154 [ please note we multiplied by 1 / 3 as per b share and total of ra ɵ o is 1 / 3 ] so b will finish the work in 54 days answer : b
Answer: b
Python program:
a = 18 * 3
Problem: in the xy - coordinate system , what is the slope of the line that goes through the origin and is equidistant from the two points p = ( 4 , 6 ) and q = ( 6 , 2 ) ?
Options: a ) 0.8 , b ) 1.0 , c ) 1.2 , d ) 1.4 , e ) 1.6
Rationale: first , get the middle coordinate between ( 46 ) and ( 62 ) . x = 4 + ( 6 - 4 ) / 2 = 5 y = 2 + ( 6 - 2 ) / 2 = 4 second , get the slope of ( 54 ) and ( 00 ) . m = 4 - 0 / 5 - 0 = 4 / 5 = 0.8 answer : a
Answer: a
Python program:
a = 6 + 2 
b = a / 2
c = 4 + 6 
d = c / 2
e = b / d
Problem: an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 15 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 80.00
Rationale: "without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 23 % , thus he must pay slightly more than $ 77 . answer : e ."
Answer: e
Python program:
a = 15 * 8
b = a / 100
c = 10 - b
d = c * 10
Problem: the perimeter of a rectangle is 60 mete ( 132 ) 7 × ( 132 ) ? = ( 132 ) 11.5 .
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "7 + x = 11.5 x = 11.5 - 7 x = 4.5 answer : d"
Answer: d
Python program:
a = 132 + 7 
b = a * 7
c = 60 / b
d = c ** 7
e = d * 132
f = e * 7
Problem: the youngest of 4 children has siblings who are 3 , 5 , and 8 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 21 , what is the age of the youngest sibling ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 21 , e ) 22
Rationale: "total age of the 4 sibling is 21 x 4 = 84 years . . we already have the total age of all the children is 4 y + 16 so , 4 y + 16 = 84 or , 4 y = 68 or , y = 17 so , age of the youngest child is 17 years . answer : a"
Answer: a
Python program:
a = 4 * 21
b = 4 + 5 
c = b + 8 
d = a - c
e = d / 4
Problem: a can do a piece of work in 15 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 2 days and b leaves after 4 days from the beginning . how long will work lost ?
Options: a ) 15 , b ) 10 , c ) 12 , d ) 11 , e ) 13
Rationale: "2 / 15 + 4 / 15 + x / 20 = 1 x = 12 answer : c"
Answer: c
Python program:
a = 4 - 2
b = 1/(15)
c = 1/(20)
d = b + c 
e = a * d
f = 1/(20)
g = 1/(15)
h = 1/(15)
i = g + h 
j = f + i 
k = j * 2
l = e + k 
m = 1 - l
n = 1/(15)
o = m / n
p = o + 4
Problem: the speed of a boat in still water is 36 kmph . what is the speed of the stream if the boat can cover 80 km downstream or 40 km upstream in the same time ?
Options: a ) 10 kmph , b ) 14 kmph , c ) 12 kmph , d ) 16 kmph , e ) 15 kmph
Rationale: "x = the speed of the stream ( 36 + x ) / ( 36 - x ) = 2 / 1 36 + x = 72 - 2 x 3 x = 36 x = 12 km / hour if the speed of the stream is 12 km / hour , then the ' downstream ' speed of the boat is 36 + 12 = 48 km / hour and the ' upstream ' speed of the boat is 36 - 12 = 24 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 48 = 96 km downstream and 2 x 24 = 48 km / hour upstream . answer : c"
Answer: c
Python program:
a = 1 + 2 
b = 36 / a
Problem: a man buys a cycle for rs . 1800 and sells it at a loss of 10 % . what is the selling price of the cycle ?
Options: a ) 1410 , b ) 1620 , c ) 1430 , d ) 1440 , e ) 1540
Rationale: "s . p . = 90 % of rs . 1800 = 90 / 100 x 1800 = rs . 1620 answer : b"
Answer: b
Python program:
a = 100 - 10
b = a * 1800
c = b / 100
Problem: if n divided by 11 has a remainder of 1 , what is the remainder when 5 times n is divided by 11 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 9 , e ) 5
Rationale: "as per question = > n = 11 p + 1 for some integer p hence 5 n = > 55 q + 5 = > remainder = > 5 for some integer q hence e"
Answer: e
Python program:
a = 5 * 1
Problem: an artist wishes to paint a circular region on a square poster that is 3.4 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ?
Options: a ) 1 / pi
b ) sqrt ( 2 / pi )
c ) 1
d ) 2 / sqrt ( pi )
e ) sqrt ( 5.78 / pi )
Rationale: area of the poster is 3.4 x 3.4 = 11.56 1 / 2 the area = 5.78 pi * r ^ 2 = 5.78 r ^ 2 = 5.78 / pi r = sqrt ( 5.78 / pi ) answer ( e )
Answer: e
Python program:
a = square_area / (
b = a / 2
c = math.sqrt(b)
Problem: the value of ( 34.31 * 0.473 * 1.567 ) / ( 0.0673 * 23.5 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.05 , d ) 2.12 , e ) 2.35
Rationale: "( 34.31 * 0.473 * 1.567 ) / ( 0.0673 * 23.5 * 7.57 ) = 25.4303 / 11.972 = 2.12 answer : d"
Answer: d
Python program:
a = 34 * 31
b = a * 1
c = 7 * 57
d = c * 0
e = b / d
f = e / 10
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 47 , then how old is b ?
Options: a ) 17 years , b ) 19 years , c ) 18 years , d ) 10 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 47 5 x = 45 = > x = 9 hence , b ' s age = 2 x = 18 years . answer : c"
Answer: c
Python program:
a = 47 - 2
b = a * 2
c = 4 + 1 
d = b / c
Problem: find the value of 658217 x 99999 = m ?
Options: a ) 65842158943 , b ) 65839570421 , c ) 65821141683 , d ) 66821785904 , e ) 65821041783
Rationale: "658217 x 99999 = 658217 x ( 100000 - 1 ) = 658217 x 100000 - 658217 x 1 = 65821700000 - 658217 = 65821041783 e"
Answer: e
Python program:
a = 99999 - 4
b = a * 658217
Problem: a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1251 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 139
Rationale: "let the required number be x . then , 43 x – 34 x = 1251 or 9 x = 1251 or x = 139 . required number = 139 . answer : e"
Answer: e
Python program:
a = 43 - 34
b = 1251 / a
Problem: calculate the largest 6 digit number which is exactly divisible by 55 ?
Options: a ) 999955 , b ) 999900 , c ) 999845 , d ) 999790 , e ) 999735
Rationale: "largest 4 digit number is 999999 after doing 999999 ÷ 55 we get remainder 44 hence largest 4 digit number exactly divisible by 88 = 999999 - 44 = 999955 a"
Answer: a
Python program:
a = 100 + 2 
b = a * 55
Problem: 10 years ago , the age of peter was one - third the age of jacob at that time . the present age of jacob is 12 years more than the present age of peter . find the present age of peter ?
Options: a ) 15 , b ) 11 , c ) 18 , d ) 16 , e ) 20
Rationale: d 16 let the present ages of peter and jacob be ' a ' and ' b ' respectively . a - 10 = 1 / 3 ( b - 10 ) - - - ( 1 ) b = a + 12 substituting b = a + 12 in first equation , a - 10 = 1 / 3 ( a + 2 ) = > 3 a - 30 = a + 2 = > 2 a = 32 = > a = 16 .
Answer: d
Python program:
a = 12 / 2
b = 10 + a
Problem: at a supermarket , john spent 1 / 2 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 8 on candy , how much did john spend at the supermarket ?
Options: a ) $ 60 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 180
Rationale: let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 2 of his money on fresh fruits and vegetables , or ( 1 / 2 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 8 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 2 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 8 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 240 = 30 t 28 t + 240 = 30 t 240 = 2 t t = 120 john spent $ 90 at the supermarket . answer : d
Answer: d
Python program:
a = 1 / 10
b = 1 / 3
c = a + b 
d = 1 / 2
e = c + d 
f = 1 - e
g = 8 / f
Problem: tough and tricky questions : exponents . if 5 ^ ( x + 1 ) * 4 ^ ( y - 1 ) = 25 ^ x * 64 ^ y , then x + y =
Options: a ) 3 / 2 , b ) - 1 / 2 , c ) - 1 , d ) 1 / 2 , e ) 2 / 3
Rationale: here is my solution . 5 ^ ( x + 1 ) * 4 ^ ( y - 1 ) = 25 ^ x * 64 ^ y here rhs 25 ^ x * 64 ^ y = 5 ^ ( 2 x ) * 4 ^ ( 3 y ) equating powers on both sides - - > x + 1 = 2 x , thus x = 1 and 2 y - 1 = 3 y giving y = - 1 / 2 so , x + y = 1 / 2 option : d
Answer: d
Python program:
a = math.gcd(64, 25)
b = a / 2
Problem: what no should be subtracted from 92555 to make it a perfect square ?
Options: a ) 128
b ) 158
c ) 178
d ) 139
e ) 140
Rationale: root 92555 = 304.228 and 304 ^ 2 = 92416 92555 - 92416 = 139 should be subtracted from 92555 to make it a perfect square answer : d
Answer: d
Python program:
a = math.sqrt(92555)
b = math.floor(a)
c = math.sqrt(92555)
d = math.floor(c)
e = b * d
f = 92555 - e
Problem: the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 6 . the true discount is
Options: a ) rs . 72 , b ) rs . 36 , c ) rs . 54 , d ) rs . 50 , e ) none
Rationale: "solution t . d = [ b . g x 100 / r x t ] = rs . ( 6 x 100 / 12 x 1 ) = rs . 50 . answer d"
Answer: d
Python program:
a = 12 / 100
b = 6 / a