mathewhe/aqua_rat huggingface dataset:
Question: How many positive integers Q less than 10,000 are such that the product of their digits is 210?
(A) 24
(B) 30
(C) 48
(D) 54
(E) 72
Rationale: 210 is the answer when 2, 3, 5 and 7 are multiplied. 210 can also be arrive using 5,6 and 7 and 1, 5, 6 and 7.
So sum of arrangements of 2357, 567 and 1567. This translates to 4! +3! + 4!, this equals to 24 + 6 + 24 = 54, D is the answer.
Answer: (D) 54
Question: A 50 ml after-shave lotion at 30% alcohol is mixed with 30 ml of pure water. What is the percentage of alcohol in the new solution?
(A) 16.75%
(B) 17.75%
(C) 18.75%
(D) 19.75%
(E) None of these
Rationale: The amount of the final mixture is given by
50 ml + 30 ml = 80 ml
The amount of alcohol is equal to the amount of alcohol in pure water ( which is 0) plus the amount of alcohol in the 30% solution. Let x be the percentage of alcohol in the final solution. Hence
0 + 30% 50 ml = x (80)
Solve for x
x = 0.1817 = 18.75%
Answer C
Answer: (C) 18.75%
Question: We have 5 people and 3 chairs. In how many ways chairs can be occupy?
(A) 58
(B) 42
(C) 60
(D) 72
(E) 80
Rationale: no. of ways they can be occupy = 5*4*3 = 60
Answer is C
Answer: (C) 60
Question: Find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 760.
(A) 120 ,122 , 124 ,126
(B) 120 ,122 , 124 ,128
(C) 120 ,121 , 122 ,123
(D) 123 ,125 , 127 ,129
(E) None of these
Rationale: Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two
x + (x + 2)
twice the sum of the last two is written as
2 ((x + 4) + (x + 6)) = 4 x + 20
sum of the first two added to twice the sum of the last two is equal to 760 is written as
x + (x + 2) + 4 x + 20 = 760
Solve for x and find all four numbers
x = 123 , x + 2 = 125 , x + 4 = 127 , x + 6 = 129
Answer D
Answer: (D) 123 ,125 , 127 ,129
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 25,000 is made?
(A) Rs. 1,10,000
(B) Rs. 1,20,000
(C) Rs. 1,24,000
(D) Rs. 1,21,000
(E) None of these
Rationale: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 25,000 is made = 96,000 + 25,000 = Rs. 1,21,000
ANSWER:D
Answer: (D) Rs. 1,21,000
Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
(A) 3
(B) 4
(C) 9
(D) 11
(E) None of these
Rationale: Answer: Option B
Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
9(x - y) = 36
x - y = 4.
Answer: (B) 4
Question: A factory has a fixed cost of $44,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
(A) 9,000
(B) 14,000
(C) 17,600
(D) 22,500
(E) 27,000
Rationale: selling price - Cost price = 2.5 so per unit profit =2.5
cost to recover =44000
no of items required = 44000/2.5 = 17600
Answer: C
Answer: (C) 17,600
Question: What is the twenty-fifth decimal to the right in the fraction 10/11?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 10/11 = 0.9090909090...
The odd-numbered decimal places are 9.
The answer is E.
Answer: (E) 9
Question: Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?
(A) 67.0 km /hr
(B) 67.2 km /hr
(C) 69.0 km /hr
(D) 69.2 km /hr
(E) None
Rationale: Solution
Required average speed	=(2xy / x+y)km/hr
= 2 x 84 x 56 /(84 + 56)
= (2 x 84 x 85 /140)
= 67.2 km/hr.
Answer B
Answer: (B) 67.2 km /hr
Question: If the numerator of a fraction be increased by 20% and its denominator be diminished by 10%, the value of the fraction is 20/21. Find the original fraction ?
(A) 1/2
(B) 3/5
(C) 4/7
(D) 5/7
(E) 7/9
Rationale: Let the original fraction be x/y
Then, 120% of x/90% of y = 20/21
120x/90y = 20/21
x/y = 5/7
Answer is D
Answer: (D) 5/7
Question: The average of runs of a cricket player of 10 innings was 42. How many runs must he make in his next innings so as to increase his average of runs by 4?
(A) 87
(B) 86
(C) 28
(D) 76
(E) 80
Rationale: Average after 11 innings = 46
Required number of runs
= (46* 11) - (42* 10) = 506 - 420
= 86.
Answer: B
Answer: (B) 86
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either red or green?
(A) 53/105
(B) 43/105
(C) 42/105
(D) 32/105
(E) 46/105
Rationale: given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are red = 4Câ‚‚/Â¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 3/21
Probability that both are green = 6Câ‚‚/Â¹âµCâ‚‚ = (2 * 1)/(15 * 14) = 1/105
Probability that one red and other is green = (4Câ‚ * 6Câ‚)/Â¹âµCâ‚‚ = (2 * 3 * 2)/(15 * 14) = 27/105
Required probability = 3/21 + 1/105 + 27/105
= 43/105
Answer:B
Answer: (B) 43/105
Question: The area of one square is x^2 + 12x + 36 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 64, what is the value of x?
(A) 0
(B) 4.3
(C) 2.5
(D) 4.67
(E) 10
Rationale: spotting the pattern of equations both are in form of (X+C)^2 so
A1= (x+6)^2A2= (2x-3)^2
L1= x+6 L2= 2x-3
P1 = 4( x+6)P2=4(2x-3)
P1+P2=64
4( x+6) +4(2x-3)=64..............> X=4.3
Answer: B
Answer: (B) 4.3
Question: By how much is 70% of 120 greater than 35% of 200.
(A) 15
(B) 14
(C) 13
(D) 16
(E) 17
Rationale: (70/100) * 120 â€“ (35/100) * 200
84 - 70 = 14
Answer: B
Answer: (B) 14
Question: Evaluate: |6 - 8(3 - 12)| - |5 - 11| = ?
(A) 40
(B) 50
(C) 72
(D) 70
(E) 80
Rationale: According to order of operations, inner brackets first. Hence
|6 - 8(3 - 12)| - |5 - 11| = |6 - 8*(-9)| - |5 - 11|
According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence
= |6 + 72| - |5 - 11|
= |78| - |-6|
= 78 - 6 = 72
correct answer C)72
Answer: (C) 72
Question: A vendor purchases binder clips at 12 for rs60.How many clips should he sell for rs60 to earn a profit of 20%?
(A) 5
(B) 8
(C) 6
(D) 10
(E) 12
Rationale: Profit of 20% means he should sell the 12 clips for 72 Rs
so for 60 Rs he should sell 10 clips
ANSWER:D
Answer: (D) 10
Question: Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is X?
(A) 50X/200
(B) 50+3X/100
(C) 50+X/40
(D) 100+X/50
(E) 100+3X/100
Rationale: 50+X/40=C
Answer: (C) 50+X/40
Question: 35 percent of the women in a college class are science majors, and the non-science majors make up 70% of the class. What percentage of the men are non-science majors if 40% of the class are men?
(A) 37.5
(B) 27.5
(C) 77.5
(D) 87.5
(E) 93.5
Rationale: 3.5/k + 2/m = 6/t
Assuming total # is 100 :
[Science - Women] will have -> 0.35 * 60 = 21
[Non-Science-Women] will have -> 39
[Science-Men] will have = 30-21 = 9
[Non-Science-men] will have - 31
S0 31/40 * 100 = 77.5%
Answer -C
Answer: (C) 77.5
Question: During a particular equestrian competition, the rider and his horse have 5 fences to jump. If the rider falls off during a jump, the rider is disqualified. The probability of the rider falling off on a jump is 12/35. What is the least number of fences that the rider can jump before the probability of falling off at least once is more than 50%.
(A) 1
(B) 5
(C) 4
(D) 2
(E) 3
Rationale: Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A ∩ B) = P(A) P(B)
The probability that the rider falls at least once in 2 jumps is 1- (23/35)^2 = 1 - 529/1,225 = 696/1,225 < 50%.
The probability that the rider falls at least once in 3 jumps is 1- (23/35)^3 = 1 - 12,167/42,875 = 30,708/42,875 > 50%.
Answer: E
Answer: (E) 3
Question: Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/5, 1/2 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?
(A) 11/8
(B) 3/80
(C) 9/64
(D) 5/64
(E) 3/64
Rationale: P(Xavier will solve)=1/5
P(Yvonne will solve)=1/2
P(Zelda will NOT solve) = 1- 5/8 = 3/8.
Now, we need to multiply all this Ps to find an answer:
p= (1/5)*(1/2)*(3/8) = 3/80.
Ans. B.
Answer: (B) 3/80
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
(A) 39:40
(B) 39:48
(C) 39:43
(D) 39:46
(E) 39:42
Rationale: 3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer: A
Answer: (A) 39:40
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 40, the dividend is:
(A) A)5322
(B) B)5330
(C) C)4040
(D) D)5340
(E) E)5342
Rationale: Divisor = (5 * 40) = 200
= 10 * Quotient = Divisor
=> Quotient = 200/10 = 20
Dividend = (Divisor * Quotient) + Remainder
Dividend = (200 * 20) + 40 = 4040.
C
Answer: (C) C)4040
Question: How many of the positive factors of 36 , 84 and how many common factors are there in numbers?
(A) 2
(B) 4
(C) 3
(D) 5
(E) 6
Rationale: factors of 36 - 1, 2, 3, 4, 6, 9, 12, 18, 36
factors of 84 - 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Comparing both, we have six common factors of 36 and 84- 1,2,3,4,6,12,
Answer(E)
Answer: (E) 6
Question: A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?
(A) 120 m
(B) 200 m
(C) 324 m
(D) Cannot be determined
(E) None of these
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12 = 200 m
ANSWER:B
Answer: (B) 200 m
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
(A) 1
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.Answer: B
Answer: (B) 5
Question: Which one of the following is not a prime number?
(A) 88
(B) 60
(C) 73
(D) 91
(E) 82
Rationale: D
91
91 is divisible by 7. So, it is not a prime number.
Answer: (D) 91
Question: The average of non-zero number and its square is 5 times the number. The number is?
(A) 9
(B) 8
(C) 6
(D) 4
(E) 3
Rationale: Let the number be x. Then,
(x + x2)/2 = 5x => x2 - 9x = 0
=> x(x - 9) = 0
=> x = 0 or x = 9
So, the number is 9.
Answer:A
Answer: (A) 9
Question: Out of 7 constants and 4 vowels how many words of 3 consonants and 2 vowels can be formed?
(A) 210
(B) 25000
(C) 25200
(D) 250
(E) 20000
Rationale: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
= 7C3 * 4C2
= 210
Number of groups each having 3 consonants and 2 vowels = 210
Each group contains 5 letters
Number of ways of arranging 5 letters among themselves
= 5! = (5 * 4 * 3 * 2 * 1)
= 210
Required number of words = (210 * 210)
= 25200
ANSWER C 25200
Answer: (C) 25200
Question: Pradeep has to obtain 40% of the total marks to pass. He got 200 marks and failed by 20 marks. The maximum marks are
(A) 300
(B) 600
(C) 550
(D) 1000
(E) 900
Rationale: Explanation :
Let their maximum marks be x.
Then, 40% of x = 200 + 20
=>40/100x= 220
x = (22000/40)
x= 550.
Answer : C
Answer: (C) 550
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
(A) 87 sec
(B) 89 sec
(C) 17 sec
(D) 18 sec
(E) 97 sec
Rationale: Speed = 240/24
= 10 m/sec.
Required time
= (240 + 650)/10
= 89 sec.
Answer:B
Answer: (B) 89 sec
Question: Consider a right triangle YBC with length of sides being x,y and z where y represents the hypotenuse , Which of these represent the radius of the circle which is inscribed in triangle YBC
(A) [A] x+y+z/3
(B) [B] x-y+z/3
(C) [C] x-y+z/2
(D) [D] (x^2 + y^2 + z^2)/3
(E) [E] cannot be determined
Rationale: Radius of a circle inscribed in the right triangle YBC r = (x + z - y)/2 where y is the hypotenuse and x and y are other two sides.
Answer: C
Answer: (C) [C] x-y+z/2
Question: Ram and Shyam have a cube each. Ram paints four faces of cube with red color and rest with blue color. Ram asks Shyam to paint his cube as well with some sides red and some side blue. They now start rolling the cubes simultaneously. After doing this for very long Ram observes that probability of both cubes coming up with same color is 1/3. How many faces of his cube did Shyam paint red ?
(A) 0
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Explanation :
Let Shyam paints n faces of the cube red. So faces painted blue = (6-n)
Probability that both show up same color is: (probability both show red) + (probability both show blue)
= 4/6 * n/6 + 2/6 * (6-n)/6
= (2n + 6)/18
But as given, (2n + 6)/18 = 1/3 => n = 0
So Shyam hasn't painted any of the face with red color.
Answer : A
Answer: (A) 0
Question: CP of 2 buffaloes are $30,000. By selling 1 at a loss of 15% and other at a profit of 19%, he foundthat SP of both buffaloes is the same. Find the CP of each?
(A) $9,500
(B) $10,500
(C) $11,500
(D) $12,000
(E) $12,500
Rationale: Let the C.P of 1st buffalo = x
∴C.P of 2nd buffalo = 30,000 - x
S.P of 1st buffalo = ( 100 - loss% )
------------------- x C.P
100
S.P = 100 - 15x
-----------= 85x/ 100
100
S.P of 2nd buffalo = ( 100 - Profit%)
--------------------- x C.P
100
S.P = (100 + 19)(30,000- x) 119(30,000 -x)
-------------------- = ----------------
100 100
S.P of 1st buffalo = S.P of 2nd buffalo
85x/ 100 = 119 ( 30,000 - x)/ 100
⇒ 85x = 119(30,000 - x)
⇒ 85x = 3,570,000 - 119x
⇒ 85x + 119 x = 3,570,000
⇒ 204x = 3,570,000
⇒ x = 3,570,000 / 204
⇒ x = $17,500
C.P of 1st buffalo = $17,500
C.P of 2nd buffalo = 30,000 - 17,500 = $12,500
E
Answer: (E) $12,500
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 12m/h. what is the speedof the person while he was going to his office?
(A) 8km/h
(B) 9km/h
(C) 10km/h
(D) 11km/h
(E) 13km/h
Rationale: u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=12
\inline \Rightarrow 1.5k = 12
\inline \Rightarrow k=8km/h
A
Answer: (A) 8km/h
Question: An unbiased die is tossed.Find the probability of getting a multiple of 3.
(A) 1/3
(B) 1/9
(C) 1/2
(D) 7/3
(E) 1/0
Rationale: Explanation:
Here S = {1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
Then, E = {3,6}
P(E) = n(E)/n(S) = 2/6 = 1/3
Answer: A) 1/3
Answer: (A) 1/3
Question: 1234+123+12+X=1221.Find the value of X.
(A) 10
(B) 148
(C) 12
(D) 13
(E) 189
Rationale: x=1234+123+12-1221
x=148
CORRECT ANSWER : B
Answer: (B) 148
Question: One of the below words are odd one out. can you identify it?
first second third forth fifth sixth seventh eighth nine ten eleven twelve thirteen fourteen fifteen sixteen
(A) forth. It should be spelled as fourth
(B) 4
(C) 14
(D) 15
(E) 16
Rationale: Correct Answer : A
forth. It should be spelled as fourth
Answer: (A) forth. It should be spelled as fourth
Question: Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many hours T would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?
(A)  22 hours
(B)  30 hours
(C)  44 hours
(D)  60 hours
(E)  It cannot be determined from the information above.
Rationale: Say the rates of machines A, B and C are a, b, and c, respectively.
Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4;
Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11.
Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the T job in 44 hours.
Answer: C.
Answer: (C)  44 hours
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
(A) 287
(B) 800
(C) 277
(D) 299
(E) 211
Rationale: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200
= 800 cm.
Answer:B
Answer: (B) 800
Question: Three cars driven by Mike, Scott and Jenny start driving around a circular race course of length 540m from the same point simultaneously in the same direction at speeds of 9 m/s, 15 m/s and 27 m/s respectively. When will they meet for the first time after they started moving?
(A) 180 seconds
(B) 45 seconds
(C) 90 seconds
(D) 60 seconds
(E) 270 seconds
Rationale: If they all meet after T seconds, it means they covered the distances 9T, 15T, and 27T respectively.
Since they all arrive to the same spot, it means that the differences taken pairwise between the distances must be positive integer multiples of the length of the track, which is 540m. So, 6T, 12T, and 18T must all be multiples of 540. 6T multiple of 540 means T multiple of 90. The smallest T with this property is 90 and is on the list of answers.
Answer C.
Answer: (C) 90 seconds
Question: If the volume of the cube is 729, then the surface area of the cube will be
(A) 486
(B) 255
(C) 2866
(D) 265
(E) 872
Rationale: Explanation:
\inline \fn_jvn a^3=729; a=9
surface area= (6 x 9 x 9) = 486\inline \fn_jvn cm^2
Answer: A) 486 sq.cm
Answer: (A) 486
Question: Ravi can do a piece of work in 24 days while Prakash can do it in 40 days. In how many days will they finish it together?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 10
Rationale: 1/24 + 1/40 = 1/15
15 days
Answer: A
Answer: (A) 15
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph, find his average speed for the total journey ?
(A) 3.1 kmph
(B) 5 kmph
(C) 6 kmph
(D) 4 kmph
(E) 7 kmph
Rationale: Explanation:
Speed of Man = 4.5 kmph
Speed of stream = 2.5 kmph
Speed in DownStream = 7 kmph
Speed in UpStream = 2 kmph
Average Speed = (2 x 7 x 2)/9 = 3.1 kmph.
Answer: A
Answer: (A) 3.1 kmph
Question: The sum of two numbers is 16 and their difference is 4. Find their product.
(A) 104
(B) 114
(C) 315
(D) 325
(E) 60
Rationale: Let the numbers be x and y.
Then x + y = 16 and x - y = 4
x = 10; y = 6
xy = 10 * 6 = 60
ANSWER: E
Answer: (E) 60
Question: A driver covers a certain distance by car driving at 40 km/hr and returns back to the starting point riding on a scooter at 10 km/hr. What was the average speed for the whole journey?
(A) 12 km/h
(B) 14 km/h
(C) 16 km/h
(D) 18 km/h
(E) 20 km/h
Rationale: time 1 = d / 40
time 2 = d / 10
total time = d/40 + d/10 = d/8
average speed = total distance / total time = 2d / (d/8) = 16 km/h
The answer is C.
Answer: (C) 16 km/h
Question: At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 11. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 1 to 5. How many cooks does the restaurant have?
(A) 4
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: Originally there were 3k cooks and 11k waiters.
The new ratio is 1:5 which equals 3:15.
15k = 11k+12
k=3
There are 9 cooks.
The answer is C.
Answer: (C) 9
Question: A sum of money place at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself?
(A) 33
(B) 77
(C) 12
(D) 88
(E) 11
Rationale: 100 ---- 200 ---- 4
400 ---- 4
800 ---- 4
------
12 years
Answer: C
Answer: (C) 12
Question: How long does a train 150 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 14.1 sec
(B) 12.1 sec
(C) 16.1 sec
(D) 13.1 sec
(E) 12.15sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 150 + 132 = 282 m.
Required time = 282/20 = 14.1 sec.
Answer:A
Answer: (A) 14.1 sec
Question: The probability of rain showers in Barcelona on any given day is 0.6. What is the probability that it will rain on exactly one out of three straight days in Barcelona?
(A) 0.144
(B) 0.072
(C) 0.432
(D) 0.72
(E) 0.288
Rationale: IMO This is just for first day! It can rain on 2nd day or 3 rd day (and not rain on other days) in 3 consecutive days!
Hence,
0.6*0.4*0.4 + 0.4*0.6*0.4+ 0.4*0.4*0.6 = 0.288
Option - E
Answer: (E) 0.288
Question: How many days are there in x weeks x days ?
(A) 7x2
(B) 8x
(C) 14x
(D) 7
(E) 8
Rationale: Solution
x weeks x days = (7x+x) days = 8x days. Answer B
Answer: (B) 8x
Question: In year Y imported machine tools accounted for 25 percent of total machine - tool sales in the United States, and Japanese imports accounted for 50 percent of the sales of imported machine tools. If the total sales of machine tools imported Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
(A) 8X/1
(B) 13X/20
(C) 80/9X
(D) 20X/13
(E) 80X/9
Rationale: IMT = 0.25T
JI = 0.50 IMT
0.50 IMT = $x b
IMT = $x/(0.50) b
T = 4*IMT = 4x/0.50 = 4x*100/50 = 8x/1
Ans: "A"
Answer: (A) 8X/1
Question: The average height of 50 pupils in a class is 150 cm. Five of them whose height is 142 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is ?
(A) 287 cm
(B) 151 cm
(C) 151.4 cm
(D) 287 cm
(E) 297 cm
Rationale: Total height = 150 * 50 = 7500 cm.
New average = [7500 - 5 * 142 + 5 * 156 ] / 50
= 151.4 cm.
Answer:C
Answer: (C) 151.4 cm
Question: Juan is a gold medalist in athletics. In the month of May, if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
(A) 10x/y
(B) 11x/y
(C) 9x/y
(D) 12x/y
(E) 13x/y
Rationale: velocity=distance/time;
since he ran at same rate both d tyms,
y/10=x/t
so t=10x/y
ANSWER:A
Answer: (A) 10x/y
Question: The average weight of 29 students is 28 kg. By the admission of a new student, the average weight is reduced to 27.8 kg. The weight of the new student is
(A) 22 kg
(B) 21.6 kg
(C) 22.4 kg
(D) 21 kg
(E) None of these
Rationale: Exp . The total weight of 29 students = 29* 28
The total weight of 30 students = 30* 27.8
Weight of the new student = ( 30*27.8 – 29*28)
= 834 - 812 = 22
Answer:A
Answer: (A) 22 kg
Question: On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 4 cups of tea. Last week Mo drank a total of 42 cups of tea and hot chocolate together. If during that week Mo drank 14 more tea cups than hot chocolate cups, then how many rainy days were there last week?
(A) 0
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: T= the number of cups of tea
C= the number of cups of hot chocolate
T+C = 42 T-C=14 -> T= 28. C=14.
Mo drinks 4 cups of tea a day then number of days that are not rainy = 28/4= 7
So number of rainy days = 7-7 = 0
A is the answer.
Answer: (A) 0
Question: 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 2553, how much was it in the beginning?
(A) 2988
(B) 2776
(C) 4400
(D) 2871
(E) 3162
Rationale: X * (95/100) * (85/100) = 2553
X = 3162
Answer:E
Answer: (E) 3162
Question: Look at this series: 0.7, 2.1, ____, 18.9, 56.7, ... What number should fill the blank?
(A) 6.3
(B) 5.3
(C) 6.2
(D) 6.1
(E) 4.3
Rationale: This is a simple multiplication series. Each number is 3 times greater than the previous number.
Answer: A
Answer: (A) 6.3