mathewhe/aqua_rat huggingface dataset:
Question: A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is
(A) 28%
(B) 30%
(C) 32%
(D) 38%
(E) 40%
Rationale: Let original length = x and original breadth = y.
Decrease in area
= xy - 80 x x 90 y
100 100
= xy - 18 xy
25
= 7 xy.
25
Decrease % = 7 xy x 1 x 100 % = 28%.
25 xy
A)
Answer: (A) 28%
Question: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops.
(A) 6
(B) 6.5
(C) 7
(D) 7.5
(E) 5
Rationale: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 210-mile journey? Assume that the train makes no intermediate stops.
I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total)
Hour miles/hour Total miles
1 10 10
2 20 30
3 30 60
4 40 100
5 50 150
6 60 210
It takes a total of nine hours to cover the 210 mile distance.
ANSWER: A 6
Answer: (A) 6
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
(A) 27
(B) 29
(C) 24
(D) 28
(E) 12
Rationale: 2c = 1/4 + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
Answer: C
Answer: (C) 24
Question: find two integers, neither of which ends in a zero, and whose product is exactly 1,000,000
(A) 64 and 15,625
(B) 60 and 15,625
(C) 64 and 15,620
(D) 64 and 15,635
(E) 64 and 16,625
Rationale: 1,000,000=10^6
=10x10x10x10x10x10
=(2x5)x(2x5)x(2x5)x(2x5)x(2x5)x(2x5)
=(2^6)x(5^6)
= 64x15625
so the numbers are 64 and 15,625
ANSWER:A
Answer: (A) 64 and 15,625
Question: Three friends (Caleb, Jerry and Elvis) are employees of a company. Their respective salaries are in the ratio of 3 : 4 : 6. Jerry and Elvis's salaries together is Rs. 10000. By what percent is Elvis's salary than that of Sarah?
(A) 500%.
(B) 400%.
(C) 300%.
(D) 200%.
(E) 100%.
Rationale: Explanation:
Let the salaries be 3x, 4x and 6x respectively.
Then,4x + 6x = 10000 => x = 1000.
Caleb's salary = Rs. 3000, , Jerry's salary = Rs. 4000, and and Elvis's salary Rs. 6000.
Excess of Elvis's salary over Caleb's=[ (3000 /3000) x 100] = 100%.
Answer: E
Answer: (E) 100%.
Question: P is four times as fast as Q and working together, they can complete a work in 16 days. In how many days can Q alone complete the work?
(A) 20 days
(B) 15 days
(C) 16 days
(D) 25 days
(E) 18 days
Rationale: P = 4Q
P + Q = 4Q + Q = 5Q
These 5Q people can do the work in 16 days, which means Q can do the work in 80 days.
Hence, P can do the work in 20 days.
ANSWER:A
Answer: (A) 20 days
Question: A man's speed with the current is 8km/hr and the speed of the current is 20km/hr. The current's speed against the man is:
(A) 3 km/hr
(B) 4 km/hr
(C) 5 km/hr
(D) 7 km/hr
(E) 9 km/hr
Rationale: Man's rate in still water = (20 - 8) km/hr = 12 km/hr.
Current's rate against the current = (12 - 8) km/hr = 4 km/hr
B
Answer: (B) 4 km/hr
Question: If one-seventh of a number exceeds its eleventh part by 100 then the number is…
(A) 770
(B) 870
(C) 1825
(D) 1925
(E) 925
Rationale: let no be :x
1/7x-1/11x=100
4x/77=100
x=7700/4=1925
ANSWER:D
Answer: (D) 1925
Question: By selling an article at 80% of its marked price, a merchant makes a loss of 12%. What % profit will the merchant make if the article is sold at 95% of its marked price?
(A) 5% profit
(B) 1% loss
(C) 10% profit
(D) 5.5% profit
(E) 4.5% profit
Rationale: Explanatory Answer
Approach: Assume cost to be $100
Let the marked price be S and the cost price of the article be $100.
When the article is sold at 80% of its marked price, it is sold at 0.8S.
Selling the article at 0.8S results in a loss of 12% of the cost.
Therefore, the loss incurred when selling at 0.8S = 12% of 100 = $12.
Hence, when selling at 80% of the marked price, the article is sold at 100 - 12 = $88.
i.e., 0.8S = $88.
or S = 88/0.8 = $110.
If the merchant sells at 95% of the marked price, he will sell the article at 95% of $110 = $104.5
The profit made = 104.5 - 100 = $4.5.
% Profit = profit/cost price=4.5/100 = 4.5%
Choice E
Answer: (E) 4.5% profit
Question: In a class there are 22 boys and 20 girls. In how many ways can a boy and a girl be selected?
(A) 288
(B) 500
(C) 440
(D) 266
(E) 255
Rationale: We can select one boy from 22 boys in 22 ways.
We select one girl from 20 girls in 20 ways
We select a boy and girl in 22 * 20 ways i.e.,
= 440 ways.
Answer: C
Answer: (C) 440
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $500 per sq. metre.
(A) $10312.50
(B) $13512.50
(C) $16512.50
(D) $14512.50
(E) $18512.50
Rationale: Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = $500
Hence, total cost
=5.5×3.75×500= $10312.50
A
Answer: (A) $10312.50
Question: The greatest common factor of positive integers m and n is 11. What is the greatest common factor of (2m^2, 2n^2)?
(A) 2
(B) 11
(C) 22
(D) 121
(E) 242
Rationale: m = 11j and n = 11k, where the greatest common factor of j and k is 1.
2m^2 = 2*11*11*j^2 and 2n^2 = 2*11*11*k^2
The greatest common factor of 2m^2 and 2n^2 is 2*11*11 = 242
The answer is E.
Answer: (E) 242
Question: The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is?
(A) 1994
(B) 1494
(C) 1349
(D) 1496
(E) 1500
Rationale: LCM = 1400
1400 - 6 = 1394
ANSWER:C
Answer: (C) 1349
Question: When you multiply a number by 5 and
then subtract 5, the result is the same as
if you first subtracted 7 from the same
number and then multiplied by 11. What
is the number?
(A) A)23
(B) B)13
(C) C)12
(D) D)31
(E) E)10
Rationale: Let x equal the number and then change the words into an equation and solve for x:
5x – 5 = 11(x – 7)
5x – 5 = 11x – 77
72 = 6x
12 = x
correct answer C)12
Answer: (C) C)12
Question: If x = a!, which of these following values of a is the least possible value (in this list) for which the last 6 digits of the integer x will all be zero?
(A) 18
(B) 24
(C) 29
(D) 34
(E) 38
Rationale: 2*5 will give one 0 at the end. We need 2^6*5^6 to get 6 zeroes at the end.
There are many 2's, so we need to find the first 6 appearances of 5.
These multiples of 5 are: 5, 10, 15, 20, 5*5...which gives us 6.
To have at least 6 zeroes at the end, a => 25.
The answer is C.
Answer: (C) 29
Question: The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?
(A) 3
(B) 4
(C) 8
(D) 9
(E) 12
Rationale: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
Answer: (C) 8
Question: What number should replace the question mark?
105, 87, ?, 52, 35
(A) 49
(B) 37
(C) 70
(D) 55
(E) 83
Rationale: C
70
The sequence progresses -18, -17, -18, -17.
Answer: (C) 70
Question: Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes and his sister’s time is currently 8 minutes 48 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
(A)  3%
(B)  5%
(C)  8%x
(D)  10%
(E)  12%
Rationale: Bob's time = 600 secs.
His sis' time = 528 secs.
Percent increase needed = (600-528/600) * 100 = 72/600 * 100 = 12%. Ans (E).
Answer: (E)  12%
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 11
(B) 50
(C) 99
(D) 88
(E) 61
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: B
Answer: (B) 50
Question: The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?
(A) 4.2
(B) 4.6
(C) 4.3
(D) 4.1
(E) 4.0
Rationale: Sum of the remaining two number
= (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
Answer: B
Answer: (B) 4.6
Question: Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5, 6, 7}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
(A) 5/32
(B) 7/64
(C) 9/64
(D) 53/512
(E) 81/512
Rationale: The number of ways to select w, x, and y is: 8*8*8=512
The number of ways to choose three different numbers from the set is 8C3=56.
There are six permutations for each group of three different numbers, but only one permutation satisfies w < x < y.
P(w < x < y) = 56/512 = 7/64
The answer is B.
Answer: (B) 7/64
Question: If x and y are integers such that x^2= 3y and xy = 36, then x – y = ?
(A) -30
(B) -20
(C) -5
(D) 5
(E) 0
Rationale: here x and y are integers .
x^2=3y,xy =36.
substitute (x^2)/3=y in xy => x^3=36*3=>x^3=108.
here x^3 is positive ,
x is also positive.
x=6 then y=6.
x-y=0
so option E is correct
Answer: (E) 0
Question: The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 60
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
(A) 51
(B) 88
(C) 90
(D) 98
(E) 162
Rationale: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics
No. of total students = 60 + (35-15) + (40-10-12) = 60+20+18 = 98
Hence, Answer will be D.
Answer: (D) 98
Question: For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/7 + 7^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is
(A) 1/4
(B) 1/5
(C) 1/6
(D) 1/7
(E) 1/8
Rationale: For all positive integers n and m,
A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,
note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2)
B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.
A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}
A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)
The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ...
missing numbers are 1/8, 1/13, 1/16, ....
B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)
here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values
The largest reciprocal that present in B(25) but not in A(5) is 1/5
Answer B
Answer: (B) 1/5
Question: The function f is defined by subtracting 25 from the square of a number and the function d is defined as the square root of one-half of a number. If d(f(x))=10, then which of the following is a possible value of x?
(A) -15
(B) -5
(C) 0
(D) 5
(E) 25
Rationale: f(x) = x^2-25
d(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).
d(f(x)) = 10
d(x^2-25) =10
sqrt((x^2-25)/2) = 10
=> (x^2-25)/2 = 100
=>x^2 = 225
=> x = 15 or -15
Answer is A.
Answer: (A) -15
Question: The difference between two no is 9 and the product of the two is 14. What is the square of their sum?
(A) 237
(B) 260
(C) 177
(D) 197
(E) 137
Rationale: We know that (a+b)2=(a−b)2+4ab(a+b)2=(a−b)2+4ab
Substituting a - b = 9, and ab = 14, (a+b)2=(9)2+4(14)=137(a+b)2=(9)2+4(14)=137
Answer:E
Answer: (E) 137
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 62.5
(B) 62.8
(C) 62.1
(D) 62.2
(E) 62.7
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer:A
Answer: (A) 62.5
Question: The arithmetic mean and standard deviation of a certain normal distribution are 16.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
(A) 10.5
(B) 11
(C) 11.5
(D) 12
(E) 13.5
Rationale: The value which isexactlytwo SD less than the mean is:mean-2*SD=16.5-2*1.5=13.5.
Answer: E.
Answer: (E) 13.5
Question: A sales executive was given a target to get annual bonus. He already reached 1/2 of his last year's target. If the target was reduced by 5% this year, what percentage target of the last year's target does he need to reach to get bonus?
(A) 9/20
(B) 6/12
(C) 7/5
(D) 10/20
(E) 3/6
Rationale: We have 1/2 and 5% that is 1/20
If we assume the last year's target to be 20
This year's target is 5% less of last year=19
The target reached this year 1/2*20=10
Remaining is 19-10=9
Required 9/20
Answer (A)
Answer: (A) 9/20
Question: Molly's age in 18 years will be four times her age three years ago. What is Molly's present age?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Let x be Molly's present age.
x + 18 = 4(x-3)
x = 10
The answer is C.
Answer: (C) 10
Question: Some pens are divided among A, B, C and D. A gets twice the number of pens that B gets. C gets the same number of pens as D gets. If A gets 25 pens more than D and the ratio of the number of pens that B and C get is 2:3, then find the number of pens that D gets?
(A) 16
(B) 76
(C) 75
(D) 88
(E) 52
Rationale: Let the number of pens that A, B, C and D get be a, b, c and d respectively.
a:b = 2:1
a = c + 25
b:c = 2:3
a:b:c:d = 4:2:3:3
a, d get 4p, 3p pens
=> 4p - 3p = 25 => p = 25
=> D gets 3p = 3 * 25 = 75 pens.
AnswerC
Answer: (C) 75
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
(A) 18
(B) 99
(C) 12
(D) 07
(E) 11
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: C
Answer: (C) 12
Question: Andrea invested a certain sum of money in a bank that paid simple interest. The amount grew to $340 at the end of 2 years. She waited for another 4 years and got a final amount of $420. What was the principal amount that she invested at the beginning?
(A) $350
(B) $300
(C) $400
(D) $375
(E) $360
Rationale: What shall be the rate of interest.? Does that is not required for the calculation?
Not really!
Keep in mind that the interest earned each year will be the same in Simple Interest.
At the end of 2 years, Amount = $340
At the end of 6 years, Amount = $420
This means she earned an interest of $80 in 4 years. Or $20 in each year.
We know that the interest earned each year will be the same.
Therefore she must have earned $40 in 2 years.
Hence Principal Amount = $340 - $40 = $300 Option B
Answer: (B) $300
Question: Find the area of a parallelogram with base 24 cm and height 16 cm.
(A) 298 cm2
(B) 288 cm2
(C) 187 cm2
(D) 384 cm2
(E) 177 cm2
Rationale: Area of a parallelogram = base * height
= 24 * 16
= 384 cm2
Answer: D
Answer: (D) 384 cm2
Question: A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 500,000?
(A) 160
(B) 200
(C) 240
(D) 300
(E) 480
Rationale: The first digit and last digit are the same so the 2 possibilities are 6 or 8.
The second and third digits can be any number from 0 to 9.
The total number of palindromic integers is 2*10*10 = 200
The answer is B.
Answer: (B) 200
Question: A bag is filled with pennies and nickels in the ratio of 5 to 3. There are 60 nickles in the bag, how many coins are there in that bag?
(A) 40
(B) 160
(C) 65
(D) 70
(E) 80
Rationale: A ratio of pennies to nickels of 5 to 3 means that we can write the number of pennies and nickels in the form
number of pennies = 5x and number of nickels = 3x
But we know the number of nickels, 60. Hence
3x = 60
Solve for x
x = 20
The total number of coins is given by
5x + 3x = 8x = 8 × 20 =160
Answer : B
Answer: (B) 160
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
(A) 26.4 m2
(B) 39.6 m2
(C) 52.8 m2
(D) 79.2 m2
(E) None of these
Rationale: Explanation:
42/360 * 22/7 * 12 * 12 = 52.8 m2
ANSWER IS C
Answer: (C) 52.8 m2
Question: What is the total cost of 2 sandwiches at $3.49 each and 4 sodas at $0.87 each?
(A) $3.36
(B) $6.85
(C) $8.46
(D) $10.46
(E) $11.85
Rationale: Answer = D
2 * 3.49 + 4 * 0.87
= 2 (3.50 - 0.01) + 4 (1.00 - 0.13)
= 7 + 4 - 0.02 - 0.52
= 11 - 0.54
= 10.46
Answer: (D) $10.46
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
(A) 4830
(B) 5120
(C) 6420
(D) 8960
(E) 7960
Rationale: Clearly, l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m3 = 5120 m3. Answer: Option B
Answer: (B) 5120
Question: n^(n/2)=4 is true when n=4 in the same way what is the value of n if n^(n/2) =8?
(A) 4
(B) 8
(C) 2
(D) 6
(E) 10
Rationale: n^(n/2)=8Apply logN/2logn=log8nlogn=2log8=log8^2=log64Logn=log64Now apply antilogn=64/nNow n=8.ANSWER:B
Answer: (B) 8
Question: Subtracting 5% of A from A is equivalent to multiplying A by how much ?
(A) 0.95
(B) 9.4
(C) 0.094
(D) 94
(E) None
Rationale: Answer
Let A - 5% of A = AB.
⇒ (95 x A) / 100 = AB
∴ B = 0.95
Correct Option: A
Answer: (A) 0.95
Question: In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 9 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
(A) 2/1
(B) 4/1
(C) 2/3
(D) 3/4
(E) 3/2
Rationale: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.
Thus Milk=4x=36 liters and Water=x=9 liters.
New ratio = 36/(9+9) = 36/18 = 2/1.
Answer: A.
Answer: (A) 2/1
Question: A dealer purchased an book at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
(A) 79%
(B) 88%
(C) 100%
(D) 94%
(E) 103%
Rationale: C
100%
MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer: (C) 100%
Question: In the class of 100 students, 70 speak Tamil and 40 speak Telugu. What is the lowest possible number of students who
speak both the languages?
(A) A)8
(B) B)10
(C) C)20
(D) D)30
(E) E)32
Rationale: let the student who speaks Tamil-x
let the student who speaks Telugu-y
as (xuy)-(xny)=total
70+40-(xny)=100
=10
B)
Answer: (B) B)10
Question: In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs.72 per Kg so that the mixture must be worth Rs.67 per Kg?
(A) 3 : 1
(B) 3 : 2
(C) 4 : 3
(D) 5 : 3
(E) 1 : 1
Rationale: Required ratio = 500 : 500 = 3 : 1
Answer E
Answer: (E) 1 : 1
Question: A pack of 52 playing cards, 2 cards aredrawn together at random. Find the probability of both the cards being king ?
(A) 2/124
(B) 3/234
(C) 1/221
(D) 2/314
(E) 3/431
Rationale: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.
∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221
C
Answer: (C) 1/221
Question: A school’s annual budget for the purchase of student computers increased by 38% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
(A) 10%
(B) 20%
(C) 15%
(D) 18%
(E) 16%
Rationale: Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100;
This year: budget = $138, price = $1.2 --> the number of computers purchased = 138/1.2 = 115.
Increase in the number of computers purchased = 15%.
Answer: C.
Answer: (C) 15%
Question: The sum of the present ages of father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
(A) 12 years
(B) 14 years
(C) 18 years
(D) 20 years
(E) 22 years
Rationale: Let the present ages of son and father be x and (60 - x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
6x = 84 => x = 14
Son's age after 6 years = (x + 6) = 20 years.
ANSWER:D
Answer: (D) 20 years
Question: A can do a piece of work in 10 days and B alone can do it in 15 days. How much time will both take to finish the work ?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea.
Time taken to finish the job = XY / (X + Y)
= 10 x 15 / (10 + 15)
= 150 / 25
= 6 days
Answer: B
Answer: (B) 6
Question: N is a positive integer. When N + 1 is divided by 4, the remainder is 3. What is the remainder when N is divided by 3?
(A) 1
(B) 2
(C) 3
(D) 0
(E) 4
Rationale: N+1 = 4a+3
i.e. N+1 = 7, 10, 13, 16, ... etc.
i.e. N = 6, 9, 12, 15, ... etc.
When N is divided by 3 Remainder is always 0
Answer: D
Answer: (D) 0
Question: Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 12 minutes
(B) 17 minutes
(C) 27 minutes
(D) 97 minutes
(E) 26 minutes
Rationale: Part filled by A in 1 min. = 1/20
Part filled by B in 1 min. = 1/30
part filled by (A + B) in 1 min. = 1/20 + 1/30 = 1/12.
Both the pipes can fill the tank in 12 minutes.
Answer: A
Answer: (A) 12 minutes
Question: A three-person committee must be chosen from a group of 7 professors and 12 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?
(A) A)70
(B) B)743
(C) C)749
(D) D)1,260
(E) E)1,980
Rationale: Total number of ways to select at least one professor = Number of ways to select 3 people from 12 students and 7 professors - Number of ways to select 3 people from 12 student (i.e. without including any professor)
= 19C3 - 12C3 = 969 - 220 = 749
ANSWER:C
Answer: (C) C)749
Question: In a certain aquarium, the number of red fish is three times the number of the green fish, and the number of blue fish is half the number of the red fish. If the ratio of green fish to red fish were to be doubled, and the ratio of red fish to blue fish were to be doubled, then the ratio of blue fish to green fish in that aquarium would be
(A) 3:2
(B) 1:1
(C) 1:2
(D) 3:4
(E) 3:8
Rationale: Lots of little places to make a mistake or panic here. =)
R = 3G
B = R/2
G/R = 1/3 ----> Doubled G/R = 2/3
R/B = 2 ----> Doubled R/B = 4
B/G = (B/R)*(R/G) = (1/4)*(3/2) = 3/8
ANSWER:E
Answer: (E) 3:8
Question: Find the value of m 82519 x 9999 = m?
(A) 724533811
(B) 353654655
(C) 825107481
(D) 725117481
(E) 477899932
Rationale: 82519 x 9999 = 82519 x (10000 - 1)
= 82519 x 10000 - 82519 x 1
= 825190000 - 82519
= 825107481
C
Answer: (C) 825107481