mathewhe/aqua_rat huggingface dataset:
Question: If 6887 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box?
(A) 1 books
(B) 2 books
(C) 3 books
(D) 4 books
(E) 5 books
Rationale: The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 6887.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 6887 = 29 and 27 is divisible by 9.
Hence, we need to remove 2 to this number for it to be divisible by 9
Correct Option: B
Answer: (B) 2 books
Question: Using all the letters of the word "SULOCHANA", how many words can be formed, which begin with M and end with M?
(A) 5040
(B) 2010
(C) 3028
(D) 6078
(E) 1025
Rationale: There are five letters in the given word.
Consider 9 blanks ....
The first blank and last blank must be filled with S and A all the remaining three blanks can be filled with the remaining 7 letters in 7! ways.
The number of words = 7! = 5040.
Answer:A
Answer: (A) 5040
Question: If Ben's income is Rs 35000, calculate his savings given that his income and expenditure are in the ratio 7:4.?
(A) Rs 4900
(B) Rs 9800
(C) Rs 9000
(D) Rs 7000
(E) Rs.15000
Rationale: Let the income and the expenditure of the person be Rs.7x and Rs.4x respectively.
Income, 7x = 35000 => x = 5000
Savings = Income - expenditure = 7x - 4x = 3x
So, savings = Rs.15000
Answer: E
Answer: (E) Rs.15000
Question: What is the perimeter of a regular polygon with sides of length 13 cm and internal angles measuring 144° each?
(A) 96 cm
(B) 108 cm
(C) 120 cm
(D) 130 cm
(E) 144 cm
Rationale: Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 144*n
from here
n = 10
So perimeter becomes 13*10= 130
answer D
Answer: (D) 130 cm
Question: Water is poured in a bath tub at a rate of 11 cubic meters per hour, the level of water in the bath tub rises at a rate of .3 meters per hour. Which of the following best approximates the diameter of the tank in meters?
(A) √33
(B) √10/2
(C) 2√35/3
(D) 5
(E) 7
Rationale: Here's my re-worked solution:
volume = 11 = pi (r^2)(0.3)
11 = 22/7 (3/10)(r^2)
10 = r^2
r = sqrt(35/3)
Diameter=2*sqrt(35/3)
Ans: C
Answer: (C) 2√35/3
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 8 m wide at the top and 2 m wide at the bottom and the area of cross-section is 770 sq m, the depth of cannel is?
(A) 150
(B) 152
(C) 154
(D) 156
(E) 158
Rationale: 1/2 * d (8+2)
= 770
d = 154
Answer: C
Answer: (C) 154
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?
(A) 388
(B) 2998
(C) 277
(D) 500
(E) 271
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85
5x/100 + 90 – 6x/100 = 85
x/100 = 5
=> x = 500.Answer: D
Answer: (D) 500
Question: A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 10/21
(B) 15/21
(C) 09/21
(D) 11/21
(E) 13/21
Rationale: Total number of balls = 2 + 3 + 2 = 7
Let S be the sample space.
n(S) = Total number of ways of drawing 2 balls out of 7 = 7C2
Let E = Event of drawing 2 balls , none of them is blue.
n(E) = Number of ways of drawing 2 balls , none of them is blue
= Number of ways of drawing 2 balls from the total 5 (=7-2) balls = 5C2
(∵ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5)
P(E) = n(E)/n(S)=5C2/7C2=(5×4/2×1)(7×6/2×1)=5×47×6=10/21
Answer is A.
Answer: (A) 10/21
Question: A man whose speed is 5.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey ?
(A) 1 kmph
(B) 5 kmph
(C) 6 kmph
(D) 4 kmph
(E) 7 kmph
Rationale: Explanation:
Speed of Man = 5.5 kmph
Speed of stream = 1.5 kmph
Speed in DownStream = 7 kmph
Speed in UpStream = 4 kmph
Average Speed = (2 x 7 x 4)/11 = 5 kmph.
Answer: B
Answer: (B) 5 kmph
Question: In Town P, 60 percent of the population are employed, and 42 percent of the population are employed males. What percent of the employed people in Town P are females?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%
Rationale: The percent of the population who are employed females is 60-42 = 18%
The percent of employed people who are female is 18% / 60% = 30%.
The answer is C.
Answer: (C) 30%
Question: How many cubes of 3cm edge can be cut out of a cube of 18cm edge
(A) 36
(B) 232
(C) 216
(D) 484
(E) 112
Rationale: number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216 Answer: C
Answer: (C) 216
Question: If F is the product of all positive integers less than 31, than what is the greatest integer k for which F/18^k is an integer?
(A) 3
(B) 6
(C) 7
(D) 14
(E) 26
Rationale: 30! F must be divisible by (3*3*2)^k.
As I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18).
Every multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly.
3 6 9*
12 15 18*
21 24 27**
30
The stars are marked as they are multiples of 9* or 27** and thus provides two or three 3's respectively.
3=3 (occurs 10 times) +10
3*3=9 (occurs 3 times) +3(adding just one additional three each as they were not counted for in the multiples of 3)
3*3*3=27 (occurs 1 time) +1 (again, adding just one as they were previously not counted)
Total: 14.
For every k we add two 3's. So we must divide 14 by 2 to get the highest integer K before we receive a non-integer result.
Answer: 7 -> Answer choice: C.
Answer: (C) 7
Question: A and B together can complete a piece of work in 4days. If A alone can complete the same work in 12days, in how many days, in how many days can B alone complete that work?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 5
Rationale: (A+B)'s 1day's work = 1/4
A's 1day's work = 1/12
B's 1days's work = (1/4)-(1/12) = 1/6
Hence, B alone can complete the work in 6days.
Answer is A
Answer: (A) 6
Question: If f(x)= 5x^3- 2x+8 and g(y)= 5y-4, then g(f(x)) =
(A) 11x^2+4x+4
(B) 11x^2-12x+44
(C) 8x^3-8x+32
(D) 25x^3-10x+36
(E) 30x^3-12x+44
Rationale: g(f(x)) = 6(f(x)) -4 = 5(5x^3- 2x+8) - 4 = 25x^3-10x+36 =>D
Answer: (D) 25x^3-10x+36
Question: The sum of two consecutive number is 87. Which is the larger number?
(A) 42
(B) 43
(C) 44
(D) 45
(E) 46
Rationale: Let consecutive number be x, x+1
Therefore sum of the consecutive number is x + x+1=87
2x+1=87
2x=86
x=43
Therefore larger number is x+1=44
ANSWER:C
Answer: (C) 44
Question: A man can row upstream at 27 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
(A) 31
(B) 92
(C) 30
(D) 32
(E) 23
Rationale: US = 27
DS = 35
M = (35 + 27)/2 = 31
Answer:A
Answer: (A) 31
Question: In a certain circle there are 9 points. What is the number of the triangles connecting 4 points of the 9 points?
(A) 80
(B) 96
(C) 108
(D) 126
(E) 132
Rationale: IMO : D
HERE we have to select 4 points out of 9 points. Order is not important
So the answer will be 9c4 = 126
Answer D
Answer: (D) 126
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day?
(A) $0.15
(B) $0.20
(C) $0.30
(D) $0.40
(E) $0.45
Rationale: We are given that orangeade is made on Day 1 with an EQUAL AMOUNT of water and orange juice. We can set this information up into a ratio using a variable multiplier:
W : OJ = x : x
Thus, orangeade quantity = amount of water + amount of OJ = x + x = 2x
We are next given that orangeade on Day 2 was made by mixing the SAME AMOUNT of orange juice with TWICE THE AMOUNT of water. We can set this information up into a ratio using a variable multiplier:
W : OJ = 2x : x
Thus, orangeade quantity = amount of water + amount of OJ = 2x + x = 3x
We also know that all orangeade made was sold and that the revenue on both days was the same. We can therefore set up the following equation:
Day 1 Revenue = Day 2 Revenue
That is,
(quantity sold Day 1)(price per glass Day 1) = (quantity sold Day 2)(price per glass Day 2)
Let a be the amount of orangeade a glass can hold, then
quantity sold Day 1 = the number of glasses of orangeade sold on Day 1 = 2x/a
Similarly,
quantity sold Day 2 = the number of glasses of orangeade sold on Day 2 = 3x/a
We also know that the price per glass on day 1 = $0.6
But we don’t know the price per glass on day 2, so let’s label it as variable p.
We now have:
(2x/a)(0.6) = (3x/a)(p)
Multiplying both sides by a, we have:
(2x)(0.6) = (3x)(p)
1.2x = 3xp
1.2 = 3p
p = 0.4
Thus, each glass of orangeade was sold for $0.40 on Day 2.
Answer D.
Answer: (D) $0.40
Question: There are 7 identical pens and 9 identical books. In how many different ways can a person select at least one object from this set?
(A) 16
(B) 31
(C) 48
(D) 79
(E) 90
Rationale: We can select from 0 to 7 pens and from 0 to 9 books.
Thus the total possible ways to select objects is 8*10 = 80
We must subtract 1 for the case with 0 pens and 0 books.
The answer is D.
Answer: (D) 79
Question: X, Y and Z started a business X's investment is 2 times of Y's investment is 5 times of Z's investment. Find the profit of Y in the total profit of Rs. 3200
(A) Rs. 25600
(B) Rs. 8500
(C) Rs. 1000
(D) Rs. 8000
(E) None of these
Rationale: Explanation:
X = 2Y and Y = 5Z
=> X : Y = 2:1 and Y : Z = 5 : 1
=> X : Y : Z = 10 : 5 : 1
Ratio of capitals of X, Y and Z = 10 : 5 : 1
Y's share = Rs.[(5/16) × 3200] = Rs. 1000
Answer: Option C
Answer: (C) Rs. 1000
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
(A) Rs.2589
(B) Rs.2380
(C) Rs.8868
(D) Rs.2477
(E) Rs.6271
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs. 2380.
Answer:B
Answer: (B) Rs.2380
Question: How much time will take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 3.5 years
(B) 4 years
(C) 4.5 years
(D) 5 years
(E) 6 years
Rationale: Time = (100 * 81) / (450 * 4.5) = 4 years
ANSWER:B
Answer: (B) 4 years
Question: A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 6 days. B can do the work alone in?
(A) 19
(B) 36
(C) 11
(D) 19
(E) 114
Rationale: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/6
6/x = 1/6 => x = 36
So, B takes 18 hours to finish the work.
Answer: B
Answer: (B) 36
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
(A) 20%
(B) 26%
(C) 42%
(D) 27%
(E) 22%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: A
Answer: (A) 20%
Question: If x^2 + 9/x^2 = 7, what is the value of x - 3/x
(A) 1
(B) 25
(C) 9
(D) 5
(E) 3
Rationale: To find : x-3/x. Let it be t.
=> x-3/x = t
=> (x^2 + 9/x^2) - 2*x*3/x = t^2 (Squaring both sides).
=> (7) - 2*3 = 1
=> t^2 = 1. Thus t=1 or t=-1.
Answer A
Answer: (A) 1
Question: If p is a natural number and p! ends with y trailing zeros, then the number of zeros that (5p)! ends with will be
(A) (p+y) trailing zeros
(B) (5p+y) trailing zeros
(C) (5p+5y) trailing zeros
(D) (p+5y) trailing zeros
(E) none of them above
Rationale: for p = 10 trailing 0's =
10/5 = 2
for 5p,
50/5 = 10, 50/25 = 2 hence total is 12
Similarly,
for p = 20 trailing 0's = 20/5 = 4
for 5p, trailing 0's = 50/5 = 10, 50/25 = 2 hence total is 10 + 2 = 12
thus we observe,
number of 0's = p + y
example p = 20, y = 4 giving 24.
Hence A.
Answer: (A) (p+y) trailing zeros
Question: Find out the next word in the series below...
FAG, GAF, HAI, IAH, ...?
(A) GAK
(B) JAK
(C) HGF
(D) JAH
(E) KHG
Rationale: In first FAG it was reodering the first and last letters and these are the continuous alphabets
ANSWER:B
Answer: (B) JAK
Question: If S=x^4 + y^4 = 100, then the greatest possible value of x is between
(A) 0 and 3
(B) 3 and 6
(C) 6 and 9
(D) 9 and 12
(E) 12 and 15
Rationale: My attempt:
If S=x^4+y^4=100, then the greatest possible value of x would be when y is minimum.
Let y^4 be 0. Now x^4 = 100. x should be definitely greater than 3 but less than 4. The only option that fits this range is B
Hence answer is --
b) 3 and 6.
Answer: (B) 3 and 6
Question: In a mixture of 60 litres, the ratio of acid to base is 2 : 1. If this ratio is to be 1 : 2, then the quantity of base (in litres) to be further added is
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Acid = 40 lts
Base = 20 lts
to make the ratio A:B = 1:2 ,
60 lts of base should be added
ANSWER:E
Answer: (E) 60
Question: A train 175 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 49
(B) 50
(C) 12
(D) 13
(E) 68
Rationale: Speed of the train relative to man = (175/10) m/sec = (35/2) m/sec. [(35/2) * (18/5)] km/hr = 63 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 63 ==> x = 68 km/hr.
Answer: Option E
Answer: (E) 68
Question: The radius of a circle is increased by 1%. Find how much % does its area increases?
(A) 2.07%
(B) 2.71%
(C) 2.05%
(D) 2.01%
(E) 2.02%
Rationale: r = 100 r = 101
r2 = 10000 r2 = 10201
10000 ---- 201
100 ---- ? => 2.01%
Answer: D
Answer: (D) 2.01%
Question: A person takes 5hrs 45 min in walking to a place and riding back. He would have gained 6 hrs by riding both ways. The time he would take to walk both ways is?
(A) 5 hours 45 min
(B) 5 hours 55 min
(C) 6 hours 45 min
(D) 11 hours 45 min
(E) 12 hours
Rationale: ----------------------------------------------------------------
Solution 1
----------------------------------------------------------------
Given that time taken for riding both ways will be 6 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 6 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 6 hours = 11 hours 45 min
D
Answer: (D) 11 hours 45 min
Question: For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 3*/5* ?
(A) 5
(B) 5/4
(C) 4/5
(D) 1/4
(E) 1/5
Rationale: When dealing with 'Symbolism' questions, it often helps to 'play with' the Symbol for a few moments before you attempt to answer the question that's asked. By understanding how the Symbol 'works', you should be able to do the latter calculations faster.
Here, we're told that K* is the PRODUCT of all the fractions of the form 1/T, where T is an integer between 1 and K, inclusive.
Based on this definition....
IF....
K = 2
K* = (1/1)(1/2) = 1/2
IF....
K = 3
K* = (1/1)(1/2)(1/3) = 1/6
We're asked to find the value of 5*/4*
Now that we know how the Symbol 'works', solving this problem shouldn't be too difficult. You can actually choose to do the math in a couple of different ways....
5* = (1/1)(1/2)(1/3)(1/4)(1/5)
Don't calculate this just yet though....since we're dividing by 4*, many of those fractions will 'cancel out.'
4* = (1/1)(1/2)(1/3)(1/4)
We're looking for the value of:
(1/1)(1/2)(1/3)(1/4)(1/5) / (1/1)(1/2)(1/3)(1/4)
Since the first four fraction in the numerator and denominator cancel out, we're left with just one fraction:
5/3
B
Answer: (B) 5/4
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
(A) 2789
(B) 2772
(C) 1991
(D) 6725
(E) 2099
Rationale: CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725.
Answer: D
Answer: (D) 6725
Question: If two negative numbers are multiplied the product is 150. If the lesser of the two is 35 less than triple the greater number, what is the greater number?
(A) -14
(B) -13
(C) -17
(D) -12
(E) -15
Rationale: Test the options. The options give you the greater number. Start from the middle option.
(C) - 17
Triple of -17 is -51 and 35 less is -16.
-16 * -17 = 272 (Not correct)
...
(E) - 15
Triple of 15 is -45 and 35 less is -10.
-10 * -15 = 150
Correct
Answer (E)
Answer: (E) -15
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 12 units?
(A) 140 sq.units
(B) 170 sq.units
(C) 190 sq.units
(D) 168 sq.units
(E) 149 sq.units
Rationale: Explanation:
Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 12 units
Area of the rectangle = lb = 14 * 12 = 168 sq.units
Answer: Option D
Answer: (D) 168 sq.units
Question: 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
(A) 66
(B) 84
(C) 80
(D) 72
(E) 68
Rationale: Let the length of the wire be h.
Radius =1/2mm=1/20cm.	Then,
(22/7)x (1/20) x (1/20) x h = 66.
h = (66 x 20 x 20 x 7)/22 = 8400 cm = 84 m.
ANSWER B
Answer: (B) 84
Question: Mixture of milk & water has been kept in two separate bowl. Ratio of milk to water in one of the bowls is 5 : 1 and that in the other bowl 7 : 2. In what ratio the mixtures of these 2 bowl should be added together so that the quantity of milk in the new mixture may become 80%?
(A) 2:3
(B) 1:3
(C) 2:5
(D) 3:7
(E) 4:5
Rationale: Lett. mixtures of the two containers be added together in the ratio of x
= = [ixoox l00%
Since the percentage quantity ofmilk in the new mixture is SO% — so% (45x + 42y) x 5 4 x 54(x y) 225x 210y 216.3E+216y
9x=6y
x:y=2:3
A
Answer: (A) 2:3
Question: The sale price sarees listed for Rs.390 after successive discount is 15% and 25% is?
(A) 298
(B) 237
(C) 248
(D) 876
(E) 291
Rationale: 390*(85/100)*(75/100)
= 248
Answer: C
Answer: (C) 248
Question: In a market there are men and horses. In all, there are 22 heads and 66 feet. How many men and how many horses are in the market?
(A) 8 men and 14 horses.
(B) 7 men and 14 horses.
(C) 6 men and 14 horses.
(D) 5 men and 14 horses.
(E) 11 men and 11 horses.
Rationale: 11 men and 11 horses.
Let M = men and H = horses. We can come up with 2 equations.
M + H = 22
2M + 4H= 66
Solving the 2 equations will give 11 men and 11 horses.
Answer E
Answer: (E) 11 men and 11 horses.
Question: A train met with an accident 80km away from station A. It completed the remaining journey at 5/6th of the original speed and reached station B 1hr 12mins late. Had the accident taken place 60km further, it would have been only 1hr late. what was the original speed of the train?
(A) 60 km/hr
(B) 55 km/hr
(C) 65 km/hr
(D) 80 km/hr
(E) 48 km/hr
Rationale: let the original speed be 6x. A/q, traveling 80 km at 5/6th of original speed costs him 12 minutes etc
80/5x =80/6x +12/60 -> x =10 , 8x= 80.
Ans D
Answer: (D) 80 km/hr
Question: An investor deposited $10,000 to open a new savings account that earned 12 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened?
(A) $10,300
(B) $10,303
(C) $10,600
(D) $10,609
(E) $10,900
Rationale: The amount in the account after 6 months is 1.03*1.03($10,000) = $10,609.
The answer is D.
Answer: (D) $10,609
Question: In a deck of cards there are 52 cards numbered from 1 to 13. There are 6 cards of each number in the deck. If you insert 12 more cards with the number 10 on them and you shuffle the deck really good, what is the probability to pull out a card with a number 10 on it?
(A) 1/4.
(B) 4/17.
(C) 5/29.
(D) 4/13.
(E) 9/32
Rationale: 6+12 tens/52+12 total cards=18/64=9/32
E
Answer: (E) 9/32
Question: A coin is tossed twice if the coin shows head it is tossed again but if it shows a tail then a die is tossed. If 8 possible outcomes are equally likely. Find the probability that the die shows a number greater than 4, if it is known that the first throw of the coin results in a tail
(A) 2/4
(B) 1/3
(C) 2/3
(D) 3/6
(E) 1/4
Rationale: Sample space S = { HH, HT, T1, T2, T3, T4, T5, T6 }
Let A be the event that the die shows a number greater than 4 and B be the event that the first throw of the coin results in a tail then,
A = { T5, T6 }
B = { T1, T2, T3, T4, T5, T6 }
Required probability = ( 2/8)/(6/8)=1/3
ANSWER:B
Answer: (B) 1/3
Question: The average of six results is 15 and that of the first five is 13. The sixth result is?
(A) 20
(B) 25
(C) 15
(D) 22
(E) 18
Rationale: 6 * 15 â€“ 5 * 13 = 25
Answer: B
Answer: (B) 25
Question: The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
(A) 40.2
(B) 40.4
(C) 40.6
(D) 40.8
(E) None of the above
Rationale: Sum of 10 numbers = 402
Corrected sum of 10 numbers
= 402 – 13 + 31 – 18 = 402
Hence, new average = 402⁄10 = 40.2
Answer A
Answer: (A) 40.2
Question: The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common ?
(A) 10 and 20
(B) 12 and 18
(C) 24 and 32
(D) 21 and 63
(E) 22 and 88
Rationale: 32 has only one prime 2 (32=2^5) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.
Answer: C.
Answer: (C) 24 and 32
Question: The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number E?
(A) 60
(B) 80
(C) 40
(D) 120
(E) 160
Rationale: (1 + 1/8)x - (1 - 1/4)x = 30
(9/8)x - (3/4)x = 30
x = 80=E
Answer: B
Answer: (B) 80
Question: There are 16 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season?
(A) 750
(B) 900
(C) 1050
(D) 1200
(E) 1350
Rationale: The number of ways to choose two teams is 16C2 = 16*15/2 = 120
The total number of games in the season is 10*120 = 1200.
The answer is D.
Answer: (D) 1200
Question: Out of the five integral numbers C is the average of A and D. B is greater than C and less than D.Also B is the average of A and E . The middle most number in the sequence ?
(A) A
(B) B
(C) C
(D) D
(E) E
Rationale: D _ C _ A --------(1)
D > B > C --------(2)
from (1) and (2)
D > B > C > A ---------(3)
Again E _ B _ A
But B > A, from (3)
So E > D > B > C > A [ Since B is the average of E and A so it is eqidistant from both E and A]
Answer: B
Answer: (B) B
Question: At what rate percent per annum will the simple interest on a sum of money be 4/5 of the amount in 10 years?
(A) 4%
(B) 7%
(C) 8%
(D) 3%
(E) 1%
Rationale: Let sum = x. Then, S.I. =4x/5, Time
= 10 years.
Rate = (100 * 4x) / (x * 5 * 10)
= 8%
Answer: C
Answer: (C) 8%
Question: Three pipes A,B and C are attached to a tank.A and B can fill it in 20 and 30 minutes respectively while C can empty it in 15 minutes.If A,B and C are kept open successively for 1 minute each, how soon will the tank be filled?
(A) 165 min
(B) 166 min
(C) 167 min
(D) 168 min
(E) 169 min
Rationale: the term successively and NOT SIMULTANEOUSLY.AT THE END OF 3 mts, i/60 part of the tank is filled.we have to consider a three-minute block starting from 3 mts, 6 mts,9 mts....etc upto 177 mts. at the end of 165 mts,55/60 part of the tank was filled. at the end of the next suceessive minutes,i.e, 166,167th minute, the part filled is 5/60.so 55/60+5/60. this means the whole tank is filled at the end of 167 th minute.
ANSWER:C
Answer: (C) 167 min