mathewhe/aqua_rat huggingface dataset:
Question: If the product of the integers a, b, c and d is 546 and if 1 < a < b < c < d, what is the value of b+c?
(A) 273
(B) 185
(C) 21
(D) 10
(E) 4
Rationale: Make prime factorization of 546: 546=2*3*7*13.
Now, since given that 1 < a < b < c < d, then a=2, b=3, c=7 and d=13 --> b+c=3+7=10.
Answer: D.
Answer: (D) 10
Question: What is the least value of x, so that 23x57 is divisible by 3
(A) 2
(B) 0
(C) 1
(D) 3
(E) 4
Rationale: Explanation:
23257 is not divisible by 3
23057 is not divisible by 3
23157 is divisible by 3
23357 is not divisible by 3
2+3+1+5+7 = 18
18/3 = 6.
x = 1
Answer: Option C
Answer: (C) 1
Question: The average of seven numbers is 18. The average of first three numbers is 16 and the average of last three numbers is 20. What is the middle number?
(A) 20
(B) 22
(C) 25
(D) 18
(E) 24
Rationale: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 16+3 X 20 = 108
So, the middle number is (126 - 108 ) = 18
D
Answer: (D) 18
Question: I chose a number and divide it by 4. Then I subtracted 18 from the result and got 7. What was the number I chose?
(A) 600
(B) 100
(C) 800
(D) 900
(E) None
Rationale: Solution:
Let x be the number I chose, then
x/4âˆ’18=7
x/4=25
x=100
Answer B
Answer: (B) 100
Question: What are the total number of divisors of 600(including 1 and 600)?
(A) 4
(B) 24
(C) 40
(D) 16
(E) 20
Rationale: Write the prime factorization.
600 = (2^3)(3^1)(5^2)
The number of divisors (including 1 and the number itself) is the product of one plus the exponents.
(3+1)(1+1)(2+1) = 24
ANSWER:B
Answer: (B) 24
Question: f n = 3^3 - 2^3, which of the following is NOT a factor of n?
(A) 18
(B) 19
(C) 38
(D) 57
(E) 76
Rationale: 27-8 = 19 . nineteen is prime umber and factor. any number not a multiplication of 19 is not a factor.
A
Answer: (A) 18
Question: A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20% while buying and by 10% while selling. What is his percentage profit?
(A) 10.22%
(B) 20.22%
(C) 21.22%
(D) 20%
(E) Can't be calculated
Rationale: The owner buys 100kg but actually gets 120kg;
The owner sells 100kg but actually gives 90kg;
Profit: (120-90)/90*100=20%
Answer: D.
Answer: (D) 20%
Question: If the average marks of three batches of 60, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is
(A) 53.33
(B) 54.54
(C) 55
(D) 57
(E) None
Rationale: Sol.
Required average = [60x50 + 60x55 + 45x60 / 60 + 60 + 45]
= [3000 + 3300 + 2700 / 165]
= 9000 / 165 = 54.54.
Answer B
Answer: (B) 54.54
Question: How many 3-digit numerals begin with a digit that represents a prime number?
(A) 16
(B) 80
(C) 400
(D) 180
(E) 240
Rationale: prime digits 2,3,5 and 7.
three digit numbers _ _ _
1st place can be filled in 4 ways
2nd place can be filled in 10 ways
3rd place can be filled in 10 ways
Total=4*10*10=400
Ans : C
Answer: (C) 400
Question: A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss?
(A) 9%
(B) 8%
(C) 2%
(D) 5%
(E) 3%
Rationale: (30*30)/100
= 9%loss
Answer: A
Answer: (A) 9%
Question: If 133,414 cans of paint need to be placed on crates and each crate can contain at most 9 cans of paint. How many cans of paint will be on the last unfilled crate?
(A) 1 bottle
(B) 3 bottles
(C) 5 bottles
(D) 7 bottles
(E) 9 bottles
Rationale: The number of cans of paint that can be placed on crates of 9 cans is the first number that is divisible by 9 that occurs before 133,414.
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 133,414 = 16 and 9 is divisible by 9.
Hence, we need to remove 7 to this number for it to be divisible by 9
Correct Option: D
Answer: (D) 7 bottles
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
(A) 100 m
(B) 125 m
(C) 130 m
(D) 150 m
(E) 160 m
Rationale: Explanation:
Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
ANSWER IS D
Answer: (D) 150 m
Question: A train with 120 wagons crosses John who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts ove(who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time after the train has crossed the Mike do the John meets to Mike?rtaking the John (he is riding on the horse) before it starts overtaking the Mike
(A) 2534
(B) 3545
(C) 3521
(D) 4564
(E) 3576
Rationale: Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then
---------- (i)
and ---------(ii)
From eq.(i) and (ii)
3(R - A ) = 2 (R + K)
R = 3A + 2K
In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram
= 1800 ( R - A) - 24 ( A + K)
Time required =
= (3600 - 24) = 3576 s
E
Answer: (E) 3576
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 225 girls, the total number of
students in the college is
(A) 420
(B) 520
(C) 585
(D) 620
(E) None of these
Rationale: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 225
=> x = 45
Total students = 8x+5x = 13x = 13(45) = 585
Answer: C
Answer: (C) 585
Question: The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 9 percent, what was the annual interest rate last year?
(A) 1%
(B) 1.1%
(C) 8.18%
(D) 10%
(E) 10.8%
Rationale: 9=1.1*x
X=8.18%
Answer C)
Answer: (C) 8.18%
Question: The perimeter of a semi circle is 216 cm then the radius is?
(A) 26
(B) 48
(C) 98
(D) 37
(E) 42
Rationale: 36/7 r = 216
=> r
= 42
Answer: E
Answer: (E) 42
Question: The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
(A) 290
(B) 240
(C) 2870
(D) 289
(E) 292
Rationale: 4a = 68 => a = 17
172 – 82 = 152
1/2 * 16 * 30 = 240
Answer: B
Answer: (B) 240
Question: In a single throw with two dice, find the probability that their sum is a multiple either of 3 or 4.
(A) 22
(B) 29
(C) 28
(D) 10
(E) 11
Rationale: Answer:B
Answer: (B) 29
Question: Avinash is twice as fast as Bharat, and Bharat is one-third as fast as Chandra. If together they can complete a piece of work in 30 days, in how many days can Avinash, Bharat and Chandra do the work respectively?
(A) 90,180,66
(B) 90,180,67
(C) 90,180,61
(D) 90,180,62
(E) 90,180,60
Rationale: Let Chandra do the work in 2x days.
Bharat can do it in 6x days and Avinash can do it in 3x days.
1/(2x) + 1/(6x) + 1/(3x) = 1/30 => (3 + 1 +2)/6x = 1/30 => x = 30
So, the time taken to complete the work by Avinash, Bharat, Chandra is 90, 180, 60 days respectively.Answer: E
Answer: (E) 90,180,60
Question: A sum at simple interests at 13 ½ % per year amounts to Rs.2502.50 after 4 years find the sum.
(A) 1265
(B) 1256
(C) 1562
(D) 1526
(E) 1625
Rationale: Let sum be Rs. x then , S.I.=Rs.(x*(27/2) *4*(1/100) ) = Rs.27x/50
therefore, amount = (Rs. x+(27x/50)) = Rs.77x/50
therefore, 77x/50 = 2502.50
= x = 2502.50 * 50/77 = 1625
Hence , sum = Rs.1625.
Answer is E.
Answer: (E) 1625
Question: A and B walk around a circular track. They start at 9 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 11.30 a.m.?
(A) 8
(B) 17
(C) 16
(D) 15
(E) 3
Rationale: Sol.
Relative speed = (2 + 3) = 5 rounds per hour.
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 17 times before 11.30 a.m.
Answer B
Answer: (B) 17
Question: A pipe can fill a cistern in 14 minutes whereas the cistern when fill can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?
(A) 17
(B) 16
(C) 28
(D) 13
(E) 12
Rationale: 1/14 - 1/28 = 1/28
28 minutes
Answer: C
Answer: (C) 28
Question: There are two sections C and D of a class, consisting of 18 and 22 students respectively. If the average weight of sections C is 20 kg and that of sections D is 18 kg. Find the average weight of the whole class
(A) 18.7
(B) 18.8
(C) 18.9
(D) 19.9
(E) None
Rationale: Solution
Total weight of(18+22)Students	= (18x20+22x18)Kg
= 756 kg.
Average weight of the whole class	= (756 /40 )
= 18.90.
Answer C
Answer: (C) 18.9
Question: A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.05. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total for a book on the fifth day it is overdue?
(A) $0.60
(B) $0.70
(C) $0.80
(D) $0.90
(E) $1.00
Rationale: 1st day fine - 0.05
2nd day fine - 0.05*2 = 0.1 (as doubling gives lower value)
3rd day fine - 0.1*2 = 0.2 (as doubling gives lower value)
4th day fine - 0.2 *2 = 0.4 (as doubling gives lower value we add 0.3 this time)
5th day fine - 0.4 +0.3 = 0.7 (as doubling gives higher value we add 0.3 this time)
Answer: B.
Answer: (B) $0.70
Question: A can do a job in 20 days and B can do it in 30 days. A and B working together will finish thrice the amount of work in ------- days?
(A) 22 days
(B) 22 days
(C) 36 days
(D) 72 days
(E) 24 days
Rationale: 1/20 + 1/30 =5/60 = 1/12
12/1 = 12 *3= 36 days
Answer: C
Answer: (C) 36 days
Question: Points M(-15,2) and N(5,-5) lie on the xy - plane. What is the midpoint of line segment MN?
(A) (5,0)
(B) (0,5)
(C) (0, (136^(1/2))/2)
(D) (-5,-3/2)
(E) (1,5)
Rationale: The midpoint of a segment is exactly halfway between its endpoints and it's location can be found using the Midpoint Theorem, which states:
• The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints.
• Likewise, the y-coordinate is the average of the y-coordinates of the endpoints.
So, x=(-15+5)/2=-5 and y=(2-5)/2=-3/2 --> coordinates of the midpoint are (-5, -3/2).
Answer: D.
Answer: (D) (-5,-3/2)
Question: Siddharth wants to borrow Rs.9000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
(A) s.21.60
(B) s.21.29
(C) s.32.40
(D) s.21.26
(E) s.21.12
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.9,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 9,000{ [1 + 6/100]2 - 1 - 12/100}
= 9,000 {(1.06)2- 1 - 0.12} = 9,000(1.1236 - 1 - 0.12)
= 9,000 (0.0036) = 9 * 3.6 = Rs.32.40
Answer: C
Answer: (C) s.32.40
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) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Sol.
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 A
Answer: (A) 4
Question: The numbers 1, 2, 3, .....n are written in the natural order. Numbers in odd places are struck off to form a new sequence. This process is continued till only one number is left.
Q 1: If n = 1997, the number left is?
Q 2: If the number left is 512, the maximum possible value of n is
(A) 1023
(B) 3667
(C) 267
(D) 288
(E) 66
Rationale: The given sequence is 1, 2, 3, ....n
After step 1, we have 2, 4, 6, 8, ......
After step 2, we have 4, 8, 12, 16, ....
After step 3, we have 8, 16, 24, 32, ......
After the last step (m th step) we have the highest power of 2m ≤ n.
1. If n = 1997, after step 10, we are left with only 1024 (as 210 ≤ 1997)
2. If the last number left is 512, the maximum possible value of n is 1023.
Answer:A
Answer: (A) 1023
Question: Find the fourth proportion to 2,3,6
(A) 18
(B) 12
(C) 9
(D) 4
(E) 6
Rationale: Explanation:
2:3 :: 6:x
=> 2/3 = 6/x
=> x = 18/2
=> x = 9
Answer:C
Answer: (C) 9
Question: What was the day of the week on 27th April, 2006?
(A) Monday
(B) Sunday
(C) Saturday
(D) Thursday
(E) Friday
Rationale: 28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days
Jan. Feb. March April
(31 + 28 + 31 + 27 ) = 117 days
117 days = (16 weeks + 5 day) 1 odd day.
Total number of odd days = (0 + 0 + 6 + 5) = 11 0 odd day.
Given day is Thursday.
Answer: Option D
Answer: (D) Thursday
Question: 4 men and 3 women are lined up in a row. What is the number of cases where they stand with each other in turn? (The number of cases in which men (or women) do not stand next to each other)
(A) 12
(B) 144
(C) 18
(D) 21
(E) 24
Rationale: The list should be WMWMW. Hence, from women 3! And men 4!, we get (3!)(4!)=144. Therefore, the correct answer is B.
Answer: (B) 144
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
(A) 15088
(B) 15086
(C) 15017
(D) 15000
(E) 15018
Rationale: The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000.Answer: D
Answer: (D) 15000
Question: The Italian size of a suit jacket is N centimeters, where N is the linear distance between the armpits when the jacket is laid on a flat surface. The American size of a suit jacket is P inches, where P is twice the linear distance between the armpits when the jacket is laid on a flat surface. If, for a particular jacket, N = P + 15, which of the following is closest to the value of N? (One inch is approximately 2.54 centimeters.)
(A) 36
(B) 47
(C) 58
(D) 68
(E) 72
Rationale: Since one inch is approximately 2.54 centimeters, then N centimeters is N/2.54 inches.
Next, since the American size (P inches) is twice the Italian size (N/2.54 inches), then P=2*N/2.54.
As given that N = P + 15, then N=2*N/2.54+15 --> N=~68.
Answer: D.
Answer: (D) 68
Question: A can do a piece of work in 4 days of 8 hours each and B alone can do it in 8 days of 8 hours each.how long will they take it to do working together
10 2/3 hours a day?
(A) 4 days
(B) 3 days
(C) 2 days
(D) 5 days
(E) 6 days
Rationale: A's work per hour=1/32
B's work per hour=1/64
A & B's work per hour together=(1/32)+(1/64)=3/64
so A & B together complete the work in 64/3 hours... if they work 10 2/3=32/3 hours a day,
it will take (64/3)/(32/3) days=2 days...
ANSWER: C
Answer: (C) 2 days
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 40 degrees. Find the temperature on Friday?
(A) 65 degrees
(B) 32 degrees
(C) 37 degrees
(D) 34 degrees
(E) 74 degrees
Rationale: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 40
Tu + W + Th = 192 -40 = 152
F = 184 – 152 = 32
Answer:B
Answer: (B) 32 degrees
Question: A certain industrial machine requires 15 quarts (480 ounces) of oil every day, and it is given a mixture of oil A and oil B. Oil A consists of 7% special additives while oil B consists of 10% special additives. If the machine needs exactly 30 ounces of the special additives to ensure smooth operation, then how much of oil A, in ounces, should be in the mixture?
(A) a.	A – 260
(B) b.	B – 280
(C) c. C – 290
(D) d.	D – 300
(E) e.	E – 600
Rationale: 7%*x + 10% *(480-x)=30
18 = 3 %*x
x=600
E
Answer: (E) e.	E – 600
Question: A rectangular plot has a concrete path running inner side of the plot is used as a lawn, which has an area of 432 sq.m. If the width of the path is 4 m and the length of the plot is greater than its breadth by 2m, what is the area of the rectangular plot?
(A) 980 m^2
(B) 975 m^2
(C) 984 m^2
(D) 960 m^2
(E) 965 m^2
Rationale: Let width of plot be 'b', length = b+2.
Then b(b+2) - (b-8)(b-6) = 432
Thus width = 30 m, length = 32 m and area = 960 sq.m
ANSWER:D
Answer: (D) 960 m^2
Question: Look at this series: 8, 43, 11, 41, __, 39, 17, ... What number should fill in the blank?
(A) 8
(B) 14
(C) 43
(D) 44
(E) 45
Rationale: Explanation: This is a simple alternating addition and subtraction series. The first series begins with 8 and adds 3; the second begins with 43 and subtracts 2.
Answer: Option B
Answer: (B) 14
Question: A trader sold an item at a loss of 35%. if he had increased the price by $80 he would have made a gain of 5%. what is the cost price of the item?
(A) $245
(B) $150
(C) $260
(D) $220
(E) $250
Rationale: Let C.P. be $x
Then 105% of x - 65% of x = 100
40% of x = 100
40/100 *x = 100
40x = 10 000
x = 250
Answer is E
Answer: (E) $250
Question: Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares ?
(A) 3
(B) 2
(C) 4
(D) 0
(E) 1
Rationale: Explanation :
If we let the four-digit number be XXYY, then this number can be expressed as:
1000X + 100X + 10Y + Y = 1100X + 11Y = 11(100X + Y) = k^2 (since it's a perfect square)
In order for this to be true, 100X + Y must be the product of 11 and a perfect square, and looks like X0Y. So now our question is "which product of 11 and a perfect square looks like X0Y?" We can test them:
11 x 16 = 176; 11 x 25 = 275; 11 x 36 = 396; 11 x 49 = 593; 11 x 64 = 704; 11 x 81 = 891
The only one that fits the bill is 704.
This means there is only one four-digit number that works, and it's 7744.
Answer : E
Answer: (E) 1
Question: The average age 9 members of a committee are the same as it was 4 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 20 years
(B) 21 years
(C) 18 years
(D) 29 years
(E) 36 years
Rationale: 9 * 4 = 36 years
Answer:E
Answer: (E) 36 years
Question: If the area of a square with sides of length 7 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?
(A) 4
(B) 8
(C) 12
(D) 13
(E) 18
Rationale: Let length of rectangle = L
7^2 = L*4
=> L = 49/4 = 13
Answer D
Answer: (D) 13
Question: When positive integer x is divided by positive integer y, the remainder is 7. If x/y = 86.1, what is the value of y?
(A) 72
(B) 71
(C) 70
(D) 30
(E) 45
Rationale: When positive integer x is divided by positive integer y, the remainder is 7 --> x=qy+7;
x/y=86.1 --> x=86y+0.1y (so q above equals to 86);
0.1y=7 --> y=70.
Answer: C.
Answer: (C) 70
Question: Alex can do a piece of in 120 days and peter can do same work in 180 days,both are working together for 30 days after that peter left the job. then in how many days Alex alone complete the remaining work?
(A) 17.5 DAYS
(B) 25 DAYS
(C) 15 DAYS
(D) 12 DAYS
(E) 30 DAYS
Rationale: First take LCM of (120,180) = 3600; Total work =3600; Alex's one day work = 3600/120 =30; peter's one day work =3600/180 = 20; One day work of both Alex+peter= 30+20 = 50; Total work completed in 30 days = 30*50=1500; remaining work is = 3600 - 1500 = 2100; remaining work completed by Alex in = 2100/120= 17.5 days. Answer =A
Answer: (A) 17.5 DAYS
Question: In an IT company, there are a total of 70 employees including 50 programmers. The number of male employees is 80, including 35 male programmers. How many employees must be selected to guaranty that we have 3 programmers of the same sex?
(A) 10
(B) 25
(C) 55
(D) 35
(E) 65
Rationale: You could pick 70 non-programmers, 2 male programmers, and 2 female programmers, and still not have 3 programmers of the same sex. But if you pick one more person, you must either pick a male or a female programmer, so the answer is 25.
B
Answer: (B) 25
Question: What is the sum of all possible solutions to |x - 4|^2 + |x - 4| = 20 ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 3
Rationale: Denote |x - 4| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x - 4|, so it's an absolute value and thus cannot be negative.
y = |x - 4| = 4 --> x = 8 or x = -1. The sum = 7.
Answer: D.
Answer: (D) 7
Question: The perimeter of an isosceles right triangle is 12 + 12 sq rt 2. What is the length of the hypotenuse of the triangle?
(A) 5
(B) 6
(C) 7
(D) 8.485
(E) 8
Rationale: side of triangle is a then perimeter = a+ a +a.sqrt2 ( right angle and pythagorus) =2a +a .sqrt 2 = 12 + 12 Sqrt2 or,
a. ( 2+ sqrt2) = 12(1 + sqrt2), a= 12*(1+sqrt2)/2+sqrt2 =12*2.414/3.414 = then hypotenuse = 8.485
D
Answer: (D) 8.485
Question: A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 5% on conveyance. If his savings at the end of the month is Rs. 3000, then his salary per month in rupees is:
(A) 20000
(B) 6000
(C) 8000
(D) 10000
(E) None of these
Rationale: Total expenditure = 40 + 25 + 15 + 5 = 85%
Saving = (100 - 85) = 15%
15/100 × Salary = 3000, Salary = 20000 Rs.
Answer:A
Answer: (A) 20000
Question: If (x + 1) times (4x + 1) is an odd integer, then x must be:
(A) an odd integer
(B) an even integer
(C) a prime number
(D) a composite number
(E) a negative integer
Rationale: Solution:
(x + 1) times (4x + 1) means (x + 1)(4x + 1)
(x + 1)(4x + 1) = 4x^2+5x+1
For 4x^2+5x+1 to be odd, 5x+1 must be odd since 4x^2 is always even.
So 5x must be even, hence x must be even.
Therefore x is an even integer.
Answer: B
Answer: (B) an even integer
Question: Q is not equal to zero and k = (Q x n - s)/2 find n?
(A) (2 x k + s)/Q
(B) (2 x s x k)/Q
(C) (2 x k - s)/Q
(D) (2 x k + s x Q)/Q
(E) (k + s)/Q
Rationale: k = (Q x n - s)/2
=> Q x n - s = 2 x k
=> Q x n = 2 x k + s
=> n = (2 x k + s)/Q
ANSWER:A
Answer: (A) (2 x k + s)/Q
Question: The average age of a committee of 9 members is 42 years. A member aged 63 years retired and his place was taken by another member aged 54 years . The average age of
present committee is;
(A) 39 years
(B) 38 years
(C) 36 years
(D) 41 years
(E) 37 years
Rationale: Total age of the committee = 42*9 = 378,
Total age when a member is retired
and a new one was joined = 378-63 +54, =369
Average age of present committee = 369/9 = 41.
ANSWER:D
Answer: (D) 41 years
Question: A certain university will select 1 of 6 candidates eligible to fill a position in the mathematics department and 2 of 9 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 216
(B) 212
(C) 214
(D) 210
(E) 120
Rationale: 1C6*2C9 = 6*36 = 216
the answer is (A)
Answer: (A) 216
Question: How many ways the letters of the word ‘ARMNUR’ can be arranged?
(A) 230
(B) 235
(C) 360
(D) 380
(E) 400
Rationale: Total number of letters = 6 and R is repeated twice.
Required arrangements = (6! / 2!) = 360
C
Answer: (C) 360
Question: The population of a city increases at the rate of 4% p.a. but there is an additional annual increase of 1% in the population due to some job seekers. The percentage increase in the population after 2 years is?
(A) 10.85%
(B) 10.85%
(C) 10.25%
(D) 10.20%
(E) 10.75%
Rationale: 100
5 ---- I
5
0.25 --- II
-----------
10.25%
Answer:C
Answer: (C) 10.25%
Question: Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards.
What is the probability that first two cards are queens and the third card drawn is an ace?
(A) 2
(B) 2/5525
(C) 2/5527
(D) 3
(E) None
Rationale: Let Q denote the event that the card drawn is queen and A be the event that
the card drawn is an ace. Clearly, we have to find P (QQA)
Now P(Q) = 4/52
Also, P (Q|Q) is the probability of second queen with the condition that one queen has
already been drawn. Now there are three queen in (52 - 1) = 51 cards.
Therefore P(Q|Q) = 3/51
P(A|QQ) is the probability of third drawn card to be an ace, with the condition
that two queens have already been drawn. Now there are four aces in left 50 cards.
Therefore P(A|QQ) = 4/50
By multiplication law of probability, we have
P(QQA) = P(Q) P(Q|Q) P(A|QQ)
= 4/52 × 3/51 × 4/50
= 2/5525.
Answer: Option 'B'
Answer: (B) 2/5525