## QBM034

Q1. The remainder obtained when a prime number greater than 6 is divided by 6 is: (1) 1 or 3

(2) 1 or 5

(3) 3 or 5

(4) 4 or 5
Q2. N = (A7A)17 is a perfect square. Which of the following statement is FALSE? (1) A is an even digit.

(2) A is divisible by 3.

(3) When N is divided by 13 we get remainder 3.

(4) None of these
Q3. ABC is a three-digit number in which A, B and C are three different prime digits. The number formed by the first two digits, i.e. AB and the numbers formed by the last two, i.e. BC, are also prime numbers. Find the sum of the digits of the number.
(1) 12

(2) 15

(3) 21 or 15

(4) None of these
Q4. A group of people buy larks together (on a lark.) If each person paid 9 Franc, there would be 11 Franc left over after the purchase. If, however, each person contributed only 6 Franc, there would be a shortfall of 16 Franc. How many people are in the group?
(a) 10

(b) 11

(c) 12

(d) 13 (e) None of the above
Q5. A 7 foot ladder is leaning against a wall and just resting on a box which is 1 foot on a side. See figure. Precisely how high up the wall is the ladder sitting, assuming it is touching higher up the wall than it is out from the wall? The answer must be exact, no approximations!
Q6.How may number of squares with total area less than or equal to 1/2 can be packed into a square S of area 1 (in such a way that any point belonging to two of the packed squares is on the boundary of both).
a. 1

b.2

c.Any

d. None
Q7. Suppose a type of glass is such that:
70% of light shining from one side is transmitted through to the other.

20% of the light is reflected.

The remaining 10% is absorbed in the glass.

How much of an original light source will be transmitted through 3 panes of glass?
Q8. rhombus, ABCD, has sides of length 10. A circle with center A passes through C (the opposite vertex.) Likewise, a circle with center B passes through D. If the two circles are tangent to each other, what is the area of the rhombus?
Q9. In a race of 200 meters, A beats S by 20 meters and N by 40 metres. If S and N are running a race of 100 metres with exactly the same speed as before, then by how many metres will S beat N?
(1)11.11 metres

(2) 10 metres

(3) 12 metres

(4) 25 metres
Q10. A mother purchase three shirts of the same color but of different size for her three sons. All the three shirts were kept in a box in a dark room. The three boys took one shirt each at random from the box. What is the probability that none of the boys this own shirt?
(1)1/2

(2)1/3

(3)2/3

(4)1/4
Q11. A square flat piece of metal was used to construct a 2-inch high open box. This was accomplished by cutting 2-inch by 2-inch squares from each corner and folding up the sides. The resulting box holds 18 cubic inches. How wide was the original square?
(a)6 inches

(b) 7 inches

(c) 8 inches

(d) 9 inches

(e) None of the above
Q12. Predict the next number in the sequence 1, 2, 4, 7, 11, 16, 22, 29, 37, 46,
a.55

b.56

c.57

d.58

e.59
Q13. A man can do a piece of work in 60 hours. If he takes his son with him and both work together then the work is finished in 40 hours. How long will the son take to do the same job, if he worked alone on the job?
A.20 hours

B.120 hours

C.24 hours

D.None of these
Q14.What is the ratio of the sides of the inner and outer square, where the boundaries of the inner square are lines drawn from the vertices of the square to the midpoint of the opposite side.
1) 1:2

2) 1:3

3) 1: √(5)

4) None of these
Q15. Given that x is a positive integer prove that f(x) = x^{2} + x + 1 will never divide by 5.
Q16. If Ram and Shyam can do a piece of work in 15 days, Shyam and Sohan in 20, and Sohan and Ram in 30 days. Ram, Shyam and Sohan can individually do the work respectively in how many days?
a) 12, 10, 13

b) 60, 20, 45

c) 40, 24, 120

d) 10, 12, 15
END

## My Answers

Q1. ANS: 1

Q2. ANS: 3

Q3. ANS: 3

Q6. ANS: ANY

Q8. Ans: 4

Q9. Ans: 3

Q12. ANS: B

Q13. Answer: 3

Q16. ANS: C