## QBM035

Q1. A person starts from the origin of the coordinate axis. He travels in
this pattern. 1 unit to right , (1/2) units up , (1/4) units right, (1/8)
units down , and continues the above pattern . At what point will he
ultimately come to stop?
(a)(4/3,2/5)

(b)(3/2,4/3)

(c)(2/5,4/3)

(d)(4/5,4/3)
Q2. Each meal costs Rs. 9 in a hotel. If one takes a monthly coupon (1 meal a day and 30 days a month), the total cost is Rs. 225. The discount per meal is
1)16 2/3%

2)Re 1

3) Rs 45

4) 15%
Q3. Three bells chime at an interval of 18, 24 and 32 minutes respectively. At a certain time they begin to chime together. What length of time will elapse before they chime together again?
(1) 2 hours 24 minutes

(2) 4 hours 48 minutes

(3) 1 hour 36 minutes

(4) 5 hours
Q4. A mathematics professor and four mathematics students are in a square room, 10 feet on a side. The four students are stationed at the room's four corners, each student armed with a water pistol having a range of 10 feet. What is the area of that portion of the room in which the professor is simultaneously in range of all four water pistols?
Q5. Several years ago, three suitors from three countries were vying for the hand of a lovely maiden. They agree to fight a pistol duel under the following conditions:
Q6. Let Hn = 1/1 + 1/2 + ... + 1/n.
Show that, for n > 1, H_{n}is not an integer.
Q7. When Darby remarked that the apples seemed very small this week, the seller offered to throw an extra apple into the dollar basket. Darby noted that this reduced the price per dozen by 5 cents and she then purchased the basket. How many apples did she get for her dollar?
(a)15

(b)16

(c)17

(d)18

(e) None of the above
Q8. What units digits exist in the product of all prime numbers between 10 and 30?
(1)5

(2)4

(3)3

(4)2
Q9. A tree was planted when it was 4 feet tall and thereafter grew an equal number of feet each year. At the end of 6 years it was twice as tall as it had been at the end of 2 years. How tall was the tree at the end of 4 years?
(a)12 feet

(b)13 feet

(c)14 feet

(d)15 feet

(e) None of the above
Q10. The captain of a luxury cruise ship wants to install windshield wipers on the portholes of the ship. The straight wipers are to be attached at a point on the circumference of the circular portholes, furthermore, the entire length of the blade must remain in contact with the flat glass at all times. How long should the wiper blade be so as to clean half of the porthole?
Q11. One may perform the following two operations on a natural number:

1. Multiply it by any natural number;

2. Delete zeros in its decimal representation.

For any natural number n, can one perform a sequence of these operations that will transform n to a one-digit number.
Q12. In an attempt to copy down from the board a sequence of six positive integers in Arithmetic Progression, a student wrote down the five numbers,
113, 137, 149, 155, 173
accidentally omitting one. He later discovered that he also miscopied one of them. Which number was miscopied?
1) 137

2) 149

3) 155

4) 173
Q13. How many whole numbers between 200 and 700 begin and/or end with 3? a. 150

b.160

c.140

d.170

e.None of these
Q14. Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How long will a woman take to do the job, if she works alone on it?
A. 18 days

B. 36 days

C. 54 days

D. None of these
Q15.It is between 2 and 3 o' clock, and in 10 minutes the minute hand will be as much after the hour hand as it is behind it now, what is the time (in minutes, post 2 o'clock)?
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## Answers

Q1. answer (a)

Q3. ANS: 2

Q4. ANS:

Q8 ANS: 3

Q15. ANS: 5 10/11 min