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1. A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?

(1) 2 ≤ x ≤ 6
(2) 5 ≤ x ≤ 8
(3) 9 ≤ x ≤ 12
(4) 11≤ x ≤ 14
(5) 13 ≤ x ≤ 18

Directions for Questions 2 and 3:

Let f(x) = ax2 + bx + c, where a, b and c are certain constants and a ≠ 0. It is known that f (5) = −3f (2) and that 3 is a root of f(x) = 0.

2. What is the other root of f(x) = 0?

(1) −7
(2) − 4
(3) 2
(4) 6
(5) cannot be determined

3. What is the value of a + b + c?

(1) 9
(2) 14
(3) 13
(4) 37
(5) cannot be determined

4. The number of common terms in the two sequences 17, 21, 25, … , 417 and 16, 21, 26, … , 466 is

(1) 78
(2) 19
(3) 20
(4) 77
(5) 22

5. Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is

(1) 60
(2) 75
(3) 45
(4) 90
(5) 72

1. The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10 n, on the nth day of 2007 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal?

(a) June 30
(b) May 21
(c) April 11
(d) May 20
(e) April 10

Ans: (d)

2. A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10?

(a) -105
(b) –119
(c) –159
(d) –110
(e) -180

Ans: (c)

3. Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?

(a) Between 0 and 45
(b) Between 0 and 90
(c) Between 0 and 30
(d) Between 0 and 60
(e) Between 0 and 75

Ans: (d)

6. The maximum guaranteed return to Shabnam is

(a) 0.30%
(b) 0.25%
(c) 0.10%
(d) 0.20%
(e) 0.15%

Ans: (d)

7. What strategy will maximize the guaranteed return to Shabnam?

(a) 30% in option A, 32% in option B and 38% in option C
(b) 100% in option A
(c) 36% in option B and 64% in option C
(d) 64% in option B and 36% in option C
(e) 1/3 in each of the three options

Ans: (c)

DIRECTIONS for questions 1 to 5: Answer these questions on the basis of the information given below.

Two traders, Chetan and Michael, were involved in the buying and selling of MCS shares over five trading days. At the beginning of the first day, the MCS share was priced at Rs. 100, while at the end of the fifth day it was priced at Rs. 110. At the end of each day, the MCS share price either went up by Rs. 10, or else, it came down by Rs. 10. Both Chetan and Michael took buying and selling decisions at the end of each trading day. The beginning price of MCS share on a given day was the same as the ending price of the previous day. Chetan and Michael started with the same number of amount of cash, and had enough of both, Below are some additional facts about how Chetan and Michael traded over the five trading days.

• Each day if the price went up, Chetan sold 10 shares of MCS at the closing price. On the other hand, each day if the price went down, he bought 10 shares at the closing price.

• If on any day, the closing price was above Rs. 110, then Michael sold 10 shares of MCS, while if it was below Rs. 90, he bought 10 shares, all at the closing price.

1. If Chetan sold 10 shares of MCS on three consecutive days, while Michael sold 10 shares only once during the five days, what was the price of MCS at the end of day 3?

(a) Rs 90

(b) Rs 100

(c) Rs 110

(d) Rs 120

(e) Rs 130

Ans: (c)

2. If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of the share at the end of day 3?

(a) Rs 90

(b) Rs 100

(c) Rs 110

(d) Rs 120

(e) Rs 130

Ans: (a)

3. What could have been the maximum possible increase in combined cash balance of Chetan and Michael at the end of the fifth day?

(a) Rs 3700

(b) Rs 4000

(c) Rs 4700

(d) Rs 5000

(e) Rs 6000

Ans: (d)

4. If Chetan ended up with Rs 1300 more cash than Michael at the end of day 5, what was the price of MCS share at the end of day 4?

(a) Rs 90

(b) Rs 100

(c) Rs 110

(d) Rs 120

(e) Not uniquely determinable

Ans: (b)

5. If Michael ended up with Rs 100 less cash than Chetan at the end of day 5, what was the difference in the number of shares possessed by Michael and Chetan (at the end of day 5)?

(a) Michael had 10 less shares than Chetan.

(b) Michael had10 more shares than Chetan.

(c) Chetan had 10 more shares than Michael.

(d) Chetan had 20 more shares than Michael.

(e) Both had the same number of shares.

Ans: (e)

DIRECTIONs For questions 1 to 6 : Answer the questions independently of each other.

1. A chemical plant has four tanks (A, B, C and D) each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows:

From A to B @20 litres/minute From C toA@ 90 litres/minute

From A to D @ 10 litres/minute From C to D @ 50 litres/minute

From B to C @ 100 litres/minute From D to B @ 110 litres/minute

Which tank gets emptied first, and how long does it take (in minutes) ,) get empty after pumping starts?

(a) A, 16.66

(b) C,20

(c) D,20

(d) D,25

Ans: (C)

4. What is the distance in em between two parallel chords oflengths 32 cm and 24 cm in a circle ofradius 20 cm?

(a) 1 or 7

(b) 2 or l4

(c) 3 or 21

(d) 4 or 28

Ans: (D)

5. For which value of k does the following pair of equations yield a unique solution for x such that the solution is positive?
x2-y2=0
(x-k)2+y2=1

(a) 2

(b) 0

(c) √2

(d) -√2

Ans: (c)

6. If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a remainder of

(a) 0

(b) 1

(c) 69

(d) 35

Ans: (A)







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