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1.

ln a bank the account numbers are all 8 digit numbers, and they all start with the digit 2. So, an account number can be represented as 2x₁ x₂ x₃ x₄ x₅ x₆ x₇ . An account number is considered to be a ‘magic’ number if x₁ x₂ x₃ is exactly the same as
x₄ x₅ x₆, or x₅ x₆ x₇ or both. x_i can take values from 0 to 9, but 2 followed by seven 0s is not a valid account number. What is the maximum possible number of customers having a ‘magic’ account number? (3 marks)
(1) 9989
(2) 19980
(3) 19989
(4) 19999
(5) 19990

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The micromanometer in a certain factory can measure the pressure inside the gas chamber from 1 unit to 999999 units. Lately this instrument has not been working properly. The problem with the instrument is that it always skips the digit 5 and moves directly from 4 to 6. What is the actual pressure inside the gas chamber if the micromanometer displays 0030l6? (3 marks)
(1) 2201
(2) 2202
(3) 2600
(4) 2960
(5) None of the above options

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Little Pika who is five and half years old has just learnt addition. However, he does not know how to carry. For example, he can add 14 and 5, but he does not know how to add 14 and 7. How many pairs of consecutive integers between 1000 and 2000 (both 1000 and 2000 included) can Little Pika add? (2 marks)
(1) 150
(2) 155
(3) 156
(4) 258
(5) None of the above

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From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.

[1]	Which position should a contender choose if he has to be the leader? (5 marks) (1) 3 (2) 67 (3) 195 (4) 323 (5) 451

[2]

One of the contending politicians, Mr. Chanaya, was quite proficient in calculations and could correctly figure out the exact position. He was the last person remaining in the circle. Sensing foul play the politicians decided to repeat the game. However, this time, instead of removing every alternate person, they agreed on removing every 300th person from the circle. All other rules were kept intact. Mr. Chanaya did some quick calculations and found that for a group of 542 people the right position to become a leader would be 437. What is the right position for the whole group of 545 as per the modified rule?
(5 marks)

(1) 3
(2) 194
(3) 249
(4) 437
(5) 543

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5.

Let an = 1 1 1 1 1 1 1….. 1, where 1 occurs n number of times. Then,
i. a741 is not a prime.
ii. a534 is not a prime.
iii. a123 is not a prime.
iv. a77 is not a prime. (5 marks)

(1) (i) is correct.
(2) (i) and (ii) are correct.
(3) (ii) and (iii) are correct.
(4) All of them are correct.
(5) None of them is correct.

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6.

a, b, c, d and e are integers such that 1 ≤ a < b < c < d < e. If a, b, c, d and e are geometric progression and lcm(m, n) is the least common multiple of m and n, then the maximum value of
1/lcm(a,b) + 1/lcm(b,c) + 1/lcm(c,d)+ 1/lcm(d,e) is
1). 1
2). 15/16
3). 79/81
4). 7/8
5). None of the above

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