# Number Theory Previous Year Questions (CAT) - Set 0011

• Previous years`s CAT questions: Number Theory

• Question 1

Let D be a recurring decimal of the form, D = 0.a1a2a1a2a1a2 ......., where digits a1 and a2 lie between 0 and 9. Further, at most one of them is zero. Then which of the following numbers necessarily produces an integer, when multiplied by D?

(1) 18

(2) 108

(3) 198

(4) 288        (CAT 2000)

• Question 2

If a1= 1 and an+1 = 2an+ 5, n = 1, 2 ... , then a100 is equal to

(1) (5 × 299 – 6)
(2) (5 × 299 + 6)
(3) (6 × 299 + 5)
(4) (6 × 299 – 5)
(CAT 2000)

• Question 3

(CAT 2000)

Â

• Question 4

If x > 2 and y > – 1, Then which of the following statements is necessarily true?

(1) xy > –2

(2) –x < 2y

(3) xy < –2

(4) –x > 2y      (CAT 2000)

• Question 5

(CAT 2000)

• Question 6

Let S be the set of prime numbers greater than or equal to 2 and less than 100. Multiply all elements of S. With how many consecutive zeros will the product end?

(1) 1

(2) 4

(3) 5

(4) 10     (CAT 2000)

• Question 7

Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?

(1) 0

(2) 9

(3) 3

(4) 6        (CAT 2000)

• Question 8

Each of the numbers x1, x2...., xn, n > 4, is equal to 1 or –1.
Suppose, x1x2x3x4 + x2x3x4x5 + x3x4x5x6 + ... + xn–3xn–2xn–1xn + xn–2xn–1xnx1+ xn–1xnx1x2 + xnx1x2x3= 0, then,

(1) n is even.

(2) n is odd.

(3) n is an odd multiple of 3.

(4) n is prime                 (CAT 2000)

• Question 9

The integers 34041 and 32506 when divided by a three-digit integer n leave the same remainder. What is n?

(1) 289

(2) 367

(3) 453

(4) 307       (CAT 2000)

• @mbatious (2^99*6-5)

• @mbatious (34041-32506) = 1535
307*5 = 1535
Hence option 4

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