CAT 2025 Lesson : Class Discussion: Numbers - Factors & Remainders: 9 to 16

Question 9

How many numbers between 200 and 350 exist such that the number when divided by 8 leaves a remainder of 3?

Answer: 19

Question 10

Where

x

is a natural number and

x > 3

, for how many values of

x

will

x – 3

perfectly divide

x^{5} – x^{3} + 6

?

Answer: 8

Question 11

When a certain number is successively divided by 6, 2 and 3, we get remainders of 4, 1 and 1 respectively. What is the remainder we get when the number is divided by 9?

		0
		2
		4
		Cannot be determined

Question 12

When each of 110, 182 and 290 are divided by a positive integer

x

, the remainder we get is 2. How many values can

x

take?

		7
		9
		11
		13

Question 13

What is the remainder when

3^{1} + 3^{2} +3^{3} + ... + 3^{50}

is divided by 28?

Answer: 12

Question 14

What is the largest 3-digit number that leaves a remainder of 8 when divided by 12 and a remainder of 4 when divided by 14?

Answer: 956

Question 15

What is the remainder when

156^{156}

is divided by 17?

Answer: 4

Question 16

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

n

?
[CAT 2000]

		289
		367
		453
		307

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