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# CAT Number system Practice Problems Set 12

Question 1:
What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?
Topic: divisibility

[1] 666
[2] 676
[3] 683
[4] 777

Question 2:
Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs. 1.01 to three different persons?
Topic: Basics

[1] 19
[2] 20
[3] 17
[4] 18

Question 3:
What is the remainder when 496 is divided by 6?
Topic: Remainders

[1] 0
[2] 2
[3] 3
[4] 4

Question 4:
Consider the sets Tn = {n, n +1, n + 2, n + 3, n + 4} ,, where n = 1, 2, 3,…, 96. How many of these sets contain 6 or any integral multiple thereof (i.e. any one of the numbers 6, 12, 18, …)?
Topic: Divisibility

[1] 80
[2] 81
[3] 82
[4] 83

Question 5:
Let n (>1) be a composite integer such that $\sqrt n$is not an integer. Consider the following statements:

A: n has a perfect integer-valued divisor which is greater than 1 and less than $\sqrt n$

B: n has a perfect integer-valued divisor which is greater than $\sqrt n$ but less than n

Topic: Basics

[1] Both A and B are false
[2] A is true but B is false
[3] A is false but B is true
[4] Both A and B are true

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