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- If the product of even integer A and odd integer B is 630, where A≠2, B≠1 and A, B > 0, then which of the following must be true?

Select__all__that apply.

- The largest value of A is 210
- B is a multiple of 3
- The smallest difference between A and B is 9

Answer: A, C

630 = 2 x 3 x 3 x 5 x 7

We are looking for statements which are DEFINITELY TRUE.

A: B≠1 and is odd so B can be 3 and A = 210

B: One of A and B must be multiple of 3 but it can be A alone A = 18, B = 35

C: A = 30 and B = 21 the smallest difference is 9

- If a + b – ab = 0 , which of the following CANNOT be a value of b ?

- 2
- 1
- 0
- -1
- -2

Answer: B

a + b – ab = 0

a(1-b) + b = 0

a = b / b−1

for b = 1 a is undefined so b cannot be 1

- When the integer N is divided by 12, the remainder is 3. Which of the following, when divided by 12, will have a remainder of 6?

Select__all__that apply.

- 2N
- 6N
- 4N + 6

Answer: A, B, C

N divided by 12 leaves remainder of 3

So N is of the form 12k + 3

A: 2N = 24k + 6 remainder: 6

B: 6N = 72k + 18 remainder: 6

C: 4N + 6 = 48k + 12 + 6 = 48k + 18 remainder: 6

- What is the smallest positive integer n for which 400 is a factor of 10
^{n}?

Answer: C

400 = 16 x 25 = 2^{4} x 5^{2}

10^{n} = 2^{n} x 5^{n}

Since we need at least 4 for the power of 2 so n = 4

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- 3a + 5
- 3a – 9
- 3a + 10
- 3a – 4
- 3a + 4

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