Explanation please

[bburton11]

Please provide explanations to the attached problems. Of note, the correct answers are in bold

[raleigh]

Problem: Is n a multiple of 15?

(1) n is a multiple of 20.
(2) n + 6 is a multiple of 3.

(1). n = 20 is not a multiple of 15. n = 60 is a multiple of 15. So (1) is insufficient.

(2) n = 3. Certainly 3 + 6 = 9 is a multiple of 3, but 3 is not a multiple of 15. Now try n = 15. 15 + 6 = 21 is a multiple of 3 and 15 is a multiple of 15. So (2) is insufficient.

(1) and (2) together:
(1) implies that n = 20a where a is an integer.
(2) implies that n + 6 is divisible by 3.

Substitute (1) into (2) and we get 20a + 6 is divisible by 3. So 3 divides 20a and 3 divides 6. 3 divides 6 doesn't give us anything, so let's look at what we get from the fact that 3 divides 20a.

This means that 3 divides 20 or 3 divides a. Three does not divide 20 so 3 must divide a. So a = 3b where b is an integer.

Substitute that into (1) and we get that n = 20*3b = 60b. 15 divides 60, so n=60b is a multiple of 15.

The answer is C.

[raleigh]

What is the value of 2x+2y?
(1)3x+3y=60
(2)5x+3y=68

(1) Multiple both sides by 2/3. You get that 2x + 2y = 40.

So (1) is sufficient.

(2) Choose y so that 3y ends with an 8. So choose y = 6 so 3y = 18. Then x = 10. Note that 2x + 2 y = 2*10 + 2*6 = 20 + 12 = 32.

Now choose another value of y so that 3y ends with an 8. Choose y=16 so 3y=48. Then x=4. Note that 2x + 2y = 2*4 + 2*16 = 8 + 32 = 40.

So (2) is insufficient.

Correct answer is A.