Please provide explanations to the attached problems. Of note, the correct answers are in bold
- Attachments
-
- Data 1.docx
- (11.03 KiB) Downloaded 117 times
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.
