Integers

[danjuma]

3. Is the integer n a multiple of 15?

a. n is a multiple of 20
b. n+6 is a multiple of 3

[beatthegmatinsept]

IMO C.
From a) we know 2, 2 and 5 are factors of n
From b) we know 3 is a factor of n

In order for n to be a multiple of 15, n should have factors: 3 and 5

Together a and b give you 2, 3 and 5 as factors of n. Hence Sufficient.

[Gurpinder]

3. Is the integer n a multiple of 15?

a. n is a multiple of 20
b. n+6 is a multiple of 3

yes/no question

(a) prime factors of n are 5,2,2 and more....... hence insufficient by itself. if we had a 3, then this one would be sufficient.
(2) since 6 is also a multiple of 3, n+6 is also a multiple of 3. which means that n is a multiple of 3.

now n can be 3 which is a multiple of 3 but not 15. or n can be 15 which is a multiple of 3 and 15.

hence insufficient.

together:

we know that n+6 is a multiple of 3. hence the prime factors of n has a 3 in it.

so taking 5,2,2 and 3 from (b), we can make a 15. hence n is a multiple of 15.

hence (c)