joyseychow wrote:If n is a positive integer and r is the remainder when 4+7n divided by 3, what is the value of r?
(1) n+1 is divisible by 3
(2) n>20
Help! I always have difficulty with remainders.
Picking numbers is a very efficient way to solve number property DS questions.
From the question stem, we know that (4+7n)/3 has a remainder of r; we want to know that value. What do we need? Information about n.
1) n+1 is a multiple of 3.
If n=2 (we're allowed to pick 2 since 2+1 is a multiple of 3), then (4+14)/3 = 18/3 = 6rem0
If n=5 (we're allowed to pick 5 since 5+1 is a multiple of 3), then (4+35)/3 = 39/3 = 13rem0
at this point you might already be conviced that you'll always get the same answer, but we could try one more just to be safe:
If n=8 (we're allowed to pick 8 since 8+1 is a multiple of 3), then (4+56) = 60/3 = 20rem0
For all 3 plug-ins we get r=0.. sufficient!
2) n > 20
If n=21, then (4+147)/3 = 151/3 = 50rem1
Note: if you really understand DS, you can actually stop right now. Here's a fundamental rule to remember:
If the answer is (D), then both statements will always give the same answer to the question.
Since we got a remainder of 1, and since statement (1) guaranteed a remainder of 0, we know that (2) cannot be sufficient!
However, if you don't see that logic, then you just pick another number:
If n=22, then (4+154)/3 = 158/3 = 52rem2.
(2) has now given us r=1 AND r=2; more than one possible value, therefore insufficient.
(1) is suff, (2) is infuff: choose A!
