What is the remainder when positive integer n, where n≥5, is divided b

Question

What is the remainder when positive integer  n , where  n≥5 , is divided by 3?
1) When  n  is divided by 6 the remainder is 5
2)  n-2  is a multiple of 9

IanStewart · Answer

You can very quickly persuade yourself the answer is D just by finding a few values n can equal, and there's nothing wrong with that sort of approach for this type of question.

Conceptually, since every multiple of 6 is a multiple of 3, Statement 1 tells us n is 5 greater than some multiple of 3. But multiples of 3 are equally spaced; if n is 5 greater than one multiple, it's 2 greater than another, which means we'll get a remainder of 2 when we divide n by 3. So Statement 1 is sufficient.

Statement 2 tells us n is 2 greater than some multiple of 9, which means precisely that the remainder is 2 when we divide n by 9. But any multiple of 9 is also a multiple of 3, so n is 2 greater than a multiple of 3, and the remainder is 2 when we divide n by 3. So Statement 2 is also sufficient and the answer is D.

Tonkotsu · Answer

I would re-write this problem to fit this form:

\frac{n}{3} = Q + \frac{x}{3}

Where Q is a quotient and x is the remainder. Goal is to find x under the LHS conditions.
This has always been helpful for me when seeking for a remainder.

1) When  n  is divided by  6  the remainder is  5

This gives us  \frac{n}{6} = Q + \frac{5}{6}

which fits the form above if we multiply both sides by 2:

\frac{n}{3} = 2* Q + \frac{5}{3}

\frac{5}{3} = 1 + \frac{2}{3}  giving us a remainder of 2  sufficient.

2)  n−2  is a multiple of  9

If we know  n-2  is a multiple of 9, then  n-1  and  n  are multiples of 10 and 11, respectively.
We can also remember that remainders of a particular multiple will always repeat itself, hence we can figure out the remainder by simply dividing  \frac{11}{3} = 3\frac{2}{3}  .  sufficient.

gmatcafe · Answer

1) When n is divided by 6 the remainder is 5. 
n=6a+5 ---> 6a is divisible by 3. The remainder when 5 is divided by 3 is 2. So the remainder when n is divide by 3 is 2.  Sufficient

2) n−2 is a multiple of 9.
n-2=9a
n=9a+2 ----> 9a is divisible by 3. The remainder when 9a+2 is divide by 3 is 2.  Sufficient. D)

IanStewart · Answer

Be careful here -- that's only rarely true. If n-2 is a positive multiple of 9, then n is one of these numbers:

11, 20, 29, 38, 47, 56, ...

and notice in this list that only the first number, 11, is a multiple of 11. You'd actually need to extend this list to 1001 to find the next number where n is a multiple of 11, n-1 is a multiple of 10, and n-2 is a multiple of 9.

What is the remainder when positive integer n, where n≥5, is divided b

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

What is the remainder when positive integer n, where n≥5, is divided b

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards