If a, b, and c are all integers divisible by 3 and a b c 0, then

Question

If a, b, and c are all integers divisible by 3 and a > b > c > 0, then which of the following must be divisible by 3?

I. a+b+c

II. a-b+c

III. abc/9

A) I only

B) III only

C) I and II

D) I and III

E) I, II, and III

Cez005 · Accepted Answer

I. a+b+c Addition and subtraction between multiples of a number result in a multiple of that number. Therefore, 3 multiples of 3 added together give another multiple of 3.

II. a-b+c Addition and subtraction between multiples of a number result in a multiple of that number. Note that the resulting multiple must be +ve, since a>b. However, even if the resulting multiple was -ve, it would still be divisible by 3. E.g. a=9, b=18, c=3, a-b+c=-6. -6/2=-3.

III. abc/9 Here, we're multiplying at least 3 powers of 3 and dividing by 2 powers of 3. This leaves at least one power of 3 and therefore the result will be divisible by 3.

Agree, give kudos! Have an improvement, please comment.

mogarza08 · Answer

I'm having difficulty understanding why answer is E and not D.

The question does not specify that negative numbers can't be used, in which case if we use a=6 b=3 and C=-3 , statement II would be insufficient since 0 is not divisible by 3. Can someone clarify?

Thanks in advance.

warriorguy · Answer

As per the question, a>b>C>0 so c=-3 is not greater than 0. Also, 0 is divisible by every integer except 0 itself.

PGTLrowanhand · Answer

Hi GMATters,

Here's my video explanation of the problem:

2Y6Yo5kUBhs

Enjoy!

Rowan

mogarza08 · Answer

Thank you all who responded. It's these little things I need to make sure I don't overlook on test day. Small detail missed = wrong solution

GAURI2828 · Answer

I think its provided that all are positive number in this sentence a > b > c > 0,

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If a, b, and c are all integers divisible by 3 and a > b > c > 0, then

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 Problem Solving (PS) Questions