If a, b and c are integers, is abc divisible by 4?

Question

(1) a + b + 2c is even.
(2) a + 2b + c is odd.

Hi Everyone,

Not sure if this has been posted before, but here is my question: I'm using the manhattan gmat advanced quant book (just because I tried doing a GMAT practice test and found that I wasn't doing as well as I hoped on the quant - 70th percentile) and I found the suggestion to use scenario charts very interesting. However, when I try using them, I can't get my time to go below 3:30s to 4 mins which I know is too long to be working on any one problem.
I'm sure people have had success with the tool, which is why MGMAT recommends it; however, does anyone have any idea on how to use the chart more efficiently?

As an example:
I'm using the chart for try-it problem 4-7 in the MGMAT advanced quant book:
If a,b and c are integers, is abc divisible by 4?

(1) a + b + 2c is even.
(2) a + 2b + c is odd.

I have 5 columns: a, b, c, 4th column: to ensure a+b+2c is even and 5th column to check if abc is divisible by 4. I try different values for a, b and c and etc till I find whether abc is always divisible by 4 or not.

MGMAT suggests to look at a, b and c as O/E numbers. I find this would not have been intuitive for me (since the question asks "is it divisible by 4," I would automatically start by trying out numbers.)

Anyways, if anyone has some tips or something that you think I should do different, please feel free to share. Any help will be appreciated!

Thanks!!

Bunuel · Accepted Answer

If a, b and c are integers, is abc divisible by 4? (1) a + b + 2c is even --> a+b+2c=even --> a+b+even=even --> a+b=even-even=even --> a and b are either both odd or both even. Not sufficient. (2) a + 2b + c is odd --> a+2b+c=odd --> a+even+c=odd --> a+c=odd-even=odd --> a is odd and c is even or vise-versa. Not sufficient. (1)+(2) If a and b are both odd (satisfies the first statement) and c is even but not a multiple of 4, then abc is NOT divisible by 4 but if a and b are both odd and c is a multiple of 4 (so even), then abc IS divisible by 4. We already have two different answers, thus no need to consider the case when a and b are both even. Not sufficient. Answer: E. As for improving your score and speeding up, check under the spoiler: ALL YOU NEED FOR QUANT: new-to-the-math-forum-please-read-this-first-140445.html HOW TO IMPROVE YOUR QUANT SCORE Improving from 30-35 to 40-44 Improving from 44 to 50 Other discussions dedicated to this issue: quant-strategy-to-go-from-q47-to-q50-q51-137078.html i-m-getting-a-consistent-q-48-49-i-m-an-engg-student-and-134999.html 3-weeks-to-increase-quant-score-134473.html improving-q-from-a-50-to-a-145212.html the-final-climb-quest-for-q-50-from-q47-129441.html help-need-for-quant-150311.html hitting-the-wall-please-share-your-prep-experience-150112.html how-to-improve-quant-score-137975.html need-pointers-to-move-q42-43-q50-148568.html a-way-to-increase-from-q35-40-to-q-138750.html do-i-need-to-change-the-way-i-study-110611.html several-people-has-asked-me-if-it-is-possible-to-improve-40820.html gmat-in-less-than-4-weeks-desperately-need-quant-advice-127092.html stuck-at-47-test-in-a-month-137521.html improve-gmat-score-from-620-to-700-need-urgent-help-144530.html calling-quant-experts-need-a-strategy-to-improve-146045.html final-weeks-calculation-silly-errors-and-speed-129408.html knocked-down-by-the-gmat-for-the-second-time-150350.html several-people-has-asked-me-if-it-is-possible-to-improve-40820.html how-to-improve-your-quant-from-q44-to-q50-141670.html help-gmat-in-3-days-134350.html HOW TO SPEED UP Want to speed up? Check this: Timing Strategies on the GMAT Other discussions dedicated to this issue: for-non-quant-beasts-128188.html how-to-speed-up-answering-math-questions-19365.html having-trouble-finishing-quant-section-any-ideas-110613.html ds-and-timing-help-108310.html final-weeks-calculation-silly-errors-and-speed-129408.html Hope it helps. P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay arrention to the rules 3 and 7. Thank you.

ankurgupta03 · Answer

Hi,

i you try to put numbers and then find out the answer you will have to make too many sets, which will be very cumbersome and time consuming.

I would directly approach the problem by looking for odd or even numbers.
I would suggest that whenever you find such problems, try to do in terms of odd or even only. 
If it is asked that the number is divided by 6, then try for 2 and 3 both.

Hope it helps!!

Regards,
Ankur

Marcab · Answer

I shall say, be flexible.

statement 1 says: either a & b are both even OR a & b are both odd.
a=3, b=3 c=2 Answer is NO
a=3, b=3, c=4 Answer is YES

Not sufficient

statement 2 says: a+c is odd.
so either of a or c is even
Still insufficient.

On combining both of these info, we are still not sure if any of these is an even multiple of 2.
Not sufficient.
+1 E

dukenukem · Answer

Thank you! And also thanks for those links Bunuel!

Posted from my mobile device

dukenukem · Answer

And apologies, spoiler: You guys are right! E is the right answer. wow so many ways to get there

(sad face only cause I didn't realize there were so many methods when solving myself!) Posted from my mobile device

FWU · Answer

Can't we solve this problem by knowing that a, b, or c could be zero? Zero is an integer and it is even.

EMPOWERgmatRichC · Answer

Hi FWU,

YES, you COULD use 0 in any of your TESTs and come up with a quick "YES" answer. You still have to be thorough enough with your work to find one of the various "NO" answers that also exists though, so that you can get to the correct answer.

GMAT assassins aren't born, they're made,
Rich

fskilnik · Answer

a,b,c\,\,{m{ints}}\,\,\,\,\left( * ight)

{{abc} \over 4}\,\,\mathop = \limits^? \,\,{\mathop{m int}}

\left( {1 + 2} ight)\,\,\,\,

\left( 1 ight)\,\,\,{{a + b + 2c} \over 2} = {\mathop{m int}} \,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * ight)} \,\,\,\,\,\,{{a + b} \over 2} = {\mathop{m int}} \,\,\,\,

\left( 2 ight)\,\,\,{{a + 2b + c} \over 2} 
e {\mathop{m int}} \,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * ight)} \,\,\,\,\,\,{{a + c} \over 2} 
e {\mathop{m int}}

\left\{ \matrix{
 \,{m{Take}}\,\,\left( {a,b,c} ight) = \left( {0,0,1} ight)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{m{YES}}} ightangle \,\, \hfill \cr 
 \,{m{Take}}\,\,\left( {a,b,c} ight) = \left( {1,1,2} ight)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{m{NO}}} ightangle \hfill \cr} ight.\,\,\,

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

TheUltimateWinner · Answer

Official Explanation:  
Evaluate the possible odd/even combinations of a, b, and c using Scenario Charts to determine the answer to the question.
(1) INSUFFICIENT: 2c must be even because c is an integer. This statement implies that a + b = Even, which occurs when a and b have the same odd/even parity. (There is no constraint on c.) An efficient Scenario Chart might look like this:  Please see the attachment (Statement 1 image)

(2) INSUFFICIENT: 2b must be even because b is an integer. Thus, this statement implies that a + c = Odd, which occurs when a and c have opposite odd/even parity. (There is no constraint on b.) --> Please see the attachment (Statement 2 image)

(1) AND (2) INSUFFICIENT: From (1) you know that a and b have the same odd/even parity, while from (2) you know that a and c have opposite odd/even parity.-->  Please see the attachment (Statement 1&2 image) 
Even with these constraints, you do not have a definitive answer to the question.  The correct answer is (E). 
Notice that in evaluating statements (1) and (2) together, you would not need to write a completely new Scenario Chart. You can reuse the work from statement (1) and statement (2) to determine the answer (for instance, by circling the scenarios in one chart that also appear in the other chart). Just be careful as you do this! Know what case you're considering.

TheUltimateWinner · Answer

fskilnik 
Sir, could you tell me how did you get statement 1 and Statement 2 insufficient with notations and rationale method?
Thanks__

bumpbot · Answer

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If a, b and c are integers, is abc divisible by 4?

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If a, b and c are integers, is abc divisible by 4?

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