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If a, b and c are integers, is abc divisible by 4? Updated on: 29 Sep 2013, 23:58
Originally posted by dukenukem on 29 Sep 2013, 19:14.
Last edited by Bunuel on 29 Sep 2013, 23:58, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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If a, b and c are integers, is abc divisible by 4?

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

Show Spoiler
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!!
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E
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If a, b and c are integers, is abc divisible by 4? 30 Sep 2013, 00:12
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dukenukem
If a, b and c are integers, is abc divisible by 4?

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

Show Spoiler
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!!
Show more

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:
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If a, b and c are integers, is abc divisible by 4? 29 Sep 2013, 23:59
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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!!
Show more

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
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If a, b and c are integers, is abc divisible by 4? 30 Sep 2013, 00:11
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If a, b and c are integers, is abc divisible by 4?

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

Show more

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
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If a, b and c are integers, is abc divisible by 4? 02 Oct 2013, 17:00
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Thank you! And also thanks for those links Bunuel!

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If a, b and c are integers, is abc divisible by 4? 02 Oct 2013, 17:05
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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!)

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If a, b and c are integers, is abc divisible by 4? 19 Dec 2014, 16:33
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Can't we solve this problem by knowing that a, b, or c could be zero? Zero is an integer and it is even.
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If a, b and c are integers, is abc divisible by 4? 24 Dec 2014, 10:02
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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.

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If a, b and c are integers, is abc divisible by 4? 07 Oct 2018, 13:05
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If a, b and c are integers, is abc divisible by 4?

(1) a + b + 2c is even.
(2) a + 2b + c is odd.
Show more
\(a,b,c\,\,{\rm{ints}}\,\,\,\,\left( * \right)\)

\({{abc} \over 4}\,\,\mathop = \limits^? \,\,{\mathop{\rm int}}\)

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

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

\(\left( 2 \right)\,\,\,{{a + 2b + c} \over 2} \ne {\mathop{\rm int}} \,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,{{a + c} \over 2} \ne {\mathop{\rm int}}\)


\(\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {0,0,1} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr \\
\,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {1,1,2} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.\,\,\,\)


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

Regards,
Fabio.
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If a, b and c are integers, is abc divisible by 4? 07 Nov 2019, 03:31
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dukenukem
If a, b and c are integers, is abc divisible by 4?

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

Show Spoiler
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!!
Show more
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.
Attachments

Statement 1 & 2 image.PNG
Statement 1 & 2 image.PNG [ 50.55 KiB | Viewed 3447 times ]

Statement 2 image.PNG
Statement 2 image.PNG [ 50.94 KiB | Viewed 3445 times ]

Statement-1 image.PNG
Statement-1 image.PNG [ 57.7 KiB | Viewed 3431 times ]

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If a, b and c are integers, is abc divisible by 4? 07 Nov 2019, 03:36
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dukenukem
If a, b and c are integers, is abc divisible by 4?

(1) a + b + 2c is even.
(2) a + 2b + c is odd.
\(a,b,c\,\,{\rm{ints}}\,\,\,\,\left( * \right)\)

\({{abc} \over 4}\,\,\mathop = \limits^? \,\,{\mathop{\rm int}}\)

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

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

\(\left( 2 \right)\,\,\,{{a + 2b + c} \over 2} \ne {\mathop{\rm int}} \,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,{{a + c} \over 2} \ne {\mathop{\rm int}}\)


\(\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {0,0,1} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr \\
\,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {1,1,2} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.\,\,\,\)


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

Regards,
Fabio.
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fskilnik
Sir, could you tell me how did you get statement 1 and Statement 2 insufficient with notations and rationale method?
Thanks__
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If a, b and c are integers, is abc divisible by 4? 29 May 2024, 13:36
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