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divisible by 3

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by j_shreyans » Thu Aug 21, 2014 3:03 am
Guys ,

Help me out with the below.

If R is an integer, is R evenly divisible by 3?
(1) 2R is evenly divisible by 3
(2) 3R is evenly divisible by 3

OAstatement2

Thanks ,

Shreyans
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by confused13 » Thu Aug 21, 2014 3:08 am
OA is A, not what OT indicated.
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by GMATGuruNY » Thu Aug 21, 2014 3:28 am
j_shreyans wrote:
If R is an integer, is R evenly divisible by 3?
(1) 2R is evenly divisible by 3
(2) 3R is evenly divisible by 3
Statement 1: 2R is evenly divisible by 3
Make a list of options for 2R:
2R = 3, 6, 9, 12, 15, 18, 21, 24...
Dividing each side by 2, we get:
R = 3/2, 3, 9/2, 6, 15/2, 9, 21/2, 12...
Since R must be an integer, R can be equal to any of the values in red:
R = 3, 6, 9, 12...
In every case, R is a multiple of 3.
SUFFICIENT.

Statement 2: 3R is evenly divisible by 3
Make a list of options for 3R:
3R = 3, 6, 9, 12, 15, 18, 21, 24...
Dividing each side by 3, we get:
R = 1, 2, 3, 4, 5, 6, 7, 8...
If R=3, then R is a multiple of 3.
If R=1, then R is NOT a multiple of 3.
INSUFFICIENT.

The correct answer is A.
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by GMATinsight » Thu Aug 21, 2014 9:48 am
j_shreyans wrote:Guys ,

Help me out with the below.

If R is an integer, is R evenly divisible by 3?
(1) 2R is evenly divisible by 3
(2) 3R is evenly divisible by 3
Given : If R is an integer

Question : Is R evenly divisible by 3?

Statement 1) 2R is evenly divisible by 3

Since the Number 2 has nothing to do with the divisibility of 2 therefore R must be divisible by 3 [already mentioned that R is an Integer]
SUFFICIENT

Statement 2) 3R is evenly divisible by 3

Since 3 R is divisible by 3 therefore there is no guarantee whether R will be divisible by 3 [R can be 2 {Not divisible by 3} as well as 3 {divisible by 3}]

Answer: Option A
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by Matt@VeritasPrep » Thu Aug 21, 2014 2:50 pm
To piggyback on Mitch's examples, here's how we'd show this algebraically.

S1 tells us that 2r is divisible by 3, so we know that 2r is a multiple of 3. Algebraically, this gives us

2r = 3k, where k is some integer

Since these integers (2r and 3k) are equal, they must have the same prime factorization. Since there is a 3 on the right hand side, there must be a 3 on the left hand side. 2 is not divisible by 3, so the other value, r, must have the 3. Hence r divides by 3; SUFFICIENT.

S2 tells us

3r = 3k, where k is some integer

Dividing both sides gives us r = k, which tells us nothing about r; it will be divisible by 3 if k is divisible by 3, but we don't know what k is! INSUFFICIENT.
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by Geneclarke89 » Thu Aug 21, 2014 11:13 pm
Guys ,

Help me out with the below.

If R is an integer, is R evenly divisible by 3?
(1) 2R is evenly divisible by 3
(2) 3R is evenly divisible by 3

THE FIRST THING I noted was that all choices would have to be even. No odd number can be divided by an odd number and come out even.
Data Set (1) itself was of no help.
I also noted that for Data Set (2) any answer would be the original value R. Thus THE ORIGINAL VALUE WOULD HAVE TO BE EVEN. However Data set (2) would not itself be enough to make a definitive answer.

I then plugged 6 and 12 in as values to these data sets together. And they both worked... Since the original question asked for an integer and not two... I would assume that multiple answers would smell up something fishy... So I'm Sticking to my guns with E. Both data sets are insufficient.
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by Brent@GMATPrepNow » Fri Aug 22, 2014 10:07 am
Geneclarke89 wrote:Guys ,

Help me out with the below.

If R is an integer, is R evenly divisible by 3?
(1) 2R is evenly divisible by 3
(2) 3R is evenly divisible by 3

THE FIRST THING I noted was that all choices would have to be even. No odd number can be divided by an odd number and come out even.
Data Set (1) itself was of no help.
I also noted that for Data Set (2) any answer would be the original value R. Thus THE ORIGINAL VALUE WOULD HAVE TO BE EVEN. However Data set (2) would not itself be enough to make a definitive answer.

I then plugged 6 and 12 in as values to these data sets together. And they both worked... Since the original question asked for an integer and not two... I would assume that multiple answers would smell up something fishy... So I'm Sticking to my guns with E. Both data sets are insufficient.
Interestingly enough, I was going to comment on the wording of this question yesterday, but never got around to it.
I don't believe I've ever seen an official GMAT question use the word "evenly" in this manner, because it's misleading.
Is saying "R is divisible by 3" different from saying "R is evenly divisible by 3"? If not, then why add the word "evenly"?

Although "even" in this question is meant to convey equal portions, others might see it to mean "even" in the sense of odd/even. I believe that this is NOT the intent of the question.

Cheers,
Brent
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by Brent@GMATPrepNow » Fri Aug 22, 2014 10:14 am
Geneclarke89 wrote:Guys ,

Help me out with the below.

If R is an integer, is R evenly divisible by 3?
(1) 2R is evenly divisible by 3
(2) 3R is evenly divisible by 3

THE FIRST THING I noted was that all choices would have to be even. No odd number can be divided by an odd number and come out even.
Data Set (1) itself was of no help.
I also noted that for Data Set (2) any answer would be the original value R. Thus THE ORIGINAL VALUE WOULD HAVE TO BE EVEN. However Data set (2) would not itself be enough to make a definitive answer.

I then plugged 6 and 12 in as values to these data sets together. And they both worked... Since the original question asked for an integer and not two... I would assume that multiple answers would smell up something fishy... So I'm Sticking to my guns with E. Both data sets are insufficient.
Be careful, Gene. The target question does NOT ask us to find the value of R; it asks us to determine whether R is divisible by 3.
You have correctly identified that R could equal 6 or 12 (or several other values), BUT if R = 6, then the answer to the target question is YES (R is divisible by 3), and if R = 12, then the answer to the target question is still YES (R is divisible by 3).
In fact, for statement 1, EVERY possible value of R will yield the SAME answer to the target question (YES, R is divisible by 3).
Since we can answer the target question with certainty (YES, R is divisible by 3), statement 1 is SUFFICIENT

Cheers,
Brent
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by sanju09 » Fri Aug 22, 2014 10:01 pm
Geneclarke89 wrote:Guys ,

Help me out with the below.

If R is an integer, is R evenly divisible by 3?
(1) 2R is evenly divisible by 3
(2) 3R is evenly divisible by 3

THE FIRST THING I noted was that all choices would have to be even. No odd number can be divided by an odd number and come out even.
Data Set (1) itself was of no help.
I also noted that for Data Set (2) any answer would be the original value R. Thus THE ORIGINAL VALUE WOULD HAVE TO BE EVEN. However Data set (2) would not itself be enough to make a definitive answer.

I then plugged 6 and 12 in as values to these data sets together. And they both worked... Since the original question asked for an integer and not two... I would assume that multiple answers would smell up something fishy... So I'm Sticking to my guns with E. Both data sets are insufficient.
Your ideas seem to be seriously mistaken on the divisibility basics. If double of an integer is evenly divisible by 3, so would the integer be, hence statement (1) alone is sufficient to answer YES to the question in chief. Further, if a statement carries a fact that we already know from the stem, it's definitely insufficient. See, for an integer R, 3R is evidently divisible by 3, no matter whether R is a multiple of 3 or not.

The phrase "evenly divisible" never means that the quotient is even, in fact "evenly divisible" means division with zero remainder.

[spoiler]Hence (A)[/spoiler]
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by Jim@StratusPrep » Tue Aug 26, 2014 9:55 am
I like to think of these as fractions.


1) 2R/3 = Integer, thus R must have a factor of 3 SUFFICIENT
2) 3R/3 = Integer, which can translate to R is an integer - this does not mean it is divisible by 3.

A
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