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
divisible by 3
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Statement 1: 2R is evenly divisible by 3j_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
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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Given : If R is an integerj_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
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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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.
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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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.
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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Interestingly enough, I was going to comment on the wording of this question yesterday, but never got around to it.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.
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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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.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.
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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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.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.
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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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
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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