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# If R is an integer, is R evenly divisible by 3?

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If R is an integer, is R evenly divisible by 3?  [#permalink]

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03 Apr 2015, 04:50
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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

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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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03 Apr 2015, 05:49
Bunuel 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

Kudos for a correct solution.

1) We see that 2R is divisible by 3. Because 2 not divisible by 3 we can say that R divisible of 3
sufficient

2) We see that 3R is divisible by 3. And we know that 3 is divisible by 3 but don't know about R it can be or not divisible by 3
insufficient

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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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03 Apr 2015, 07:53
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Bunuel 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

Kudos for a correct solution.

Let's revisit the rules of divisibility. For an integer x*y to be divisible by 3, either x OR y must be divisible by 3 (or both).

I) 2 is not divisible by 3, so for 2R to be divisible by 3, R must be divisible by 3. SUFFICIENT
II) 3 is divisible by 3, so R may or not be divisible by 3. Think about it, R can be any integer and 3R is still divisible by 3. INSUFFICIENT.

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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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03 Apr 2015, 09:43
Bunuel 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

Kudos for a correct solution.

1. 2 is not divisible by 3, so if 2R is divisible by 3, it means that R is divisible by 3--->Sufficient

2. 3 is divisible by 3. So R may or maynot be divisible by 3. Unsure--->Insufficient

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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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03 Apr 2015, 16:29
Hi hsbinfy,

When dealing with DS questions, you have to make sure that you are answering the question that is ASKED.

Here, we're asked if R is evenly divisible by 3. This is a YES/NO question.

When dealing with Fact 1, you correctly determined that R could be 3 or 6 (among other values), but you considered that to be insufficient.

IF R = 3, then the answer to the question is YES
IF R = 6, then the answer to the question is still YES
This evidence proves that Fact 1 is SUFFICIENT. Any additional values that you would come up with would ALSO be multiples of 3, so those answers would ALSO be YES.

Losing sight of the details on DS questions can cost you dearly on Test Day. Here, your examples were perfect, but your note-taking was 'off' and it cost you the question. To maximize your score, a bit more note-taking and attention-to-detail is required.

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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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05 Apr 2015, 00:40
Is R is evenly divisible by 3?

1. 2R is divisible by 3; it can only happen when R is divisible by 3. sufficient
2. 3R is divisible by 3; R ma or may not be divisible by 3, as 3 is divisible by 3. Insufficient

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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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05 Apr 2015, 03:04
Bunuel 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

Kudos for a correct solution.

1. 2R is evenly divisible by 3. R has to be a multiple of 3.
2. 3R is evenly divisible by 3. R may/may not be a mutilple of 3. Not sufficient.
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If R is an integer, is R evenly divisible by 3?  [#permalink]

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05 Apr 2015, 03:12
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

Evenly divisible means ---> The quotient after division done should leave NO REMAINDER ---> Simply means perfectly divisible
1) 2R is evenly divisible by 3--> Here 3 cannot divide 2 , definitely R must be divisible and as such EVENLY divisible as quoted
so A sufficient

2) 3 R is evenly divisible----> Here 3 can be divided by 3 and We cannot quote about R without ambiguity if it can divide 3 or not
B is NOT SUFFICIENT

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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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05 Apr 2015, 21:34
Bunuel
looks like a simple question, but i'm a bit confused in the Question "is R evenly divisible by 3?"
Does it mean simply that R is divisible by 3? or Does it mean that R is evenly divisible, ie R/3 = some Even integer.
so when R = 3, R is divisible by 3, but R is not evenly divisible by 3.
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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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05 Apr 2015, 22:44
Hi SherLocked2018,

The phrase "evenly divisible" means "divides and forms an integer"

If the prompt wants you do know that something is an "even integer", then the prompt will use that phrase (or equivalent).

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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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15 Mar 2016, 09:40
As 2 is not divisible by 3 so statement 1 is true
but statement 2 is not as R can be any integer
so A
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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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19 Apr 2016, 01:20
kashishh wrote:
Q. 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
Since 2 is not a multiple of 3, hence # should be a multiple of 3
Sufficient

Statement 2: 3R is evenly divisible by 3
Since 3 is a multiple of 3, R may or may not be a multiple of 3
Case 1: R = 2, 3R = 6. Here R is not a multiple of 3.
Case 2: R = 3, 3R = 9. Here R is a multiple of 3.
Insufficient

Correct option: A
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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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19 Jul 2017, 21:57
Bunuel 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

Kudos for a correct solution.

Simple question

St 1

If 2R/3 = some even integer K then R must be a positive multiple of 3- sufficient

St 2

3R/3= some even integer K - R must be even but it doesn't necessarily have to be a multiple of 3(8)/3 for example

A
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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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11 Aug 2017, 23:51
I have a query for all the explanations that are given and with the answer as well.

If we decide that answer is A, we accept that A is 'evenly divisible' means that integer should be divisible with an even integer, with remainder 0.

But then why we are avoiding the word 'evenly' in question as well.

If we take A, that means that '3' can be the value of R. Which is not evenly divisible by 3, as it is divisible by 1.

This means that statement A is not sufficient.

I think answer should be 'C', as when we combine both statement, that 2R and 3R both evenly divisible by 3, we are left with only one value of R i.e. 6, which is evenly divisible by 3.

Someone kindly explain to me why I should avoid the word 'evenly' in the question or not mean it divisible by an integer which is even.
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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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12 Aug 2017, 01:24
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Prathit wrote:
I have a query for all the explanations that are given and with the answer as well.

If we decide that answer is A, we accept that A is 'evenly divisible' means that integer should be divisible with an even integer, with remainder 0.

But then why we are avoiding the word 'evenly' in question as well.

If we take A, that means that '3' can be the value of R. Which is not evenly divisible by 3, as it is divisible by 1.

This means that statement A is not sufficient.

I think answer should be 'C', as when we combine both statement, that 2R and 3R both evenly divisible by 3, we are left with only one value of R i.e. 6, which is evenly divisible by 3.

Someone kindly explain to me why I should avoid the word 'evenly' in the question or not mean it divisible by an integer which is even.

Evenly divisible = simply divisible, it does not mean that the result of division should be even.
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Re: If R is an integer, is R evenly divisible by 3?  [#permalink]

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13 Aug 2017, 10:16
1) 2R is divisible by 3
2R can be 0,6,12,18 .... and so on positive and negative
R can be 0,3,6,9....... so on, both positive and negative
clearly R is divisible by 3. so A,D can be answer.
2) 3R is divisible by 3
3R can be 0,3,6,9,12,15.....and so on both positive and negative
R can be 0,1,2,3,4,5.......and so on both positive and negative
1 is not divisible by 3 , whereas 3 is divisible by 3. INSUFFICIENT
D is Ruled out and Answer is A
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Re: If R is an integer, is R evenly divisible by 3?   [#permalink] 13 Aug 2017, 10:16
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