If @ denotes one of two arithmetic operations, addition or : GMAT Data Sufficiency (DS)
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# If @ denotes one of two arithmetic operations, addition or

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07 Aug 2007, 14:23
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If @ denotes one of two arithmetic operations, addition or multiplication, and if k is an integer, what is the value of 3 @ k?

(1) 2 @ k = 3

(2) 1 @ 0 = k
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Mar 2012, 14:50, edited 1 time in total.
Edited the question and added the OA
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Re: DS - arithmetic operations. [#permalink]

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07 Aug 2007, 14:38
leeye84 wrote:
If X denotes one of two arithmetic operations, addition or multiplication, and if k is an integer, what is the value of 3 X k?

1) 2 X k = 3
2) 1 X 0 = k

Got E.

X can be multiply or add. For simplicity sake, I am going to change that to @.
So, 3@k can be 3+k or 3*k.

1) 2@k = 3. Two equations here. 2+k = 3 or 2*k = 3.
Possible k are 1 or 2/3. k is an integer, so k=1.
This gives 3+1 = 4 or 3*1 = 3
Either 4 or 3, INSUFFICIENT.

2) 1@0 = k. Two equations: 1+0 = k, 1*0 = k
k can be 1 or 0
for k=1, plug in: 3+1 = 4, 3*1 =3
for k=0, plug in: 3+0 = 3, 3*0 = 0
So it can be either 4, 3, or 0
INSUFFICIENT.

Together, still get either 4 or 3. INSUFFICIENT.
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07 Aug 2007, 16:52
I think it's A. and I'm guessing that they're trying to say that X is either multiplication or addition but it cannot be both. Since 1 shows that is HAS to be addition and k has to be 1 you can get 3 + 1 = 4

that's my guess anyway. otherwise you could never be sure.
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07 Aug 2007, 16:59
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St1:
We know k is an integer, and 2xK results in an intger, 3.So x cannot be multiplication since that would require k to be a non-integer (3/2). Thus x must be addition, and k must be 1. and 3xk = 4. Sufficient.

St2:
Insufficient. It could be 1*0 = 0 (k=0) or 1+0 = 1 (k=1).

Ans A
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07 Aug 2007, 18:25
the reason it's not e is because X can be either addition or subtraction -- but it can't be both. so a suffices because the only way 3Xk=4 is if k is 1 and X is addition. that means that for the purposes of the problem, using a X is addition --- a takes multiplication completely out of the picture. so now we're left with a or d as the possible answers. d alone certainly not sufficient - so it has to be a.
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08 Aug 2007, 21:27
i got A as well

Since K is an integer and X is either addition or multiplication:

1) Stmt 1 can only imply addition since 2 + 1 = 3 (1 being K)
and if we use multiplication, the answer would not be an integer: 2 * 1.5 = 3. We can now solve for 3 X k, since we know which operation X is.
SUFFICIENT

2) Stmt 2 both addition and multiplication is true in this case 1 + 0 = 1 (K) and 1 * 0 = 0 (K) since both generates an integer we cannot solve for 3 X K.
thus INSUFFICIENT
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Re: If X denotes one of two arithmetic operations, addition or [#permalink]

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03 Mar 2012, 11:25
I think this question is worded extremely poorly.
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Re: If X denotes one of two arithmetic operations, addition or [#permalink]

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03 Mar 2012, 15:19
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Expert's post
bschoolnewbie2011 wrote:
I think this question is worded extremely poorly.

This question is perfectly OK. Here are several GMAT Prep questions about the same concept:
the-symbol-represents-one-of-the-four-arithmetic-operation-107575.html
if-the-operation-is-one-of-the-four-arithmetic-operations-101283.html

As for the solution:
If @ denotes one of two arithmetic operations, addition or multiplication, and if k is an integer, what is the value of 3 @ k?

(1) 2 @ k = 3 --> @ can only by addition because if it's multiplication then 2*k=3 -- k=3/2, which is not an integer as stated in the stem. So, we have 2+k=3 --> k=1 --> 3@k=3+1=4. Sufficient.

(2) 1 @ 0 = k --> @ can be both addition and multiplication, since 1+0=1=k=integer and 1*0=0=k=integer, so we also have two values of k: 1 and 0. In this case 3@k=3+1=4 or 3@k=3*0=0, two different answers. Not sufficient.

Hope it helps.
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Re: If X denotes one of two arithmetic operations, addition or [#permalink]

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03 Mar 2012, 15:24
Bunuel wrote:
bschoolnewbie2011 wrote:
I think this question is worded extremely poorly.

As for the solution:
If @ denotes one of two arithmetic operations, addition or multiplication, and if k is an integer, what is the value of 3 @ k?

(1) 2 @ k = 3 --> @ can only by addition because if it's multiplication then 2*k=3 -- k=3/2, which is not an integer as stated in the stem. So, we have 2+k=3 --> k=1 --> 3@k=3+1=4. Sufficient.

(2) 1 @ 0 = k --> @ can be both addition and multiplication, since 1+0=1=k=integer and 1*0=0=k=integer, so we also have two values of k: 1 and 0. In this case 3@k=3+1=4 or 3@k=3*0=0, two different answers. Not sufficient.

Hope it helps.

I understand the answer behind it. I did everything you did. I still picked E because it did not say that symbols in different equations had to be the same. Yes you are able to know what k is, but that doesn't mean you know what the answer to the equation is because the operation could be either.

This question did not test mathematics in my opinion, but rather an obscure interpretation of a poorly worded question.
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Re: If X denotes one of two arithmetic operations, addition or [#permalink]

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03 Mar 2012, 15:33
bschoolnewbie2011 wrote:
Bunuel wrote:
bschoolnewbie2011 wrote:
I think this question is worded extremely poorly.

As for the solution:
If @ denotes one of two arithmetic operations, addition or multiplication, and if k is an integer, what is the value of 3 @ k?

(1) 2 @ k = 3 --> @ can only by addition because if it's multiplication then 2*k=3 -- k=3/2, which is not an integer as stated in the stem. So, we have 2+k=3 --> k=1 --> 3@k=3+1=4. Sufficient.

(2) 1 @ 0 = k --> @ can be both addition and multiplication, since 1+0=1=k=integer and 1*0=0=k=integer, so we also have two values of k: 1 and 0. In this case 3@k=3+1=4 or 3@k=3*0=0, two different answers. Not sufficient.

Hope it helps.

I understand the answer behind it. I did everything you did. I still picked E because it did not say that symbols in different equations had to be the same. Yes you are able to know what k is, but that doesn't mean you know what the answer to the equation is because the operation could be either.

This question did not test mathematics in my opinion, but rather an obscure interpretation of a poorly worded question.

First of all it's a GMAT Prep question, so it's a GMAT wording. If you are preparing for the GMAT it's better to get used to it.

Next, from (1) you are able to get that @ can denote ONLY addition, which gives unique value of k: 1. So, the answer to the question: "what is the value of 3@k?" is 4 since 3+1=4.

Hope it's clear.
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Re: If @ denotes one of two arithmetic operations, addition or [#permalink]

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21 Jun 2013, 01:51
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Re: If @ denotes one of two arithmetic operations, addition or [#permalink]

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22 Jun 2013, 02:42
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leeye84 wrote:
If @ denotes one of two arithmetic operations, addition or multiplication, and if k is an integer, what is the value of 3 @ k?

(1) 2 @ k = 3

(2) 1 @ 0 = k

Here, keep in mind we need to find two values, i.e. k=? and the operator + or * ?

(1) 2 @ k = 3

k is an integer, hence, 2 + 1 seems like the obvious choice.
Since, 2 * 3/2 = 3, however, k is an integer so ruled out.
If k hadnt been integer, then we would have to worry a bit, but this makes things easier.

k=1 and operator = + => Sufficient.

(2) 1 @ 0 = k

We dont know the outcome which is k,
so we could have either
1 + 0 = 1
or
1 * 0 = 0
We dont know. Hence insufficient => A answer
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Re: If @ denotes one of two arithmetic operations, addition or [#permalink]

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27 Dec 2014, 08:46
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Re: If @ denotes one of two arithmetic operations, addition or [#permalink]

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17 Sep 2016, 01:17
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Re: If @ denotes one of two arithmetic operations, addition or   [#permalink] 17 Sep 2016, 01:17
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