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# GMAT Diagnostic Test Question 12

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GMAT Diagnostic Test Question 12 [#permalink]

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06 Jun 2009, 22:09
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GMAT Diagnostic Test Question 12
Field: special characters, divisibility
Difficulty: 700

If N = 1234@ and @ represents the units digit, is N a multiple of 5?

(1) @! is not divisible by 5
(2) @ is divisible by 9

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
D. EACH statement ALONE is sufficient
E. Statements (1) and (2) TOGETHER are NOT sufficient
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Last edited by Bunuel on 07 Oct 2013, 00:08, edited 3 times in total.
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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26 Jul 2009, 07:33
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First: For N to be divisible by 5 it has to end with 0 or 5.

Statement (1) @! is not divisible by 5

From this you can conclude that:

- @ is not higher than 4 since all factorials above include a 5 as a factor and are therefore divisible by 5.

- important: with @ = 0 there is also an option in which @! is not divisible by 5 (0! is 1), but N is.

-> From this statement alone N could be divisible by 5 (with 0) or not (with 1,2,3,4).

(2) @ is divisible by 9

- @ could be 0 or 9.

-> From this statement alone N could be divisible by 5 (with 0) or not (with 9).

Conclusion: When using both statement the only intersection is 0, which is divisible by 5. Hence, only both statements together are sufficient (C).
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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07 Jun 2009, 17:02
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Explanation

1234@ to be divisible by 5, symbol "@" should represent either 0 or 5. So the question asks whether @ equals to 0 or 5.

(1) @! is not divisible by 5 --> @ can be 0, 1, 2, 3, or 4 (note that 0!=1). Not sufficient.
(2) @ is divisible by 9 --> @ can be 0 or 9 (note that zero is divisible by every integer except zero itself). Not sufficient.

(1)+(2) Intersection of the values for @ from (1) and (2) is @=0. Sufficient.

Solution 2:

From 1: @ could be 0, 1 or 2 or 3 or 4.
If @ = 0, @! = 1, N is divisible by 5.
If @ = 1, @! = 1, N is not divisible by 5.
If @ = 2, @! = 2, N is not divisible by 5.
If @ = 3, @! = 6, N is not divisible by 5.
If @ = 4, @! = 24, N is not divisible by 5.

So @ could be 0, 1 or 2 or 3 or 4 but not >4. NSF

2: @ could be 0 or 9. NSF

From 1 and 2 together: @ is 0. So 1 and 2 are sufficient and OA is C.
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Last edited by bb on 28 Sep 2013, 13:04, edited 2 times in total.
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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18 Jul 2009, 12:55
I just don't get it how @ can be 0 from the 2)

Do you really thing that 0 is devisible by 9

Or am I going nuts!!!!

Thanks for explanations
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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19 Jul 2009, 11:12
I would also like to know the answer to the above question as well.

How can @ be possibly 0? I answered E, but according to this that's incorrect. Thanks in advance.
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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19 Jul 2009, 18:45
Expert's post
I just don't get it how @ can be 0 from the 2)

Do you really thing that 0 is devisible by 9

Or am I going nuts!!!!

Thanks for explanations

Yes, zero is divisible by any number, though this is usually not tested on the GMAT
0 *5 = 0, so similarly $$\frac{0}{5} = 0$$. Again, this is outside of GMAT scope but helpful to know.
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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23 Jul 2009, 10:45
I had no idea 0! = 1......
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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23 Jul 2009, 11:12
Expert's post
benpack03 wrote:
I had no idea 0! = 1......

Not usually tested on the GMAT.
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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24 Jul 2009, 11:50
Hi, I may ask a veru stupid question but how can we know from statement 1 that @ can not be >4???
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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27 Jul 2009, 20:55
I dont think this question represents a question likely to appear on gmat as the concepts tested in this q have never appeared in my experience. Suggestions?
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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28 Jul 2009, 00:20
Expert's post
sher676 wrote:
I dont think this question represents a question likely to appear on gmat as the concepts tested in this q have never appeared in my experience. Suggestions?

Are you talking about 0! and $$\frac{0}{5}$$ or is there something else?
I believe these are two minor points that do come up as a part of the explanation but do not play a big role in the question
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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28 Jul 2009, 08:46
bb wrote:
sher676 wrote:
I dont think this question represents a question likely to appear on gmat as the concepts tested in this q have never appeared in my experience. Suggestions?

Are you talking about 0! and $$\frac{0}{5}$$ or is there something else?
I believe these are two minor points that do come up as a part of the explanation but do not play a big role in the question

Yes I was talking about the 0! and 0/5. It is definitely good to know about it before the test date though.
Thanks
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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02 Sep 2009, 09:02
Need to understand this.

In case 2:
@ could definitely be 0 or 9
however when one looks at N = 1234@

Substituting @
@ = 0 ==> 12340 and it is not divisible by 9
@ = 9 ==> 12349 and it is neither divisible by 9

I feel there is a problem in the question itself. Also if the above is considered, we should be able to get the answer to the question from B along.

Hence B.

So i have a question here.
When it says N is a multiple of 5, can N be a non-integer too? OR will it always be an integer.
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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02 Sep 2009, 22:59
keepsmilin wrote:
Need to understand this.

In case 2:
@ could definitely be 0 or 9
however when one looks at N = 1234@

Substituting @
@ = 0 ==> 12340 and it is not divisible by 9
@ = 9 ==> 12349 and it is neither divisible by 9

I feel there is a problem in the question itself. Also if the above is considered, we should be able to get the answer to the question from B along.

Hence B.

So i have a question here.
When it says N is a multiple of 5, can N be a non-integer too? OR will it always be an integer.

The highlited part above in red is 5 not 9.

N has to be an integer to be divisible by 5.
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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03 Dec 2009, 19:37
N = 1234@ and @ represents the units digit, is N a multiple of 5?

(1) @! is not divisible by 5
(2) @ is divisible by 9

=======
(1)@! is not divisible by 5 so @ is not 0 or 5==> N is not a multiple of 5==> can answer the question
(2)@ is divisible by 9 so @ is 0 or 9; if it is 0 ==> N is a multiple of 5; if @ is 9 N is not a multiple of 5==>Not sufficiency!
I choose A
Please give me the feedback !
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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20 Apr 2010, 13:37
Please explain how "@ could definitely be 0 or 9". I'm sorry but I just can't seem to grasp this one. I think that the answer is B becuse if 1234@ is divisible by 9, the only number that @ could possibly be is 8, and if @ is 8 then we definitely know that 1234@ is not divisible by 5, hence 2 is sufficient and the answer is B.

Please explain where I have gone wrong here.

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Re: GMAT Diagnostic Test Question 11 [#permalink]

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20 Apr 2010, 20:28
previous poster - it says that @ is divisible by 9, not 1234@ is divisible by 9.

Can someone cite an official source that claims 0 is divisible by every number? I've never heard this and couldn't find it with a quick google search. I understand the problem otherwise...but that seems like such a technicality that 0 is divisible by any number... not something real.
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Re: GMAT Diagnostic Test Question 11 [#permalink]

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23 Apr 2010, 03:25
I can't find an official source citing that. Zero is divisible by any non-zero number. Think of it this way.

Any number multiplied by zero gives zero. Thus, zero is divisible by any number. Analogy:

$$3*3=9$$ --> 9 is divisible by 3
$$3*0=0$$ --> 0 is divisible by 3

$$\frac{9}{3} = 3$$ --> 9 is divisible by 3
$$\frac{0}{3} = 0$$ --> 0 is divisible by 3 (and any non-zero number)

I know it may seem weird. Folks, please correct me if I'm wrong.

I'm not 100% sure if you can face this concept on the GMAT though.
shammokando wrote:
previous poster - it says that @ is divisible by 9, not 1234@ is divisible by 9.

Can someone cite an official source that claims 0 is divisible by every number? I've never heard this and couldn't find it with a quick google search. I understand the problem otherwise...but that seems like such a technicality that 0 is divisible by any number... not something real.

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Re: GMAT Diagnostic Test Question 11 [#permalink]

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23 Apr 2010, 07:58
I understand the technical aspects. But it's like how 1 is a factor to every number. It's obviously true but widely understood that you never need to specify or rely on that fact as a rule to solve something.

dzyubam wrote:
I can't find an official source citing that. Zero is divisible by any non-zero number. Think of it this way.

Any number multiplied by zero gives zero. Thus, zero is divisible by any number. Analogy:

$$3*3=9$$ --> 9 is divisible by 3
$$3*0=0$$ --> 0 is divisible by 3

$$\frac{9}{3} = 3$$ --> 9 is divisible by 3
$$\frac{0}{3} = 0$$ --> 0 is divisible by 3 (and any non-zero number)

I know it may seem weird. Folks, please correct me if I'm wrong.

I'm not 100% sure if you can face this concept on the GMAT though.
shammokando wrote:
previous poster - it says that @ is divisible by 9, not 1234@ is divisible by 9.

Can someone cite an official source that claims 0 is divisible by every number? I've never heard this and couldn't find it with a quick google search. I understand the problem otherwise...but that seems like such a technicality that 0 is divisible by any number... not something real.

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Re: GMAT Diagnostic Test Question 11 [#permalink]

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23 Apr 2010, 12:44
Hi!
(2) @ is divisible by 9

- @ could be 0 or 9. and 1 81/9=9 so figure 1 could be as well
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Re: GMAT Diagnostic Test Question 11   [#permalink] 23 Apr 2010, 12:44

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# GMAT Diagnostic Test Question 12

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