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Manager  Joined: 13 Aug 2010
Posts: 142
If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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9 00:00

Difficulty:   95% (hard)

Question Stats: 31% (01:32) correct 69% (01:20) wrong based on 352 sessions

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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

My understanding is that if @! is not divisible by 5 then @ is less than 5 so not divisible by 5

and since @ is divisible by 9, it is not divisible by 5, since 9 is a prime number, so i picked D. but the OA is something else .can some one please explain. Thank you
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Math Expert V
Joined: 02 Sep 2009
Posts: 55228
If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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6
4
prab wrote:
If N=1233AND @ represents the units digit, is @ a multiple of 5?

1. @! is not divisible by 5
2 @ is divisible by 9

My understanding is that if @! is not divisible by 5 then @ is less than 5 so not divisible by 5

and since @ is divisible by 9, it is not divisible by 5, since 9 is a prime number, so i picked D. but the OA is something else .can some one please explain. Thank you

Red parts are not correct.

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

For $$1233@$$ 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.

Answer: C.
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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prab wrote:
If N=1233@ and @ represents the units digit, is [highlight]@ a multiple of 5[/highlight]?

1. @! is not divisible by 5
2 @ is divisible by 9

My understanding is that if @! is not divisible by 5 then @ is less than 5 so not divisible by 5

and since @ is divisible by 9, it is not divisible by 5, since 9 is a prime number, so i picked D. but the OA is something else .can some one please explain. Thank you

A multiple of 5 means it can be 0 or 5.

So when you're considering statement 1, it says that @! is not divisible by 5, ruling out the option that it's 5. It could still be zero.

However the second statement negates this, and hence helps reach a conclusion.

In my opinion, this is poorly worded. But, yeah.
Manager  Joined: 13 Aug 2010
Posts: 142
Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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thank you, for your explanations. Well i didn't know there was any thing like 0!, but since there is, option C is correct.
Manager  Joined: 25 Aug 2010
Posts: 62
Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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very good explanation.. i was expecting ! also a number... and i wanted to give ans as E.

But once i saw explanation from Bunuel, understood better...
Intern  Joined: 10 Jul 2010
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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Bunuel I missed "0" Senior Manager  Joined: 24 Mar 2011
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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1
If $$N = 1234@$$ and $$@$$ represents the units digit, is $$N$$ a multiple of 5?

$$@!$$ is not divisible by 5
$$@$$ is divisible by 9
Veritas Prep GMAT Instructor D
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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2
1
agdimple333 wrote:
If $$N = 1234@$$ and $$@$$ represents the units digit, is $$N$$ a multiple of 5?

$$@!$$ is not divisible by 5
$$@$$ is divisible by 9

This is how you would analyze this question:

N = 1234@
Question: Is N a multiple of 5?
How do you figure whether a number is a multiple of 5 or not? You see the last digit to decide. If the last digit is 0/5, the number is divisible by 5, else it is not.

1. @! is not divisible by 5.
If @ = 0, 0! is 1 which is not divisible by 5. In this case N (12340) is divisible by 5.
If @ = 1, 1! is 1 which is not divisible by 5. In this case N (12341) is not divisible by 5.
So satisfying statement 1 is not sufficient to know whether N is divisible by 5.

2. @ is divisible by 9.
There are only 2 digits that are divisible by 9: 0 and 9
If @ = 0, N (12340) is divisible by 5.
If @ = 9, N (12349) is not divisible by 5.
So satisfying statement 2 is not sufficient to know whether N is divisible by 5.

Using both, The only value of @ that satisfies both statements is 0. (9! is divisible by 5 hence @=9 doesn't satisfy statement 1.)
If @ = 0, N (12340) is divisible by 5.
Hence, using both together, we know that N is divisible by 5. Sufficient.
Answer (C).
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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a the digit can be 0,1,2,3,4. 5! and above will be divisible by 5. Not sufficient.

b the number can be 0 | 9. Not sufficient.

a+b gives digit = 0. as 9! is divisible by 5.

Hence C.
Intern  Joined: 09 May 2011
Posts: 17
Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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Are you sure it's not N is divisible by 9 for the second piece of data?
Senior Manager  Joined: 24 Mar 2011
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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jaschen27 wrote:
Are you sure it's not N is divisible by 9 for the second piece of data?

Yeh the Q is right, i have not hand typed it, but copied and pasted.
Intern  Joined: 28 Dec 2010
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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Hi ,
I need to understand the 2nd statement . Is it right that '0' is divisible by 9 ? I thought this would be only 9 which is divisible by 9 . Please clarify .

Thanks,
VCG
Manager  Joined: 29 Jul 2011
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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Good one.

1. @! not divisible by 5 means @ = 0,1,2,3,4. 0 satisfies, but 1,2,3,4 does not suff.
2. @ div by 9 means @ = 0,9. Same as 1, insuff.

Together, @ = 0 is common, which is div by 5 as units digit of N. Suff.

C
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Intern  Joined: 28 Dec 2010
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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I will still dont have the answer -
Is it right that '0' is divisible by 9 ? I thought this would be only 9 which is divisible by 9 .
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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verycoolguy33 wrote:
I will still dont have the answer -
Is it right that '0' is divisible by 9 ? I thought this would be only 9 which is divisible by 9 .

Yes, 0 is divisible by 9. 0/9 = 0
Similarly, 0 is divisible by 2, 234, 109845 etc
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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That was a really tricky one...what would be the level of that question by the way??
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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samramandy wrote:
That was a really tricky one...what would be the level of that question by the way??

In my opinion, it would be in 650 - 700 range.
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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Bunuel wrote:
prab wrote:
If N=1233AND @ represents the units digit, is @ a multiple of 5?

1. @! is not divisible by 5
2 @ is divisible by 9

My understanding is that if @! is not divisible by 5 then @ is less than 5 so not divisible by 5

and since @ is divisible by 9, it is not divisible by 5, since 9 is a prime number, so i picked D. but the OA is something else .can some one please explain. Thank you

Red parts are not correct.

1233to 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.

Answer: C.

Does it say that 1233Has to be divisible by 5 in the question???
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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Arnav180 wrote:
Bunuel wrote:
prab wrote:
If N=1233AND @ represents the units digit, is @ a multiple of 5?

1. @! is not divisible by 5
2 @ is divisible by 9

My understanding is that if @! is not divisible by 5 then @ is less than 5 so not divisible by 5

and since @ is divisible by 9, it is not divisible by 5, since 9 is a prime number, so i picked D. but the OA is something else .can some one please explain. Thank you

Red parts are not correct.

1233to 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.

Answer: C.

Does it say that 1233Has to be divisible by 5 in the question???

There was a typo in the original post. The question reads:

If $$N = 1234@$$ and @ represents the units digit, is N a multiple of 5?
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GMAT 1: 580 Q37 V33 GMAT 2: 580 Q39 V31 GMAT 3: 560 Q40 V28 GMAT 4: 580 Q37 V32 GMAT 5: 680 Q45 V37 GMAT 6: 690 Q47 V37 Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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0! is equal to 1? i know i might be asking a very basic question but please enlighten me Re: If N = 1234 and represents the units digit, is N a multiple of 5?   [#permalink] 27 Jun 2016, 07:38

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