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

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Manager
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If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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11 Oct 2010, 19:06
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95% (hard)

Question Stats:

31% (00:42) correct 69% (00:42) wrong based on 334 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
Math Expert
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If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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11 Oct 2010, 19:41
5
3
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.

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

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11 Oct 2010, 19:32
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.
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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11 Oct 2010, 20:44
thank you, for your explanations. Well i didn't know there was any thing like 0!, but since there is, option C is correct.
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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12 Oct 2010, 10:31
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...
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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12 Oct 2010, 21:27
Bunuel I missed "0"
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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17 May 2011, 12:10
1
If $$N = 1234@$$ and $$@$$ represents the units digit, is $$N$$ a multiple of 5?

$$@!$$ is not divisible by 5
$$@$$ 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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17 May 2011, 13:44
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.
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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18 May 2011, 06:50
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.
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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18 May 2011, 10:57
Are you sure it's not N is divisible by 9 for the second piece of data?
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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18 May 2011, 11:08
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.
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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08 Jan 2012, 06:03
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,
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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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08 Jan 2012, 18:52
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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Re: If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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09 Jan 2012, 03:56
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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09 Jan 2012, 04:33
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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09 Jan 2012, 11:41
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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09 Jan 2012, 21:11
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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16 Sep 2014, 07:40
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.

Does it say that 1233Has to be divisible by 5 in the question???
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Posts: 49208
If N = 1234 and represents the units digit, is N a multiple of 5?  [#permalink]

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16 Sep 2014, 13:38
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.

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

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27 Jun 2016, 07:38
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? &nbs [#permalink] 27 Jun 2016, 07:38

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