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

Question

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

Bunuel · Accepted Answer

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.

whiplash2411 · Answer

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.

prab · Answer

thank you, for your explanations. Well i didn't know there was any thing like 0!, but since there is, option C is correct.

vitamingmat · Answer

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...

5va · Answer

Bunuel I missed "0" :oops:

agdimple333 · Answer

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

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

KarishmaB · Answer

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).

amit2k9 · Answer

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.

jaschen27 · Answer

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

agdimple333 · Answer

Yeh the Q is right, i have not hand typed it, but copied and pasted.

verycoolguy33 · Answer

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

shinbhu · Answer

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

verycoolguy33 · Answer

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 .

KarishmaB · Answer

Yes, 0 is divisible by 9. 0/9 = 0
Similarly, 0 is divisible by 2, 234, 109845 etc

samramandy · Answer

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

KarishmaB · Answer

In my opinion, it would be in 650 - 700 range.

Arnav180 · Answer

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

Bunuel · Answer

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?

bhamini1 · Answer

0! is equal to 1? i know i might be asking a very basic question but please enlighten me

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

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

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