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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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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.
_________________

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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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?

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
_________________

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

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 !

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.

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.

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.

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.