Interpretation of Question (Number Theory)

[asishkm]

Hi,

Ques: 2ab5 is a four-digit number divisible by 25. If the number formed from the two digits ab is a multiple of 13, then ab = ____

The options have both 10 and 52 present.

Should the question be interpreted as to be asking for the two digit number formed by ab?

OR

Should it be interpreted as asking the value of a*b?


How do you decide which one is being asked? (Of course if only one of 10 or 52 was present, it would be evident. However, in this case, both are present)

Thanks.

[xerocoool]

Hi,

The question is asking for the value of "ab" such that:

-> the value of just "ab" is a multiple of 13
-> and when the value of "ab" is plugged back into "2ab5", the new number (the entire four digit number) should be divisible by 25

lets consider the value of ab = 52 (which is a multiple of 13)
when plugged back into "2ab5" we get "2525", the new number formed is also divisible by 25 (gives an integer result)

So the answer must be 52 :)

Thanks

[asishkm]

Thanks for the answer.

I don't know why I thought "ab" meant I had to find out "a*b".

I should stop over-thinking things and yes, the answer is indeed 52 :)

[tommywallach]

No no no. This is a badly written question. "ab" in common parlance DOES mean a*b. That is the standard interpretation of it. This question should not be written this way. Again, what book is this from?

-t

[xerocoool]

If the number formed from the two digits ab is a multiple of 13

What I meant was a*b (where "a" and "b" could be any numbers) but the result of multiplying "a" and "b" should be a multiple of 13.
Since they have not asked for any individual value, the conclusion can be made right ? (that a*b = 52)

Here is the question from Nova's

2ab5 is a four-digit number divisible by 25. If the number formed from the two digits ab is a multiple
of 13, then ab=

(A) 10
(B) 25
(C) 52
(D) 65
(E) 75

a*b = 65 also works, but then the 4 digit number is not divisible by 25. I hope the logic is right.

[asishkm]

In addition to what xero said, the Official Guide does mention that:

Sometimes juxtaposition of letters does not denote multiplication, as in "consider a three-digit integer denoted by XYZ, where X, Y, and Z are digits." The meaning is taken from the context.

[tommywallach]

GUYS! I promise I know what I'm talking about. This is a terrible question. And who the heck is Nova?

First off, the example you give from the OG is very different. In that case it EXPLAINS in the question itself that XYZ does not stand for multiplication. The Nova example does not.

More importantly, this is ridiculous: only two of the answer choices are divisible by 13 to begin with. So you're already down to a 50/50 guess right there? Terrible terrible terrible.

Nova Grade: F.

-t