Terminating decimal Manhattan CAT problem

[Everything OR Nothing]

If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer.

(2) 28x is an integer.


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 one ALONE is sufficient.

D.EACH statement ALONE is sufficient.

E.Statements (1) and (2) TOGETHER are NOT sufficient.

OA: C

But the explanation in Manhattan CAT review totally went out of my head . WHat is the best way to solve this kind of problem?

[RonPurewal]

hi,
please don't just post a problem. if you do that, then our response will be essentially identical to the answer key that you already have.

instead, tell us what you've already tried.
what did you understand?
how did you try to set up the problem?
where did you get stuck?
what other methods did you try?
did you read the answer key? if so, what did (or didn't) you understand?
etc.

once you've outlined the steps you've already taken, we can give some input that will actually help you solve future problems. (if we just provide a full solution from beginning to end, that won't provide any "value added" beyond the existing answer key.)

[Everything OR Nothing]

Dear Ron,
I did not understand anything and I had no clue how to solve the problem. 2 minutes I waited and none of the bulbs in my head got lightened up.So I asked how to approach for a solution of this problem? I have purely no clue about how to proceed even a single step in this problem.

[RonPurewal]

well, again, i don't just want to write out a complete solution, because that would be just like having the answer key -- which you presumably already have. (in fact, i wrote the answer key for this problem, so i would almost certainly end up writing something exactly like the answer key.)

try just writing out some lists of numbers that satisfy these statements. then see what happens with the question.

statement 1:
write out a list of fractions x for which 24x = 1.
then, determine whether these are terminating decimals.

statement 2:
write out a list of fractions x for which 28x = 1.
then, determine whether these are terminating decimals.

together (if necessary):
if neither of the individual statements turns out to be sufficient -- find the fractions that are in both of your lists.
then, determine whether these are terminating decimals.

go ahead and give it a shot.

[jake.kramer]

Hi Ron,

In the question stem, it states, "If 0 < x < 1, is it possible to write x as a terminating decimal?"

I understood that to mean would it be possible given the statements 1 or 2, that x could be a terminating decimal.
In statement 1, 24x is an int, would 1/2 not suffice? In this case, it would be possible to write x as a terminating decimal. I understand how DS works but I rarely come across a question stem in DS that asks if "it is possible."
If the question stem was instead, "If 0 < x < 1, is x a terminating decimal?" it would be a lot clearer to me.

Am I reading into this too much? Can I expect to see this type of language on the GMAT?

[jlucero]

Hi Ron,

In the question stem, it states, "If 0 < x < 1, is it possible to write x as a terminating decimal?"

I understood that to mean would it be possible given the statements 1 or 2, that x could be a terminating decimal.
In statement 1, 24x is an int, would 1/2 not suffice? In this case, it would be possible to write x as a terminating decimal. I understand how DS works but I rarely come across a question stem in DS that asks if "it is possible."
If the question stem was instead, "If 0 < x < 1, is x a terminating decimal?" it would be a lot clearer to me.

Am I reading into this too much? Can I expect to see this type of language on the GMAT?

It's probably good to be able to understand this type of language, but I do 100% agree with you that the way the OG problems would probably word this question is more similar to the style that you phrased it at the bottom. My #1 takeaway is that if you are privy enough about how the GMAT words these DS type problems, then you've clearly done your homework.

[jake.kramer]

Got it, thanks for your prompt response, Joe.

[tim]

:)

[RonPurewal]

I don't agree.

"Is it possible to write ____ as a terminating decimal?" is a perfectly straightforward question. The answer is either "Yes, you can" or "No, you can't"——and the wording specifically clarifies that the current form of the number (i.e., a fraction) isn't the point.

With a question like "Is this number a terminating decimal?", on the other hand, THEN you've got issues. What if it's written as a fraction? Can you actually say that a fraction is a decimal? (You can't, really; that's why mathematicians—including the people who write the official problems—will ALWAYS go out of their way to write that a fraction is "equal to" or "equivalent to" a certain decimal. You will never see "This fraction IS this decimal" written by a competent mathematician.)

[RonPurewal]

More importantly—

The official problems NEVER contain "tricky" wordings.

Never.
Never ever ever. Not a single once.
They just don't.

So, if you are ever deliberating between (a) a straightforward, Occam's-razor interpretation and (b) some "tricky", a-ha-I-got-you interpretation ... well, it's (a). Every time.

In fact, the official problems really never contain any "tricks" at all. That's probably my single favorite thing about this test.

[ABHIMANYUG854]

i had a doubt ,that if i take x as 1/9 or 1/13 or reciprocal of any prime number greater than 9, will the solution provided in the MGMAT suffice

[RonPurewal]

i had a doubt ,that if i take x as 1/9 or 1/13 or reciprocal of any prime number greater than 9, will the solution provided in the MGMAT suffice

none of these values will satisfy statement 1. nor will any of them satisfy statement 2. therefore, they are all irrelevant.

you may want to go back and brush up on the very basics of how data sufficiency works. you have to start with values that actually satisfy the statement(s) under consideration!

[JacobW468]

After reviewing this problem, the answer makes sense. I'm also seeing a pattern, prime factorization helps nearly 100% of the time in divisibility/prime number questions. However, in the answer explanation, it is writtem: "The only prime factors that 24 and 28 share are 2 and 2(2^2)." What exactly is the last part trying to say? I understand they share 2 and 4, but that isn't what is written here.

[RonPurewal]

After reviewing this problem, the answer makes sense. I'm also seeing a pattern, prime factorization helps nearly 100% of the time in divisibility/prime number questions. However, in the answer explanation, it is writtem: "The only prime factors that 24 and 28 share are 2 and 2(2^2)." What exactly is the last part trying to say? I understand they share 2 and 4, but that isn't what is written here.

hm, is that really what it says?
that's... not what it should say. |:

the only PRIME factor shared by those two numbers is 2. all of the other dithering is superfluous, since 4 is not prime in the first place.

i'll submit this to the people who revise these things.

[RonPurewal]

and thanks for pointing that out, by the way.