If x is a positive integer less than 140 and 35x/100 is also an intege

Question

If x is a positive integer less than 140 and 35x/100 is also an integer, then how many different positive prime factors could x have?

A. 1
B. 2
C. 3
D. 4
E. 5

thule123 · Answer

Hi everyone,
I'm a newbie to GMAT club. I'm answering above question. However i dont know where to find the answer. 
Is there anyone can help?
Thank u much.

Posted from my mobile device

Bunuel · Answer

The OA (Official Answer) will be automatically revealed on Tuesday 4th of June 2019 01:06:46 PM Pacific Time Zone. When the OA is revealed you can find it under the spoiler, saying OA, in the first post.

Hope it helps.

jfranciscocuencag · Answer

thule123

X<140

35 = 7*5

\frac{5*7*x}{5^2*2^2}  = INTEGER

x must be at least 20 (5*2^2) to be div by 100.

So

20 * 3 = 60 ... less than 140... Prime numbers = 2,3,5.

20 * 7 = 140 ... cant be cuz x must be less than 140.

Hence C

Arro44 · Answer

I am a little confused by this question, are we looking for the maximum number of possible prime factors for x?

jfranciscocuencag · Answer

Yes,  Arro44

Considering than x must be at least 20.

Arro44 · Answer

Thank you, then I understand your solution and also agree that it is the correct one.

I was a little confused by the worked which led me to check the number of prime factors for 20...

Best regards,
Chris

CareerGeek · Answer

x<140.
35x/100 = 7x/20 is an integer
—> x should be a multiple of 20 less than 140.

So, possible values of x are
20 = 2^2*5 (2 possible prime factors)
40 = 2^3*5 (2 possible prime factors)
60 = 2^2*3*5 (3 possible prime factors)
80 = 2^4*5 (2 possible prime factors)
100 = 2^2*5^2 (2 possible prime factors)
120 = 2^3*3*5 (3 possible prime factors)

So, x can have either 2 or 3 possible prime factors.

IMO Option should be B or C.

Or question should have asked maximum possible prime factors for answer to be C.

Bunuel  The question looks ambiguous. Pls help

Posted from my mobile device

Arro44 · Answer

After re-reading the question twice I now feel like the part "how many different prime factors could x have" implies that we are looking for the maximum number.
However, I had the same problem initially.

CareerGeek · Answer

I believe any question in GMAT should convey one exact meaning irrespective whosoever is reading. As we can clearly see x can have either 2 or 3 values, I’m not convinced with the assumption.

If x is a positive integer less than 140 and 35x/100 is also an intege

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