Review Help

[oquiella]

If a positive integerr n, is divisible by both 5 and 7, the n must also be divisible by which of the following?

I. 12
II. 35
III. 70


A. None
B. I only
C. II only
D. I and II
E. II and III


Why not III?

[Bullzi]

Hello,
This is how I could approach the problem, I'll let the experts confirm if this approach is right..

The smallest integer multiple of both 5 and 7 is 35 and hence all subsequent multiples must be a multiple of 35. The question has this phrase 'must also be divisible'. Taking 35 as an example case and working with the answer choices, starting with the least,
1. 12 doesn't divide 35, so, not true
2. Divisible, should be true
3. Not divisible (70 doesn't divide 35)

So, I'll go with Option C

Thanks
Bullzi

[[email protected]]

Hi oquiella,

Bulzi's solution is perfect. This question asks for what N MUST be divisible by, so we have to start with the simplest option and work from there.

Since N is a POSITIVE INTEGER, and divisible by 5 and 7, the simplest option is 35. Since 35 is NOT divisible by 12 or 70, Roman Numerals 1 and 3 are eliminated (and we can eliminate Answers B, D and E).

The subsequent values of N will all be multiples of 35 (re: 35, 70, 105, 140, etc.), so they are all evenly divisible by 35.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[Brent@GMATPrepNow]

Here are some related questions to practice with

- https://www.beatthegmat.com/divisible-pr ... 20262.html
- https://www.gmatprepnow.com/module/gmat- ... /video/827
- https://www.beatthegmat.com/n-divisible- ... 79266.html

Cheers,
Brent

[oquiella]

Hi oquiella,

Bulzi's solution is perfect. This question asks for what N MUST be divisible by, so we have to start with the simplest option and work from there.

Since N is a POSITIVE INTEGER, and divisible by 5 and 7, the simplest option is 35. Since 35 is NOT divisible by 12 or 70, Roman Numerals 1 and 3 are eliminated (and we can eliminate Answers B, D and E).

The subsequent values of N will all be multiples of 35 (re: 35, 70, 105, 140, etc.), so they are all evenly divisible by 35.


hi there,

i dont understand. 70 is a multiple of 35. but its not divisible? im confused. why not 70?

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[[email protected]]

Hi oquiella,

No positive integer is evenly divisibly by another integer that is GREATER than it.

35 is NOT divisible by 70. Since N could be 35, N isn't always divisible by 70.

GMAT assassins aren't born, they're made,
Rich