Vincen wrote: ↑

Tue Jun 02, 2020 7:55 am

If \(x\) is an integer divisible by 15 but not divisible by 20, then \(x\) CANNOT be divisible by which of the following?

A. 6
B. 10
C. 12
D. 30
E. 150

[spoiler]OA=C[/spoiler]

Source: Princeton Review

There are at least two different ways to solve this question:
1) Determine what properties of x are required so that x is divisible by 15 but not divisible by 20, and then use those results to identify the correct answer
2) Test values

When it comes to solving Integer Properties questions, testing values is often a very fast and effective approach. So let's do that.

Important: The question asks "x CANNOT be divisible by which of the following?"
So if we can show that x CAN be divisible by a certain value, we can ELIMINATE that answer choice.

If x is divisible by 15 but not divisible by 20, then x COULD be 30
Check the answer choices....
Since 30 IS divisible by 6, 10 and 30, we can ELIMINATE answer choices A, B and D

Now let's test another possible value of x

If x is divisible by 15 but not divisible by 20, then x COULD be 150
Since 150 IS divisible by 150, we can ELIMINATE answer choice E.

By the process of elimination, the correct answer is C

Cheers,
Brent

Vincen wrote: ↑

Tue Jun 02, 2020 7:55 am

If \(x\) is an integer divisible by 15 but not divisible by 20, then \(x\) CANNOT be divisible by which of the following?

A. 6
B. 10
C. 12
D. 30
E. 150

[spoiler]OA=C[/spoiler]

Solution:

Since x is divisible by 15 and not 20, and 15 = 5 x 3 and 20 = 2^2 x 5, we see that x will never be divisible by a number with two 2s in its prime factorization. Thus, x will not be divisible by 12, because 12 = 2^2 x 3^1.

Answer: C