DS Problem

beatthegmat wrote:Posting on behalf of galit...

hi, my name is galit, I am new here, wanted to ask a question which is taken from the princeton review book:

if x and y are positive integers, is x a factor of 12?

1.the product xy is a factor 12

2.y=3

When solving DS number property questions, we generally have two options: use our knowledge of number property rules or plug in numbers.

If you read a question and/or statement and the rules jump out at you, then using them will almost certainly be the most efficient approach; if they don't jump out at you, then you can't afford to waste time staring at the screen hoping for inspiration to strike from above - you have to either get your hands dirty and plug in numbers or guess and move on.

This question is a perfect example.

We know that x and y are positive integers - we don't know anything else.

Q: is x a factor of 12? In other words, is 12 a multiple of x? Or, another way we could phrase it, is 12/x an integer? It's the 3rd way of phrasing it that will help us quickly answer this question.

(1) xy is a factor of 12.

So, 12/xy = integer. Multiplying both sides by y, we get:

12/x = y*integer. Since y is an integer, y*int is also an integer.

In other words, 12/x is an integer - the definition of a factor. Therefore, x is definitely a factor of 12: sufficient.

(2) y=3. No information about x: insufficient.

(1) is sufficient, (2) isn't: choose (a).

I tried doing the problem by subsituition,

Case 1

x=4 and y=3

In this case xy =12 and is a factor of 12.

But still x=4 is not a factor of 12.

Case 2

x= 12 y =2

xy =24

x =12 is a factor of 12

Therfore A is insufficient

Please explain

[email protected] wrote:I tried doing the problem by subsituition,

But still x=4 is not a factor of 12.


Please explain

Explanation:

umm.. 4 IS a factor of 12!