If |2x| = |3y|, what is the value of |2x + 3y|?

This question can be solved just by using reasoning and no math is required to arrive at the answer.

What we know

|2x| = |3y|

Inference: The distance of 2x from 0 = The distance of 3y from 0

We do not know if 3y and 2x lie on the same side of 0 or they lie on the opposite side of 0.

Question

|2x+3y| = ?

Inference: At what distance from 0 does the sum of 2x and 3y lie ?

Reasoning

1) If both 2x and 3y lie on the same side of zero, the distance of the sum will be twice the original distance.
2) If 2x and 3y lie on the opposite side of zero, then the sum will be zero as the positive value and the negative value will cancel out.

So all we need to find to solve this question is answer to the question "Do 2x and 3y lie on the same side of zero or do they lie on opposite side of zero".

With this pre-thinking, let's dive into the options.

Statement 1

3x - 2y = 10

Well we know that 3x lies to the right of 2y as the difference is positive. However, we do not know on the position with reference to 0.

Hence, this statement is not sufficient. We can eliminate A and D.

Statement 2

xy < 0

Well ! if the product of x and y is less than 0, it means x and y hold opposite signs. Thus 3y and 2x will lie on the opposite side of 0, we don't know which number is greater than 0 and which one is less, but that's not required to answer the question.

Therefore, this statement provides us the information that we are looking for and is sufficient to find the value of |2x + 3y|.

Option B

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