MathRevolution wrote:
[GMAT math practice question]
If \(0<2x+3y<10\) and \(-10<3x+2y<0\), then which of the following must be true?
\(I. x<0\)
\(II. y<0\)
\(III. x<y\)
A. I only
B. II only
C. I & II
D. I & III
E. I, II, &III
We see that x and y can’t be both positive or both negative. If x and y are both positive, then the second inequality will not hold. Similarly, if x and y are both negative, then the first inequality will not hold. Therefore, we must consider two separate cases: (1) x is negative and y is positive and (2) x is positive and y is negative.
Case 1. Let’s assume that x is negative and y is positive.
For example, If x = -5 and y = 5, we see that we do have 0 < 2x + 3y < 10 and -10 < 3x + 2y < 0.
Case 2. Now let’s assume that x is positive and y is negative. We see that the absolute value of y must be greater than the absolute value of x in order for the second inequality to hold.
For example, if x = 2, y has to be less than -3 in order to have -10 < 3x + 2y < 0. However, in that case, the first inequality will never hold since 2x + 3y will be negative. Thus we can’t have x as positive and y as negative.
Thus it must be true that x is negative and y is positive and in that case we also have x < y. Thus, Statements I and III must be true.
Answer: D
_________________
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.