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# 6. -10 is less than x plus y...

PowerScore StaffJoined: 10/31/2016
edited Thu Feb 1, 2018 in Q1

# Description

• Type: Quantitative Comparison
• Topic: Inequalities, Algebra
• Multiple Variables
• Answer: D, The Relationship Cannot Be Determined

# Explanation

Consider scratch work above.
1. Start by Recording What You Know™ and getting your Possibility Matrix™ and answer choices set up.
2. Separate the top inequality out so that you can work with both parts separately.
3. The second inequality just gives you a range of values that work for x. As long as x can be between 5 and 10, we're in business.
4. Let's just try out a couple values for y to try to illustrate whether it can be greater than or less than -15.
6. Now work through the top inequality to see what happens.
7. If y = -12, then -10 < x -12, so 2 < x.
8. Also, x - 12 < 20, so x < 32.
9. Put it together. 2 < x < 32. Do any values here fall within our range of possible values for x, 5 < x < 10? Sure, that's all possible. In other words, y can equal -12 because that does not violate the restrictions on x.
10. Since y can equal -12, eliminate B and C.
11. Now let's make y less than -15. Let's try y = -16.
12. By the same process as above, we determine with y = -16, 6 < x < 36.
13. These values also overlap with 5 < x < 10. Therefore -16 is a possible value for y too.
14. We've made y less than -15, so eliminate answer choice A.
15. We've made Column A both greater than and less than Column B, so the relationship cannot be determined.