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

# Description

- Type: Quantitative Comparison
- Topic: Inequalities, Algebra
- Multiple Variables

- Answer:
**D, The Relationship Cannot Be Determined**

# Explanation

Consider scratch work above.

- Start by Recording What You Know™ and getting your Possibility Matrix™ and answer choices set up.
- Separate the top inequality out so that you can work with both parts separately.
- The second inequality just gives you a range of values that work for x. As long as x
between 5 and 10, we're in business.**can be** - Let's just try out a couple values for y to try to illustrate whether it can be greater than or less than -15.
- Start with greater than. Let's make y equal to -12.
- Now work through the top inequality to see what happens.
- If y = -12, then -10 < x -12, so 2 < x.
- Also, x - 12 < 20, so x < 32.
- 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.
- Since y can equal -12, eliminate B and C.
- Now let's make y less than -15. Let's try y = -16.
- By the same process as above, we determine with y = -16, 6 < x < 36.
- These values also overlap with 5 < x < 10. Therefore -16 is a possible value for y too.
- We've made y less than -15, so eliminate answer choice A.
- We've made Column A both greater than and less than Column B, so the relationship cannot be determined.
**The answer is D.**

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