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

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


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


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.
  5. Start with greater than. Let's make y equal to -12.
  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.
  16. The answer is D.
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