Practice GMAT Problem Solving Question

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5n + 2 > 12 and 7n - 5 < 44; n must be between which numbers?
Correct Answer: D
  1. We have two inequalities and we need to find an upper and a lower bound for the value of n. Start with the first inequality to find one of these bounds:
    5n+2>12
    5n>10
    n>2
  2. Subtract 2 from both sides to yield: 5n>10.
  3. Divide by 5 on both sides to yield: n>2. Thus, 2 is one of the limits. This rules out choices A and C.
  4. Take the second inequality to find the upper bound:
    7n-5<44
    7n<49
    n<7
  5. Add 5 to both sides of the inequality to yield: 7n<49.
  6. Divide both sides by 7 to yield the upper bound: n<7.
  7. Combining the answers from both inequalities yields that n is between 2 and 7. Thus, choice D is correct.

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