# 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**- 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 - Subtract 2 from both sides to yield: 5n>10.
- Divide by 5 on both sides to yield: n>2. Thus, 2 is one of the limits. This rules out choices A and C.
- Take the second inequality to find the upper bound:

7n-5<44

7n<49

n<7 - Add 5 to both sides of the inequality to yield: 7n<49.
- Divide both sides by 7 to yield the upper bound: n<7.
- Combining the answers from both inequalities yields that n is between 2 and 7. Thus, choice D is correct.

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