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Last Updated on May 4, 2023
GMAT OFFICIAL GUIDE PS
Solution:
1< 5n + 5 < 25 is a compound inequality. Compound inequalities often need to be manipulated, and we can use the rules of algebra that we already know to do this. Just as with equations, whatever we do to one part of a compound inequality, we must do to all parts of the compound inequality. Let’s first isolate n within the inequality.
1< 5n + 5 < 25
We first subtract 5 from all three parts of the inequality, and we obtain:
-4 < 5n < 20
Next, we divide both sides of the inequality by 5 and we get:
-4/5 < n < 4
The integers that are greater than -4/5 and less than 4 are 0, 1, 2, and 3. Thus, there are 4 integers that satisfy the inequality 1 < 5n + 5 < 25.
Answer: B
