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GRE Quantitative Reasoning QUESTION #8070
Question 1

Given the inequality $x + 2y > 8$, compare:

Column A: $2x + 4y$

Column B: 20

  • Column A is greater
  • Column B is greater
  • The two quantities are equal
  • The relationship cannot be determined✔️
Correct Answer Explanation

From the given inequality: $x + 2y > 8$

Multiplying both sides by 2: $2(x + 2y) > 2(8)$

This gives us: $2x + 4y > 16$

So we know that Column A $> 16$, but we cannot determine whether $2x + 4y$ is greater than, less than, or equal to 20 without additional information.

For example:

  • If $x = 5, y = 2$: then $x + 2y = 9 > 8$ ✓, and $2x + 4y = 18 < 20$
  • If $x = 10, y = 5$: then $x + 2y = 20 > 8$ ✓, and $2x + 4y = 40 > 20$

Since different valid values give different relationships, the answer cannot be determined from the information given.