If a, b and c are different positive integers, is c the greatest value?

(1) c = b - a - 5

(2) a = 2c - b

Answer: D

Source: www.gmatprepnow.com

## If a, b and c are different positive integers, is c the greatest value?

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### GMAT/MBA Expert

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**Posts:**16136**Joined:**08 Dec 2008**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1268 members**GMAT Score:**770

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[email protected] wrote: ↑Mon Jul 18, 2022 6:54 amIf a, b and c are different positive integers, is c the greatest value?

(1) c = b - a - 5

(2) a = 2c - b

Answer: D

Source: www.gmatprepnow.com

**Given: a, b and c are different positive integers**

**Target question:**

**Is c the greatest value?**

**Statement 1: c = b - a - 5**

In other words, to find the value of c, we take b and SUBRACT a and 5, which means c must be less than b, which means c can't be the greatest value.

The answer to the target question is NO, c is not the greatest value

Since we can answer the target question with certainty, statement 1 is SUFFICIENT

**Statement 2: a = 2c - b**

Let's isolate the value of c.

Add b to both sides: a + b = 2c

Divide both sides by 2 to get:

**(a + b)/2 = c**

This means c is the AVERAGE (arithmetic mean) of a and b, which means c must be BETWEEN a and b, which means c can't be the greatest value.

The answer to the target question is NO, c is not the greatest value

Since we can answer the target question with certainty, statement 2 is SUFFICIENT

**Answer: D**