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

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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
Brent Hanneson - Creator of GMATPrepNow.com
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GMAT/MBA Expert

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[email protected] wrote:
Mon Jul 18, 2022 6:54 am
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
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
Brent Hanneson - Creator of GMATPrepNow.com
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