What is the average (arithmetic mean) of a and b?

(1) The average (arithmetic mean) of a + 2 and b + 7 is 12

(2) The average (arithmetic mean) of a, b and 6 is 7

Correct answer marked below

Statement (1) ALONE is sufficient

Statement (2) ALONE is sufficient

BOTH statements TOGETHER are sufficient

EACH statement ALONE is sufficient

Correct

Statements (1) and (2) TOGETHER are NOT sufficient

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Explanation

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Comments

BerkayAug 3

thanks, this one was quick once I set up the two equations

AmanAug 7

same, i just wrote out (a+2+b+7)/2 = 12 and it fell right out

GuillaumeJun 2

wait for statement 1, do i need to find a and b individually or just their sum? i kept trying to solve for each one lol

AmandaJun 14

you only need the sum. the question asks for the mean, so the sum is enough

VindhyaMay 11

why is the answer EACH alone? i thought you needed both together to get one value

ChristinaMay 14

each statement gives you a different sum but each is enough by itself to get the mean

What this question tests

Your fluency with the order of operations, fractions, decimals, and basic number sense — the foundation every quant question leans on.

Applying the order of operations out of sequence or rounding intermediate values before the final step.

What is the average (arithmetic mean) of a and b?(1) The average (arithmetic mean) of a + 2 and b + 7 is 12(2) The average (arithmetic mean) of a, b and 6 is 7