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If # denotes one of the four arithmetic operations addition

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by VJesus12 » Mon Apr 08, 2019 5:45 am

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B

C

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E

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If # denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the value of 1 # 2?

(1) n # 0 = n for all integers n
(2) n # n = 0 for all integers n

[spoiler]OA=B[/spoiler]

Source: GMAT Prep
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Apr 08, 2019 8:51 pm
VJesus12 wrote:If # denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the value of 1 # 2?

(1) n # 0 = n for all integers n
(2) n # n = 0 for all integers n

[spoiler]OA=B[/spoiler]

Source: GMAT Prep
Let's take each statement one by one.

(1) n # 0 = n for all integers n

"¢ # as addition

We see that n # 0 = n + 0 = n;

So, 1 # 2 = 1 + 2 = 3.

"¢ # as subtraction

We see that n # 0 = n - 0 = n;

So, 1 # 2 = 1 - 2 = -1.

No unique value of 1 # 2. Insufficient.

(2) n # n = 0 for all integers n

"¢ # as subtraction

We see that n # n = n - n = 0

No other operator can be #.

So, 1 # 2 = 1 - 2 = -1. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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