Data Sufficiency

BTGmoderatorDC wrote:The symbol Ω represents one of the following operations: addition, subtraction, multiplication or division. What is the value of 1 Ω 1?

(1) 2 Ω 2 = 4
(2) 0 Ω 1 = 0

Target question: What is the value of 1 Ω 1?

Given: Ω represents one of the following operations: addition, subtraction, multiplication or division.

Statement 1: 2 Ω 2 = 4
2 - 2 = 0, so Ω CANNOT represent subtraction.
2 ÷ 2 = 1, so Ω CANNOT represent division.
2 + 2 = 4, so Ω COULD represent addition. In this case, the answer to the target question is 1 Ω 1 = 1 + 1 = 2
2 x 2 = 4, so Ω COULD represent multiplication. In this case, the answer to the target question is 1 Ω 1 = 1 x 1 = 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 0 Ω 1 = 0
0 - 1 = -1, so Ω CANNOT represent subtraction.
0 ÷ 1 = 0, so Ω COULD represent division. In this case, the answer to the target question is 1 Ω 1 = 1 ÷ 1 = 1
0 + 1 = 1, so Ω CANNOT represent addition.
0 x 1 = 0, so Ω COULD represent multiplication. In this case, the answer to the target question is 1 Ω 1 = 1 x 1 = 1

IMPORTANT: from statement 2, we can conclude that Ω represents EITHER division OR multiplication. Because Ω could represent two different operations, some students will incorrectly conclude that statement 2 is not sufficient.
However, the target question is NOT asking "What operation does Ω represent?" The target question is asking What is the value of 1 Ω 1?

In BOTH of the above cases (for statement 2), 1 Ω 1 = 1.
Since we get only one answer to the target question, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

BTGmoderatorDC wrote:The symbol Ω represents one of the following operations: addition, subtraction, multiplication or division. What is the value of 1 Ω 1?

(1) 2 Ω 2 = 4

(2) 0 Ω 1 = 0

OA B

Source: Magoosh

Question: What's the value of 1 Ω 1?

Let's take each statement one by one.

(1) 2 Ω 2 = 4

2*2 = 4 or 2 + 2 = 4. So, Ω can be either multiplication or addition.

So, 1 Ω 1 is either 1 + 1 = 2 or 1*1 = 1. No unqiue answer. Insufficient.

(2) 0 Ω 1 = 0

0*1 = 0 or 0/1 = 0. So, Ω can be either multiplication or division.

So, 1 Ω 1 is either 1/1 = 1 or 1*1 = 1. Unqiue answer. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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