Data Sufficiency

swerve wrote:The symbol ⊗ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 7⊗4?

(1) 4⊗7 < 1

(2) 4⊗3 > 1

The OA is C.

I need help to solve this DS question. Please, can any expert explain it for me? Thanks.

We have to the value of 7⊗4. To get this, we must know what operation ⊗ does.

Question rephrased: What operation ⊗ does?

(1) 4⊗7 < 1

1. Assuming that ⊗ is addition, then 4⊗7 < 1 => 4 + 7 (= 11) > 1. Not correct.
2. Assuming that ⊗ is subtraction, then 4⊗7 < 1 => 4 - 7 (= -3) < 1. Correct.
3. Assuming that ⊗ is multiplication, then 4⊗7 < 1 => 4 x 7 (= 28) < 1. Not correct.
4. Assuming that ⊗ is division, then 4⊗7 < 1 => 4 ÷ 7 (= 0.5) < 1. Correct.

⊗ can either be subtraction or division. No unique answer. Insufficient.

(2) 4⊗3 > 1

1. Assuming that ⊗ is addition, then 4⊗3 > 1 => 4 + 3 (= 7) > 1. Correct.
2. Assuming that ⊗ is subtraction, then 4⊗3 > 1 => 4 - 3 (= 1) = 1. Not correct.
3. Assuming that ⊗ is multiplication, then 4⊗3 > 1 => 4 x 3 (= 12) > 1. Correct.
4. Assuming that ⊗ is division, then 4⊗3 > 1 => 4 ÷ 3 (= 1.33) > 1. Correct.

⊗ can either be addition, multiplication or division. No unique answer. Insufficient.

(1) and (2) combined:

After combing, we get that ⊗ is a division. No unique answer. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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