Data Sufficiency

BTGmoderatorDC wrote:If the operation # is one of the four arithmetic operations addition, subtraction, multiplication and division, is (6#2)#4 = 6#(2#4)

(1) 3#2 > 3

(2) 3#1 = 3

OA A

Source: GMAT Prep

Let's take each statement one by one.

(1) 3#2 > 3

Say # is:

1. Addition: Thus, 3#2 > 3 => 3+2 > 3 => 5 > 3. Thus, # can be addition.
2. Subtraction: Thus, 3#2 > 3 => 3-2 > 3 => 1 < 3. Thus, # cannot be subtraction.
3. Multiplication: Thus, 3#2 > 3 => 3 x 2 > 3 => 6 > 3. Thus, # can be multiplication.
4. Division: Thus, 3#2 > 3 => 3÷2 > 3 => 1/5 < 3. Thus, # cannot be subtraction.

Thus, # is either addition or multiplication.

Let's find out the value of (6#2)#4 = 6#(2#4)

Case 1: Say # is addition.

=> (6#2)#4 = 6#(2#4) => (6+2)+4 = 6+(2+4). It's a valid result. The answer is Yes.

Case 2: Say # is multiplication.

=> (6#2)#4 = 6#(2#4) => (6x2)x4 = 6x(2x4). It's a valid result. The answer is Yes.

Unique answer. Sufficient.

(2) 3#1 = 3

1. Addition: Thus, 3#1 = 3 => 3+1 = 3 => 4 ≠ 3. Thus, # cannot be addition.
2. Subtraction: Thus, 3#1 = 3 => 3 - 1 = 3 => 2 ≠ 3. Thus, # cannot be subtraction.
3. Multiplication: Thus, 3#1 = 3 => 3x1 = 3 => 3 = 3. Thus, # can be multiplication.
4. Division: Thus, 3#1 = 3 => 3÷1 = 3 => 3 = 3. Thus, # can be division.

Thus, # is either division or multiplication.

In Statement 1, we have already seen that # can be multiplication and the answer to the question is Yes. Let's check whether # can also work as division.

=> (6#2)#4 = 6#(2#4) => (6÷2)÷4 = 6÷(2÷4) => 3÷4 ? 6÷0.5 => 0.75 ≠ 12. The answer is No.

There is no unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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