Data Sufficiency

swerve wrote:Source: GMAT Prep

If the operation # is one of the four operations - addition, subtraction, multiplication and division. Is (6#2)#4 = 6#(2#4)

(1) 3#2 > 3.
(2) 3#1 = 3.

Target question: Is (6#2)#4 = 6#(2#4)?
This is a good candidate for rephrasing the target question.

Under what circumstances does (6#2)#4 = 6#(2#4) ?
Let's test each possible operation:

ADDITION: If # represents addition, we get: (6+2)+4 = 6+(2+4)
Simplify to get: 12 = 12. WORKS!
So, (6#2)#4 = 6#(2#4) when # represents addition

SUBTRACTION: If # represents subtraction, we get: (6-2)-4 = 6-(2-4)
Simplify to get: 4-4 = 6-(-2).
Doesn't work.

MULTIPLICATION: If # represents multiplication, we get: (6x2)x4 = 6x(2x4)
Simplify to get: 12x4 = 6x8. WORKS!
So, (6#2)#4 = 6#(2#4) when # represents multiplication

DIVISION: If # represents division, we get: (6÷2)÷4 = 6÷(2÷4)
Simplify to get: 3÷4 = 6÷(1/2)
Evaluate to get: 3/4 = 12
Doesn't work.

So, (6#2)#4 = 6#(2#4) when # represents EITHER addition OR multiplication
REPHRASED target question: Does # represent EITHER addition OR multiplication?

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: 3#2 > 3
This inequality holds true when # represents addition or multiplication
Case a: If # represents addition, then the answer to the REPHRASED target question is YES, # DOES represent either addition or multiplication
Case b: If # represents multiplication, then the answer to the REPHRASED target question is YES, # DOES represent either addition or multiplication
In both cases, we get the SAME answer to the REPHRASED target question
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 3#1 = 3
The above equation holds true when # represents division or multiplication
Case a: If # represents division, then the answer to the REPHRASED target question is NO, # does NOT represent either addition or multiplication
Case b: If # represents multiplication, then the answer to the REPHRASED target question is YES, # DOES represent either addition or multiplication
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

swerve wrote: ↑

Mon Aug 06, 2018 9:35 am

Source: GMAT Prep

If the operation # is one of the four operations - addition, subtraction, multiplication and division. Is (6#2)#4 = 6#(2#4)

(1) 3#2 > 3.
(2) 3#1 = 3.

The OA is A.

Please, can anyone explain this DS question? I need help. Thanks.

Solution:

Since the operations addition and multiplication are associative (but subtraction and division are not), we see that if # is either addition or multiplication, then we have (6#2)#4 = 6#(2#4).

Statement One Only:

3#2 > 3

We see that the inequality holds if # is either addition or multiplication. Since # is either addition or multiplication, we have (6#2)#4 = 6#(2#4).

Statement one alone is sufficient.

Statement Two Only:

3#1 = 3

We see that the equality holds if # is either multiplication or division. If # is multiplication, then we have (6#2)#4 = 6#(2#4). However, if # is division, then we DO NOT have (6#2)#4 = 6#(2#4).

Statement two alone is not sufficient.

Answer: A