ravitejapandiri 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

Attachment:

DS3.PNG

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: http://www.gmatprepnow.com/module/gmat-data-sufficiency?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 multiplicationCase b: If # represents multiplication, then the answer to the REPHRASED target question is

YES, # DOES represent either addition or multiplicationIn both cases, we get the SAME answer to the

REPHRASED target questionSince we can answer the

target question with certainty, statement 1 is SUFFICIENT

Statement 2: 3#1 = 3The 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 multiplicationCase b: If # represents multiplication, then the answer to the REPHRASED target question is

YES, # DOES represent either addition or multiplicationSince we cannot answer the

target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,

Brent

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Brent Hanneson – GMATPrepNow.com

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