M7MBA wrote: ↑Sun Dec 26, 2021 3:34 pm
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) \(3\#1 = 3\)
Answer:
A
Source: GMAT Prep
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
