The symbols $ and # each represent one of the following operations: addition, subtraction, multiplication or division. W

[BTGModeratorVI]

The symbols $ and # each represent one of the following operations: addition, subtraction, multiplication or division. What is the value of 1 $ 1 # 1?

1) 2 $ 2 # 2 = 3
2) 3 $ 2 # 1 = 5

Answer: A
Source: GMAT Prep Now

[Jay@ManhattanReview]

The symbols $ and # each represent one of the following operations: addition, subtraction, multiplication or division. What is the value of 1 $ 1 # 1?

1) 2 $ 2 # 2 = 3
2) 3 $ 2 # 1 = 5

Answer: A
Source: GMAT Prep Now

To know that value of $ and #, we must know what operation $ and # represent.

Let's take each statement one by one.

1) 2 $ 2 # 2 = 3

• Say $ = multiplication; So, we have 2 x 2 # 2 = 3.

Given that # is one among addition, subtraction, multiplication or division, 2 x 2 # 2 cannot be equal to 3. Pl. try yourself. So, $ cannot be multiplication.

• Say $ = division; So, we have (2/2) # 2 = 3 => 1 # 2 = 3

=> # must be addition.

So, we have if $ = division, then # is addition.

Thus, 1 $ 1 # 1 = 1/1 + 1 = 2 ---(1)

• Say $ = addition; So, we have 2 + 2 # 2 = 3.

# cannot be subtraction since 2 + 2 –2 ≠ 3;
# cannot be addition since 2 + 2 + 2 ≠ 3;
# cannot be multiplication since 2 + 2 x 2 ≠ 3;

# cann be division since 2 + 2/2 = 3

So, we have if $ = addition, then # is division.

Thus, 1 $ 1 # 1 = 1 + 1/1 = 2. ---(2) Same answer as we got in (1).

• Say $ = subtraction; So, we have 2 – 2 # 2 = 3.

# cannot be subtraction since 2 – 2 – 2 ≠ 3;
# cannot be addition since 2 – 2 + 2 ≠ 3;
# cannot be multiplication since 2 – 2 x 2 ≠ 3;
# cannot be division since 2 – 2/2 ≠ 3;

So, we have 1 $ 1 # 1 = 2. A unique answer. Sufficient.


2) 3 $ 2 # 1 = 5

• $ cannot be division since if were so, 3/2 = 1.5 and whatever be operations # be, it's not going to render an integer 5.

• Say $ = subtraction; So, we have 3 – 2 # 1 = 5.

Whatever operations # be, we cannot get 3 – 2 # 1 = 5.

• Say $ = multiplication; So, we have 3 x 2 # 1 = 5.

# can be subtraction since 3 x 2 – 1 = 5. Thus, 1 $ 1 # 1 = 1 x 1 – 1 = 0 ---(3)
# cannot be multiplication since 3 x 2 x 2 ≠ 5
# cannot be addition since 3 x 2 + 2 ≠ 5

• Say $ = addition; So, we have 3 + 2 # 1 = 5.

# can be subtraction since 3 + 2 – 1 = 5. Thus, 1 $ 1 # 1 = 1 + 1 – 1 = 1 ---(4)

Since the value from (3) and (4) are not the same, statement 2 is insufficient.

Correct answer: A

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

The symbols $ and # each represent one of the following operations: addition, subtraction, multiplication or division. What is the value of 1 $ 1 # 1?

1) 2 $ 2 # 2 = 3
2) 3 $ 2 # 1 = 5

Answer: A
Source: GMAT Prep Now

Target question: What is the value of 1 $ 1 # 1?

Statement 1: 2 $ 2 # 2 = 3
There are two possible cases in which 2 $ 2 # 2 = 3
Case a: $ represents +, and # represents ÷. We get 2 + 2 ÷ 2 = 3, which works. In this case, the answer to the target question is 1 $ 1 # 1 = 1 + 1 ÷ 1 = 2
Case b: $ represents ÷, and # represents +. We get 2 ÷ 2 + 2 = 3, which works. In this case, the answer to the target question is 1 $ 1 # 1 = 1 ÷ 1 + 1 = 2
Since, we get the SAME answer to the target question (1 $ 1 # 1 = 2) in both cases, it MUST be the case that 1 $ 1 # 1 = 2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 3 $ 2 # 1 = 5
There are three possible cases in which 3 $ 2 # 1 = 5. Here are two such cases:
Case a: $ represents +, and # represents ÷. We get 3 + 2 ÷ 1 = 5, which works. In this case, the answer to the target question is 1 $ 1 # 1 = 1 + 1 ÷ 1 = 2
Case b: $ represents x, and # represents -. We get 3 x 2 - 1 = 5, which works. In this case, the answer to the target question is 1 $ 1 # 1 = 1 x 1 - 1 = 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent