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The symbols $ and # each represent one of the following operations:

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The symbols $ and # each represent one of the following operations:  [#permalink]

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New post 06 Aug 2019, 08:11
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Question Stats:

44% (01:59) correct 56% (01:33) wrong based on 18 sessions

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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

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Re: The symbols $ and # each represent one of the following operations:  [#permalink]

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New post 06 Aug 2019, 09:54
1
From 1:

2 $ 2 # 2 = 3

If $ is /, then # is +.
If $ is +, then # is /.
In both cases, the value of 1 $ 1 # 1 is the same, i.e, 2.
Sufficient.

From 2:

3 $ 2 # 1 = 5

If $ is x, then # is -.
If $ is +, then # is /.
In both cases, the value of 1 $ 1 # 1 is NOT the same.
Insufficient.

A is the answer.
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Re: The symbols $ and # each represent one of the following operations:  [#permalink]

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New post 07 Aug 2019, 09:51
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GMATPrepNow wrote:
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


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

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Brent
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Re: The symbols $ and # each represent one of the following operations:   [#permalink] 07 Aug 2019, 09:51
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The symbols $ and # each represent one of the following operations:

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