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

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GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4882
GMAT 1: 770 Q49 V46
The symbols \$ and # each represent one of the following operations:  [#permalink]

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06 Aug 2019, 07:11
Top Contributor
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Difficulty:

75% (hard)

Question Stats:

48% (02:07) correct 52% (01:35) wrong based on 33 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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NUS School Moderator
Joined: 18 Jul 2018
Posts: 1121
Location: India
Concentration: Operations, General Management
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE: Engineering (Energy and Utilities)
Re: The symbols \$ and # each represent one of the following operations:  [#permalink]

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06 Aug 2019, 08:54
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.
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4882
GMAT 1: 770 Q49 V46
Re: The symbols \$ and # each represent one of the following operations:  [#permalink]

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07 Aug 2019, 08:51
Top Contributor
1
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

Cheers,
Brent
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Re: The symbols \$ and # each represent one of the following operations:   [#permalink] 07 Aug 2019, 08:51

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

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