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OG The symbol # denotes one of the four

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OG The symbol # denotes one of the four

by AbeNeedsAnswers » Fri Aug 18, 2017 5:47 pm
The symbol # denotes one of the four arithmetic operations: addition, subtraction, multiplication, or division. If 6#3 <= 3, which of the following must be true?

I. 2#2 = 0
II. 2#2 = 1
III. 4#2 = 2

A) I only
B) II only
C) III only
D) I and II only
E) I, II and III

C
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by [email protected] » Mon Aug 21, 2017 1:07 pm
Hi AbeNeedsAnswers,

We're told that the symbol # denotes one of the four arithmetic operations: addition, subtraction, multiplication, or division and that 6#3 <= 3. We're asked which of the three Roman Numerals must be true.

To start, let's do a bit of analysis on the inequality that we're given (and determine which math operation COULD fit this):
6#3 <= 3

6 + 3 = 9 which is NOT <= 3
6 - 3 = 3 which IS <= 3
(6)(3) = 18 which is NOT <= 3
6/3 = 2 which IS <=3

Thus, the symbol # must be either subtraction or division (although we don't know which one for sure).

I. 2#2 = 0

We've proven that the symbol is either subtraction or division, so let's see if either of those operations 'fits' this information...
2 - 2 = 0
2/2 = 1
Thus, if the symbol is subtraction, then Roman Numeral 1 IS true. However, if the symbol is division, then Roman Numeral 1 is NOT true. There's no way to know which symbol is involved though, so Roman Numeral 1 is not necessarily true.
Eliminate Answers A, D and E.

II. 2#2 = 1

With the work that we've done in Roman Numeral 1 (above), we already know that the outcome of 2#2 could be 0 or 1. This inconsistency also provides that Roman Numeral 2 is not necessarily true.
Eliminate Answer B.

There's only one answer remaining....

III. 4#2 = 2

You can still prove that Roman Numeral 3 is always true...
4 - 2 = 2
4/2 = 2
Both outcomes 'fit' the information in Fact 3, so regardless of what operation is represented, the statement IS true.

Final Answer: C

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by Blackishmamba » Mon Jul 30, 2018 7:32 am
AbeNeedsAnswers wrote:The symbol # denotes one of the four arithmetic operations: addition, subtraction, multiplication, or division. If 6#3 <= 3, which of the following must be true?

I. 2#2 = 0
II. 2#2 = 1
III. 4#2 = 2

A) I only
B) II only
C) III only
D) I and II only
E) I, II and III

C
When the question itself says that the sign represents "one" of arithmetic operation, why do we want the answer choice that satisfies both operations: subtraction, and division?
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by regor60 » Mon Jul 30, 2018 8:58 am
Blackishmamba wrote:
AbeNeedsAnswers wrote:The symbol # denotes one of the four arithmetic operations: addition, subtraction, multiplication, or division. If 6#3 <= 3, which of the following must be true?

I. 2#2 = 0
II. 2#2 = 1
III. 4#2 = 2

A) I only
B) II only
C) III only
D) I and II only
E) I, II and III

C
When the question itself says that the sign represents "one" of arithmetic operation, why do we want the answer choice that satisfies both operations: subtraction, and division?
While the # sign represents only one operation, that one operation could be either subtraction or division since either operation is consistent with 6#3<=3.

In other words, one of these two operations, but you don't know which one.

The "must be true" language is crucial because it requires that the question be correct whether the operation is division OR subtraction - true in either case - no matter what.

As demonstrated in the prior post, I is correct only for the subtraction operation but not for division. And II is the same issue in reverse. Only III is true for both division and subtraction.
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by Scott@TargetTestPrep » Fri Aug 10, 2018 5:57 pm
AbeNeedsAnswers wrote:The symbol # denotes one of the four arithmetic operations: addition, subtraction, multiplication, or division. If 6#3 <= 3, which of the following must be true?

I. 2#2 = 0
II. 2#2 = 1
III. 4#2 = 2

A) I only
B) II only
C) III only
D) I and II only
E) I, II and III
First we need to determine which operation # represents. Since we are given that 6#3 ≤ 3, we can see that # can't be addition or multiplication. However, it can be either subtraction or division. It can be subtraction since 6 - 3 = 3 and it can also be division since 6/3 = 2.

Now let's analyze the given Roman numeral choices.

I. 2#2 = 0

If # is subtraction, then 2#2 = 2 - 2 = 0. However, if # is division, then 2#2 = 2/2 = 1.

We see that I might not be true.

II. 2#2 = 1

If # is division, then 2#2 = 2/2 = 1. However, if # is subtraction, then 2#2 = 2 - 2 = 0.

We see that II might not be true.

III. 4#2 = 2

If # is subtraction, then 4#2 = 4 - 2 = 2. If # is division, then 4#2 = 4/2 = 2.

We see that III is true regardless of whether # is subtraction or division.

Answer: C

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