The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency

Question: 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?

1. 2∆2 = 0
2. 2∆2 = 1
3. 4∆2 = 2

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“The symbol ∆ denotes one of the four arithmetic operations”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

If we consider the problem statement in question 6 ∆ 3 ≤ 3, then the ∆ operator is subtraction AND division.

6 - 3 = 3, which satisfies the equation

6/3 = 2, which also satisfies the equation (2 is less than 3).

The operator cannot be addition or multiplication. The reason is that 6 + 3 = 9, which is > 3. And 6 * 3 = 18, also > than 3.

Now, considering the above fact, if we look at the options I, II, and III that are provided, we will be able to get the solution.

1. If we consider 2 ∆ 2 = 0. If ∆ we're only subtraction, this would be fine. 2 - 2 = 0.

However,

2/2 = 1. This equation is not true when ∆ is divided. Hence, it is Incorrect.

2. 2 ∆ 2 = 1. If ∆ were only a division, this would be fine as 2/2=1.

But when ∆ is subtracted, then 2 - 2 = 0. This equation does not hold true when ∆ is subtraction. Incorrect.

3. 4 ∆ 2 = 2. This must be true for both subtraction and division.

It holds true for subtraction since 4 - 4 = 2
And it holds for division:
4/2 = 2 is also correct.

Correct Answer: C

Approach Solution 2:

∆ could be either Subtraction or Division in order to fulfill condition 6∆3≤ 3. The reason is that 6/3=2 which is less than 3 and 6-3=3. It cannot be addition or multiplication.

The reason it cannot be addition or multiplication is because 6*3=18, which is greater than 3 and 6+3=9 which is also greater than 3.

Now, we will consider the options provided in the questions to see which is the correct one.

The first equation:
I - 2∆2=0 - In this condition, ∆ denotes only subtraction and not Division. 2-2=0 is the only condition that is satisfied. 2/2=1 and this is not equal to 0. Hence, this is not the correct one.

The second equation:
II - 2∆2=1 - In this condition, ∆ denotes only Division and not subtraction. 2/2=1 is satisfied. However, if we consider subtraction, we get 2-2=0. Since 0 is not equal to 1, the condition is not satisfied.

The third equation:
III - 4∆2=2 - In this condition, ∆ denotes either Division or subtraction. To justify the answer, we will check both scenarios.

It holds true for subtraction since 4 - 4 = 2
And it holds for division:
4/2 = 2 is also correct.

Correct Answer: C

Approach Solution 3:

The operator is subtraction AND division if we take the problem statement in question 6 ∆ 3 ≤ 3 into consideration.

The equation is satisfied since 6 - 3 = 3.

Equation is also satisfied by the fact that 6/3 Equals 2.

Multiplication or addition cannot be the operator. This is because 6 Plus 3 equals 9, which is greater than 3. And 6 + 3 Equals 18, which is greater than 3.

Now that we are aware of the aforementioned information, we may find the answer by looking at alternatives I, II, and III that are offered.

Considering that 2 ∆ 2 Equals 0, This would be okay if all we were doing was subtracting. 2 - 2 = 0.
However,

2/2 = 1. When ∆ is divided, this equation does not hold true. It is therefore incorrect.

2 ∆ 2 = 1. This would be OK it were only a division because 2/2=1.
However, if is subtracted, 2 - 2 equals 0. When is subtracted, this equation is invalid. Incorrect.

4 ∆ 2 = 2. Both division and subtraction must be true.
It applies to subtraction since 4 - 4 = 2.
It also applies to division: 4/2 = 2 is the right answer.

Correct Answer: C

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