The symbol ∆ denotes one of the four arithmetic operations:addition,su

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

If 6 ∆ 3 ≤ 3, then the ∆ operator is subtraction AND division.

6 - 3 = 3, which satisfies the equation

\(\frac{6}{3}\) = 2, which also satisfies the equation (2 is less than 3).

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

Check I, II, and III.

I. 2 ∆ 2 = 0. If ∆ were only subtraction, this would be fine. 2 - 2 = 0.

But \(\frac{2}{2}\) = 1. This equation is not true when ∆ is division. Incorrect.

II. 2 ∆ 2 = 1. If ∆ were only division, this would be fine.\(\frac{2}{2}\) = 1. But when ∆ is subtraction, then 2 - 2 = 0. This equation does not hold true when ∆ is subtraction. Incorrect.

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

It holds for subtraction. 4 - 4 = 2
And it holds for division: \(\frac{4}{2}\)= 2. Correct.

Answer C

VeritasKarishma | Bunuel

As a test taker -- how are we supposed to know that ∆ should represent BOTH division AND subtraction

I assumed, the conditions applied individually (subtraction OR division) and thus opted for E

It's clear one or the other works

Since the question says 6∆3=<3
6/3 = 2
OR
6-3 = 3

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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

Why is E wrong?

The equation suggests 6∆3≤ 3 ie., 6∆3 is either less than 3 or equal to 3

so, why wouldn't choosing option E solve all of the conditions? Don't we have to just pass either of the two conditions?

If 6 ∆ 3 ≤ 3, then the ∆ operator is subtraction AND division.

6 - 3 = 3, which satisfies the equation

\(\frac{6}{3}\) = 2, which also satisfies the equation (2 is less than 3).

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

Check I, II, and III.

I. 2 ∆ 2 = 0. If ∆ were only subtraction, this would be fine. 2 - 2 = 0.

But \(\frac{2}{2}\) = 1. This equation is not true when ∆ is division. Incorrect.

II. 2 ∆ 2 = 1. If ∆ were only division, this would be fine.\(\frac{2}{2}\) = 1. But when ∆ is subtraction, then 2 - 2 = 0. This equation does not hold true when ∆ is subtraction. Incorrect.

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

It holds for subtraction. 4 - 4 = 2
And it holds for division: \(\frac{4}{2}\)= 2. Correct.

Answer C