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The symbol [m]\triangle[/m] denotes one of the four arithmetic operati

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The symbol [m]\triangle[/m] denotes one of the four arithmetic operati  [#permalink]

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New post 17 Jun 2017, 03:12
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The symbol \(\triangle\) denotes one of the four arithmetic operations : addition, subtraction ,multiplication,or division.If 6\(\triangle\)3\(\leq{3}\) ,which of the following must be true ?

I. 2\(\triangle\)2=0
II. 2\(\triangle\)2=1
III. 4\(\triangle\)2=2

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

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Re: The symbol [m]\triangle[/m] denotes one of the four arithmetic operati  [#permalink]

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New post 17 Jun 2017, 03:24
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AbdurRakib wrote:
The symbol \(\triangle\) denotes one of the four arithmetic operations : addition, subtraction ,multiplication,or division.If 6\(\triangle\)3\(\leq{3}\) ,which of the following must be true ?

I. 2\(\triangle\)2=0
II. 2\(\triangle\)2=1
III. 4\(\triangle\)2=2

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


6\(\triangle\)3\(\leq{3}\)

\(\frac{6}{3} = 3\)

\(6 - 3 = 3\)


\(\triangle\) has to be division and subtraction both.

Checking the options, we get;

I. 2\(\triangle\)2=0

\(2 - 2 = 0.\)

\(\frac{2}{2}\) = 1 ---------- (Must Not be true)

II. 2\(\triangle\)2=1

\(\frac{2}{2}\) = 1.

\(2-2 = 0\) ---------- (Must Not be true)

III. 4\(\triangle\)2=2

\(4-2 = 2.\)

\(\frac{4}{2}\) = 2 -----------(Must be true)

Only III must be true. Answer (C).
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Re: The symbol [m]\triangle[/m] denotes one of the four arithmetic operati  [#permalink]

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New post 09 Mar 2018, 11:17
sashiim20 wrote:
AbdurRakib wrote:
The symbol \(\triangle\) denotes one of the four arithmetic operations : addition, subtraction ,multiplication,or division.If 6\(\triangle\)3\(\leq{3}\) ,which of the following must be true ?

I. 2\(\triangle\)2=0
II. 2\(\triangle\)2=1
III. 4\(\triangle\)2=2

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


6\(\triangle\)3\(\leq{3}\)

\(\frac{6}{3} = 3\)

\(6 - 3 = 3\)


\(\triangle\) has to be division and subtraction both.

Checking the options, we get;

I. 2\(\triangle\)2=0

\(2 - 2 = 0.\)

\(\frac{2}{2}\) = 1 ---------- (Must Not be true)

II. 2\(\triangle\)2=1

\(\frac{2}{2}\) = 1.

\(2-2 = 0\) ---------- (Must Not be true)

III. 4\(\triangle\)2=2

\(4-2 = 2.\)

\(\frac{4}{2}\) = 2 -----------(Must be true)

Only III must be true. Answer (C).


Hi sashiim20

i think there is one typo in your post :) try to find it :)
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The symbol [m]\triangle[/m] denotes one of the four arithmetic operati  [#permalink]

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New post 09 Mar 2018, 11:30
Since the symbol \(\triangle\) is one of the four primary arithmetic operations - addition, subtraction, multiplication, or division

6\(\triangle\)3 could mean one of the four things
1. 6 + 3 = 9
2. 6 - 3 = 3
3. 6 * 3 = 18
4. 6 / 3 = 2

Of these options only 2. subtraction and 4. division can be the arithmetic operation as they satisfy the condition 6\(\triangle\)3\(\leq{3}\)

Of the three options, we need to examine
I. 2\(\triangle\)2=0 is true for subtraction but not for division
II. 2\(\triangle\)2=1 is true for division but not for subtraction
III. 4\(\triangle\)2=2 is possible for both subtraction and division.

Therefore, Option C(III only) is the only option which must be true for both the arithmetic operations.
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The symbol [m]\triangle[/m] denotes one of the four arithmetic operati &nbs [#permalink] 09 Mar 2018, 11:30
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