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△ is one operation of addition, subtraction, multiplication, or divisi

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4898
GPA: 3.82

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31 Aug 2017, 00:24
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Difficulty:

15% (low)

Question Stats:

83% (00:35) correct 17% (00:28) wrong based on 47 sessions

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△ is one operation of addition, subtraction, multiplication, or division. Is 1△3=3△1？

1) 1△1=1
2) 2△3=6
[Reveal] Spoiler: OA

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31 Aug 2017, 01:06
MathRevolution wrote:
△ is one operation of addition, subtraction, multiplication, or division. Is 1△3=3△1？

1) 1△1=1
2) 2△3=6

1) $$1△1=1$$

$$1*1 = 1$$

$$\frac{1}{1} = 1$$

Therefore operation $$△$$ could be multiplication or division.

$$1△3=3△1$$

$$1*3 = 3*1 = 3$$

$$\frac{1}{3}$$ is not equal to $$\frac{3}{1}$$

We are getting two values. Hence I is Not Sufficient.

2) $$2△3=6$$

$$2*3 = 6$$

Only multiplication of $$2$$ and $$3$$ gives $$6$$.

Therefore operation $$△$$ is multiplication.

$$1△3=3△1$$

$$1*3 = 3*1 = 3$$

Hence II is Sufficient.

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Re: △ is one operation of addition, subtraction, multiplication, or divisi [#permalink]

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31 Aug 2017, 02:35
△ is one operation of addition, subtraction, multiplication, or division.
We have to find if 1△3=3△1.

This is only true if △ is either + or multiplication ... else for - and division it will be false.

1) 1△1=1
by above equation we can conclude △ is either multiplication or division.
So Not sufficient

2) 2△3=6
Above equation is only possible if △ is multiplication. For all other operations it will not sattis fy the equation.
so △ = multiplication and by this : 1△3=3△1 is True

So Sufficient

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4898
GPA: 3.82
Re: △ is one operation of addition, subtraction, multiplication, or divisi [#permalink]

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03 Sep 2017, 17:40
=> 1) 1△1=1
△ could be the multiplication or the division.
If △ is the multiplication, 1△3 = 3△1.
If △ is the division, 1△3 is not equal to 3△1.
This is not sufficient.

1) 2△3=6
△ should be the multiplication only.
Then we have 1△3 = 3△1.
This is sufficient.

Ans: B
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Re: △ is one operation of addition, subtraction, multiplication, or divisi   [#permalink] 03 Sep 2017, 17:40
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