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# If, for all x and y, x#y = xy^2, which of the following is equal to 3#

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If, for all x and y, x#y = xy^2, which of the following is equal to 3#  [#permalink]

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25 Mar 2018, 09:58
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Difficulty:

15% (low)

Question Stats:

69% (00:46) correct 31% (00:46) wrong based on 55 sessions

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If, for all x and y, x#y = xy^2, which of the following is equal to 3#4?

1. 4#3
2. 1#6
3. 2#6
4. 12#1
5. 12#2

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Joined: 16 Sep 2016
Posts: 236
WE: Analyst (Health Care)
Re: If, for all x and y, x#y = xy^2, which of the following is equal to 3#  [#permalink]

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25 Mar 2018, 10:21
QZ wrote:
If, for all x and y, x#y = xy^2, which of the following is equal to 3#4?

1. 4#3
2. 1#6
3. 2#6
4. 12#1
5. 12#2

This is a strange operator question and the new operator # is defined as x#y = xy^2

First trap in the question is the differentiation between (xy)^2 & xy^2 ... the question states the later which means $$x * y^2$$ ( based on the precedence rules for normal operators)

So it is clear that x#y is not equal to y#x.

$$3#4 = 3*4^2 = 3*16 = 48$$

Trying out various options it is clear that $$12#2 = 12 * 2^2 = 12 * 4 = 48$$

Hence Option (E) is correct.

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Target Test Prep Representative
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Posts: 2759
Re: If, for all x and y, x#y = xy^2, which of the following is equal to 3#  [#permalink]

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09 Apr 2018, 16:37
QZ wrote:
If, for all x and y, x#y = xy^2, which of the following is equal to 3#4?

1. 4#3
2. 1#6
3. 2#6
4. 12#1
5. 12#2

3#4 = (3)(4^2) = 3 x 16 = 48

Of the answer choices, we see that E is equivalent to 48.

12#2 = (12)(2^2) = 12 x 4 = 48

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Re: If, for all x and y, x#y = xy^2, which of the following is equal to 3#  [#permalink]

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09 Apr 2018, 17:10
QZ wrote:
If, for all x and y, x#y = xy^2, which of the following is equal to 3#4?

1. 4#3
2. 1#6
3. 2#6
4. 12#1
5. 12#2

We can use the power of the unit digit without calculating the full numbers.

3#4 = (3) (4)^2 = 3 * 16 = ....8

Let's the choices

1. 4#3.....4 * 3^2 =..... 6 (Eliminate)

2. 1#6.....1 * 6^2 =..... 6 (Eliminate)

3. 2#6.....2 * 6^2 = .....2 (Eliminate)

4. 12#1....12 * 1^1 = ....2 (Eliminate) ......Only once choice but we can check

5. 12#2....12 * 2^2 = ....8 (Done)

Re: If, for all x and y, x#y = xy^2, which of the following is equal to 3# &nbs [#permalink] 09 Apr 2018, 17:10
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