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If x£y = 2(x^2)(y^3), which of the following represents possible value

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If x£y = 2(x^2)(y^3), which of the following represents possible value  [#permalink]

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25 Jul 2018, 20:52
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If x£y = 2(x^2)(y^3), which of the following represents possible values for (x,y) when x£y = 1,350?

A. (3, 5)
B. (5, 3)
C. (10, 5)
D. (13, 5)
E. (13, 50)

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If x£y = 2(x^2)(y^3), which of the following represents possible value  [#permalink]

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Updated on: 25 Jul 2018, 21:19
If x£y = 2(x^2)(y^3), which of the following represents possible values for (x,y) when x£y = 1,350?

A. (3, 5) =2*9*125 -looks A high number ,no need to multiply
B. (5, 3) =2*25*27 =1350
C. (10, 5) -looks A high number ,no need to multiply
D. (13, 5) - looks A high number ,no need to multiply
E. (13, 50) -looks A high number ,no need to multiply

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Originally posted by AnkitOrYadav on 25 Jul 2018, 21:09.
Last edited by AnkitOrYadav on 25 Jul 2018, 21:19, edited 1 time in total.
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If x£y = 2(x^2)(y^3), which of the following represents possible value  [#permalink]

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25 Jul 2018, 21:14
Bunuel wrote:
If x£y = 2(x^2)(y^3), which of the following represents possible values for (x,y) when x£y = 1,350?

A. (3, 5)
B. (5, 3)
C. (10, 5)
D. (13, 5)
E. (13, 50)

Given

$$x£y = 2(x^2)(y^3)$$

we are looking for the value of $$x£y = 1,350?$$

So, $$2(x^2)(y^3) = 1350$$

Prime factorization of 1350 will provide us the value of x and y

$$1350 = 2*5^2*3^3$$

$$2(x^2)(y^3) = 2*5^2*3^3$$

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Re: If x£y = 2(x^2)(y^3), which of the following represents possible value  [#permalink]

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25 Jul 2018, 21:17
B

2(x^2)(y^3) = 1350
(x^2)(y^3) = 675
(x^2)(y^3) = (5^2)(3^3)
x=5, y=3

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Re: If x£y = 2(x^2)(y^3), which of the following represents possible value  [#permalink]

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25 Jul 2018, 22:32

Solution

Given:
• x£y = $$2(x^2)(y^3)$$

To find:
• The option that represents (x,y) when x£y = 1,350

Approach and Working:

• x£y = $$2(x^2)(y^3)$$=1,350
• $$2(x^2)(y^3)= 2* 3^3* 5^2$$
• Hence, x=5 and y=3

Hence, the correct answer is option B.

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Re: If x£y = 2(x^2)(y^3), which of the following represents possible value  [#permalink]

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30 Jul 2018, 10:30
Bunuel wrote:
If x£y = 2(x^2)(y^3), which of the following represents possible values for (x,y) when x£y = 1,350?

A. (3, 5)
B. (5, 3)
C. (10, 5)
D. (13, 5)
E. (13, 50)

We have:

2(x^2)(y^3) = 1350

(x^2)(y^3) = 675

Since 675 = 25 x 27 = 5^2 x 3^3, we see that x = 5 and y = 3 would satisfy x£y = 1,350.

Note: The reason (5,3) is a “possible” value and not the only value is that we are not given that x and y are integers; in other words, (x, y) where x = √675 and y = 1 is another possible value.

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Re: If x£y = 2(x^2)(y^3), which of the following represents possible value &nbs [#permalink] 30 Jul 2018, 10:30
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