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If x is an integer, then which of the following is the product of the

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If x is an integer, then which of the following is the product of the  [#permalink]

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New post 13 Jun 2017, 10:48
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If x is an integer, then which of the following is the product of the next two integers greater than 2(x + 1)?

(A) \(4x^2 + 14x + 12\)

(B) \(4x^2 + 12\)

(C) \(x^2 + 14x + 12\)

(D) \(x^2 + x + 12\)

(E) \(4x^2 + 14x\)

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If x is an integer, then which of the following is the product of the  [#permalink]

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New post 13 Jun 2017, 10:53
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The integer can be written as 2(x+1) = 2x + 2.

The two consecutive integers which are greater that this integer are 2x + 3 and 2x + 4.

The product of these two integers is \((2x + 3)(2x + 4)\) or \(4x^2 + 14x + 12\)(Option A)
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Re: If x is an integer, then which of the following is the product of the  [#permalink]

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New post 13 Jun 2017, 11:54
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Bunuel wrote:
If x is an integer, then which of the following is the product of the next two integers greater than 2(x + 1)?

(A) \(4x^2 + 14x + 12\)

(B) \(4x^2 + 12\)

(C) \(x^2 + 14x + 12\)

(D) \(x^2 + x + 12\)

(E) \(4x^2 + 14x\)


2(x + 1) = 2x + 2
So, the NEXT two integers are 2x + 2 + 1 and 2x + 2 + 2
In other words, the NEXT two integers are 2x + 3 and 2x + 4

So, the required product is (2x + 3)(2x + 4)
Apply the FOIL method to get: (2x + 3)(2x + 4) = 4x² + 8x + 6x + 12 = 4x² + 14x + 12

Answer:

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Re: If x is an integer, then which of the following is the product of the  [#permalink]

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New post 13 Jun 2017, 12:15
Assume, x=1, then 2(1+1) = 4.
Next two numbers are 5 and 6 and their product is 30.
Answer choice A) 4.1^2+ 14.1+12=30. No need to check the rest, as this option gives the product 30
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Re: If x is an integer, then which of the following is the product of the  [#permalink]

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Re: If x is an integer, then which of the following is the product of the &nbs [#permalink] 22 Aug 2018, 05:13
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