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

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Math Expert
Joined: 02 Sep 2009
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If x is an integer, then which of the following is the product of the  [#permalink]

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13 Jun 2017, 09:48
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80% (01:39) correct 20% (02:00) wrong based on 115 sessions

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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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13 Jun 2017, 09:53
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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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13 Jun 2017, 10:54
Top Contributor
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

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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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13 Jun 2017, 11:15
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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22 Aug 2018, 04:13
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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, 04:13
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