## Discussion

If *x* is an integer, then which of the following is the product of the next two integers greater than 2(*x* + 1)?

(A) | 4 |

(B) | ... |

(C) | ... |

(D) | ... |

(E) | ... |

(F) | ... |

The solution is

Posted: 12/29/2011 22:41

How is it equal to thirty?

Tanisha, I guess you refer to the example 5 times 6 is product 30.

Another example would be x=5:

2(5+1)=12 -> the next two integers greater than this are 13 and 14.

13 times 14 gives us product 182

Now, if we take choice A and plug in x=5:

4(5^2)+14(5)+12=

4(25)+70+12=

100+82=182

Niels

Greetings from Holland

Another example would be x=5:

2(5+1)=12 -> the next two integers greater than this are 13 and 14.

13 times 14 gives us product 182

Now, if we take choice A and plug in x=5:

4(5^2)+14(5)+12=

4(25)+70+12=

100+82=182

Niels

Greetings from Holland

Posted: 03/28/2012 19:59

How do we know to use 5 as the integer? Would we be able to use 1 or 3?

Posted: 03/28/2012 20:12

Joana, you could.

How is E not the answer? If I used 1=x in 4x^2+14. Was I supposed to use 1^2 first or 4*1 first ?

Tyra, power / exponential operation is first, before multiplication. Remember PEMDAS: parentheses, exponent, multiplication, division, addition, subtraction.

Posted: 11/30/2012 10:18

what do they mean by next 2 integers ?

Pattyl,

When I refer to 12 then the next integer is 13 and the next integer 14, thus 'the next 2 integers' of N is N+1 and N+2.

Niels

When I refer to 12 then the next integer is 13 and the next integer 14, thus 'the next 2 integers' of N is N+1 and N+2.

Niels

Posted: 11/30/2012 12:56

Pattyl, the next 2 integers are simply x+1 and x+2.

Posted: 01/01/2013 07:07

Can somebody explain the question for me .. Thank you .

If x is an integer, then which of the following is the product of the next two integers greater than 2(x+1)?

We start by creating our definitions:

Def.1 x is from set N(atural numbers)

Def.2 a product is the result of a multiplication

Def.3 'the next two integers' are n+1 and n+2

Def.4 n > 2(x+1)

If def.4 says this is n, we can use it for def.3 to substitute for n, thus

2(x+1)+1 and 2(x+1)+2 instead of n+1 and n+2

Def.2 tells us to multiply the two thus (n+1)*(n+2) which we just found is equal to:

( 2(x+1)+1 ) * ( 2(x+1)+2 )

( 2x+2+1 ) * ( 2x+2+2 )

( 2x+3 ) * ( 2x+4 )

4x^2 + 8x + 6x + 12

4x^2 + 14x + 12

Niels

We start by creating our definitions:

Def.1 x is from set N(atural numbers)

Def.2 a product is the result of a multiplication

Def.3 'the next two integers' are n+1 and n+2

Def.4 n > 2(x+1)

If def.4 says this is n, we can use it for def.3 to substitute for n, thus

2(x+1)+1 and 2(x+1)+2 instead of n+1 and n+2

Def.2 tells us to multiply the two thus (n+1)*(n+2) which we just found is equal to:

( 2(x+1)+1 ) * ( 2(x+1)+2 )

( 2x+2+1 ) * ( 2x+2+2 )

( 2x+3 ) * ( 2x+4 )

4x^2 + 8x + 6x + 12

4x^2 + 14x + 12

Niels

Posted: 08/09/2014 10:19

Thank you Neil