OG Green Book Question

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OG Green Book Question

by ket » Wed Aug 12, 2009 11:25 am
IF w+z=28 what is the value of wz?

(1) w and z are positive integers
(2) w and z are consecutive odd integers

I solved this problem by plugging in numbers and got the correct answerB

But my problem is this... the OG Book has an explanation like this:
'to look at this problem more formally, let the consecutive odd integers w and z be represented 2n+1 and 2n+3, where n is any integer. The equation in the problem can thus be expressed as... w+z= (2n+1) + (2n+3) and solved for n the result is w=2X6+1=13 and z=2X6+3=15, " i.e. B is sufficient.

What I don't understand here is that how come 2n+1 and 2n+3 express
consecutive odd integers? Because for instance 7 and 11 are consecutive odd integers but they cannot be expressed as 2n+1 and 2n+3...

I am confused, can someone explain why OG explanation is correct?


Thanks a lot
Source: — Data Sufficiency |

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by ashis979 » Wed Aug 12, 2009 11:42 am
OG explanation is fine.

2n is an even integer for any integer value of n. Therefore, 2n+1, 2n+3, 2n+5, and so on have to be consecutive odd integers.

7 and 11 are consecutive prime numbers NOT consecutive odd integers. It's 7 and 9. So when n=3, 2n+1=7 and 2n+3=9.

2n+1+2n+3=28 => 4n=24 => n=6
So, 2n+1=13 and 2n+3=15 => 13+15=28. So, B alone is SUFFICIENT

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by ket » Wed Aug 12, 2009 11:54 am
ashis979 wrote:OG explanation is fine.

2n is an even integer for any integer value of n. Therefore, 2n+1, 2n+3, 2n+5, and so on have to be consecutive odd integers.

7 and 11 are consecutive prime numbers NOT consecutive odd integers. It's 7 and 9. So when n=3, 2n+1=7 and 2n+3=9.

2n+1+2n+3=28 => 4n=24 => n=6
So, 2n+1=13 and 2n+3=15 => 13+15=28. So, B alone is SUFFICIENT
Thanks ashis979... I really missed the part that 7 and 11 are consecutive prime integers not odd ones :)