Algebra Problem

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Tue Aug 16, 2011 5:49 am

Here is a problem from the Manhattan guides. I'm having a little bit of trouble figuring this one out.

* Mr. and Mrs. Wiley have a child every J years. Their oldest child is now T years old. If
they have a child 2 years from now, how many children will they-have in total?

The answer choices are in the attachment. I've kinda figured this one out using smart numbers. Hoping someone can show me how to do this entirely algebraically. Detailed explanations would be appreciated. Thanks

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Source: Beat The GMAT — Problem Solving | Tue Aug 16, 2011 5:49 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Tue Aug 16, 2011 5:59 am

Hi,
Let's say the child to be born in 2 years be nth child.
1st child is born in year 0, right.
Next child(2nd) is born in year J
Next child(3rd) is born in year 2J
.
.
Last child(nth child) is born in year (n-1)J.
But this (n-1)J is given as T+2
So, n = (T+2)/J + 1.
Hence, A
This is more of an arithmetic progression question.

Cheers!

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Aug 16, 2011 6:06 am

I posted two different approaches here:

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Aug 16, 2011 6:08 am

knight247 wrote:Mr. and Mrs. Wiley have a child every J years. Their oldest child is now T years old. If they have a child 2 years from now, how many children will they-have in total?

2 years from now, their first child was born (T + 2) years ago and last child was born 0 years ago. So in this [(T + 2) - 0] years they had [(T + 2) - 0] /J + 1 = [T + 2]/J + 1 children.

The correct answer is A.

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