VIC problem

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Mr.Hollywood: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Mon Oct 24, 2011 2:04 pm; Thanked: 1 times

by Mr.Hollywood » Mon Jan 16, 2012 3:57 pm

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

A) [(T+2)/J]+1
B) JT+1
C) (J/T)+(1/T)
D) TJ-1
E) (J+T)/J

It seems easier (a lot easier) if we approach this question by pick smart numbers and just test each answer choices afterwards. And the answer is: A
However my question is how to solve this question with Algebra?

Thanks guys!

PS: Is there any way we can express fraction on a computer like we do on paper?

Source: Beat The GMAT — Problem Solving | Mon Jan 16, 2012 3:57 pm

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Mon Jan 16, 2012 4:19 pm

this question is confusing, as one may assume that the function T/J discontinues by now or continues further. I would opt for ans. E, but yours in OA is A, therefore the assumption made is function T/J continues (though it clearly specifies "If they have a child 2 years from now")
algebra: they have had some children every J years for the period of T years -> T/J. Two years from now they will have another child -> (T+2)/J +1

the other scenario would be - just a child two years from now, +1 and T/J +1= (T+J)/J

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

A) [(T+2)/J]+1
B) JT+1
C) (J/T)+(1/T)
D) TJ-1
E) (J+T)/J

It seems easier (a lot easier) if we approach this question by pick smart numbers and just test each answer choices afterwards. And the answer is: A
However my question is how to solve this question with Algebra?

Thanks guys!

PS: Is there any way we can express fraction on a computer like we do on paper?

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Mon Jan 16, 2012 5:13 pm

Age of the oldest kid = T years
In 2 years age of the oldest kid = T+2
Total number of kids = [(T+2)/J] (total number of kids till then) +1 (new born). = [(T+2)/J]+1

Graphical Representation below
|_|_|_|_|....
Here | is the point of a kid's birth and _ is the interval = J years.
Total of _'s = T+2.
Total number of |'s = Total number of _'s + 1

Anil Gandham
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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 » Mon Jan 16, 2012 9:53 pm

I posted both approaches (plugging in and algebra) here:

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