Age

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Imsukhi: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Thu Jun 20, 2013 7:58 pm; Thanked: 1 times

by Imsukhi » Sat Jun 29, 2013 2:33 am

A father is three times as old as his son. The product of fathers age and son,s age 3 years ago is 16 Times the present age of the son.
What is fathers age..?

24
25
27
29

Pls equate

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Source: Beat The GMAT — Problem Solving | Sat Jun 29, 2013 2:33 am

usmabama: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sat Jun 29, 2013 5:04 am; Thanked: 1 times

by usmabama » Sat Jun 29, 2013 5:33 am

This is how I set it up:

The problem tells us F=3S and (F-3)(S-3)=16S

FS-3F-3S+9=16S

We can also plug 3S in for F because that was given to us, so:

3S^2-9S-3S+9=16S
3S^2-28S+9=0
(3S-1)(S-9)

So S can only equal 9.
Plug that into the original equation and F=3(9)=27
It checks out for the other equation too
(27-3)(9-3)=16(9)
(24)(6)=16(9)...reduce to make it easier
(3)(2)=(2)(3)...
Answer=27

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Jun 29, 2013 6:10 am

Imsukhi wrote:A father is three times as old as his son. The product of fathers age and son,s age 3 years ago is 16 Times the present age of the son.
What is fathers age..?
24
25
27
29
Pls equate

A father is three times as old as his son.
On GMAT age problems, the ages of the individuals are typically integers.
So, we can expect the father's age to be a multiple of 3.
Since only 24 and 27 are multiples of 3, we can eliminate the other answers and just test 24 and 27 and see which one works.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Jun 29, 2013 6:15 am

The product of father's age and son's age 3 years ago is 16 Times the present age of the son.

By the way, the wording here is somewhat ambiguous.
Does 3 years ago refer to the son's age only, or both the son's age AND the father's age?
So, we have two possible scenarios:
1) The product of father's current age and son's age 3 years ago . . . .
2) The product of father's age 3 years ago and son's age 3 years ago . . . .

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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