ratio help

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sgr21: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Mon Oct 21, 2013 12:52 am

by sgr21 » Mon Oct 21, 2013 10:52 am

The age of John 21 years from now will be half that of Parson at that time. Currently the ratio of John's age to Parson's age is 5:17. What was the age of Parson 2 years ago?
(A) 15 years
(B) 49 years
(C) 32 years
(D) 11 years

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Source: Beat The GMAT — Problem Solving | Mon Oct 21, 2013 10:52 am

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Oct 21, 2013 11:20 am

John's Present Age = J
Parson's Present Age = P

J/P = 5:17

(J+21) = (P+21)/2
2J + 42 = P + 21
P - 2J = 21

P - 2*5P/17 = 21
17P - 10P = 21*17
7P = 21*17
P = 51

Age two years ago = 49 years

R A H U L

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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 » Mon Oct 21, 2013 11:25 am

sgr21 wrote:The age of John 21 years from now will be half that of Parson at that time. Currently the ratio of John's age to Parson's age is 5:17. What was the age of Parson 2 years ago?
(A) 15 years
(B) 49 years
(C) 32 years
(D) 11 years

One approach is to test the answer choices, and see which one works. In fact, I suspect this might be the fastest approach.

I'll leave you to try that approach. Here's the algebraic approach.

Let J = John's present age
Let P = Parson's present age

21 years in the future
J + 21 = John's age
P + 21 = Parson's age
The age of John 21 years from now will be half that of Parson at that time
So, John's age = (Parson's age)/2
In other words, J + 21 = (P + 21)/2
Multiply both sides by 2 to get: 2(J + 21) = P + 21
Simplify: 2J - P = - 21

Currently the ratio of John's age to Parson's age is 5:17
So, J/P = 5/17
Cross multiply to get: 17J = 5P
Simplify: 17J - 5P = 0

From here, if we solve this system . . .
2J - P = - 21
17J - 5P = 0

. . . we get P = 51, which means Parson's present age is 51.
So, 2 years ago, he was 49

Answer: B

Aside: If anyone is interested, we have a free video on solving GMAT age problems: https://www.gmatprepnow.com/module/gmat- ... ems?id=908
Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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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 Oct 21, 2013 11:38 am

sgr21 wrote:The age of John 21 years from now will be half that of Parson at that time. Currently the ratio of John's age to Parson's age is 5:17. What was the age of Parson 2 years ago?
(A) 15 years
(B) 49 years
(C) 32 years
(D) 11 years

Now:
Since J : P = 5:17, we get the following options:
J=5, P=17
J=10, P=34
J=15, P=51
J=20, P=68

21 years from now, John's age will be equal to half Parson's age:
Adding 21 to the options above, we get:
J = 5+21 = 26, P=17+21 = 38
J = 10+21 = 31, P=34+21 = 55
J = 15+21 = 36, P = 51+21 = 72

We can stop here.
The case in red satisfies the constraint that J = (1/2)P.
Since P=51 now, 2 years ago P = 51-2 = 49.

The correct answer is B.

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by [email protected] » Mon Oct 21, 2013 7:19 pm

Hi sgr21,

There are a variety of explanations in this string of posts, but since the answers are sufficiency "spaced out", you can logically choose the correct answer without doing much math at all. Here's how:

We're told that in 21 YEARS, John will be half Parson's age. This means that Parson will be AT LEAST 42. We're asked how old Parson was 2 years ago....he would have to be at least 40....

There's only one answer that fits: B

GMAT assassins aren't born, they're made,
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Contact Rich at [email protected]

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