Problem Solving

sgr21 wrote:If the ages of Steve and Jack are currently in the ratio of 3:5. After six years their ages are in the ratio of 2:3. What will be Jack's age after 4 years?

Let S = Steve's present age
Let J = Jack's present age

The ages of Steve and Jack are currently in the ratio of 3:5
So, we can write: S/J = 3/5
Cross multiply to get: 3J = 5S
Rearrange to get: 3J - 5S = 0

After six years...
This next piece of information deals with their ages 6 years in the FUTURE.
Before we can deal with this information, we must find expressions that represent these FUTURE ages.
If S = Steve's present age, then S + 6 = Steve's age in 6 years
If J = Jacks's present age, then J + 6 = Jacks's age in 6 years

...their ages are in the ratio of 2:3
So, we can write: (S + 6)/(J + 6) = 2/3
Cross multiply to get: 2(J + 6) = 3(S + 6)
Expand: 2J + 12 = 3S + 18
Rearrange to get: 2J - 3S = 6

We now have the following two equations:
3J - 5S = 0
2J - 3S = 6

To solve for J, we need to ELIMINATE the S terms. To do so, let's take the top equation and multiply both sides by 3. AND we'll take the bottom equation and multiply both sides by 5 to get:
9J - 15S = 0
10J - 15S = 30

At this point, we can SUBTRACT the bottom equation from the top equation to get:
-J = -30
So, J = 30
This means that Jack's PRESENT age is 30.

What will be Jack's age after 4 years?
Jack will be 34 years old in 4 years.

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If anyone is interested, we have a free video lesson on how to solve past/present/future ages questions: https://www.gmatprepnow.com/module/gmat- ... ems?id=908
Once you've watched that video, you can try answering this question: https://www.gmatprepnow.com/module/gmat- ... ems?id=909

Here are a few more questions to practice with:
- https://www.beatthegmat.com/mother-and-d ... 71014.html
- https://www.beatthegmat.com/equations-t269315.html
- https://www.beatthegmat.com/jack-and-bil ... 74426.html
- a little trickier: https://www.beatthegmat.com/ratio-help-t271009.html

Cheers,
Brent

Hi sgr21,

The responses to your questions emphasize various ways to do the algebra or to "brute force" the possibilities. Each of these approaches is worth knowing. You should keep in mind though that if this were a PS question, you would have 5 answers to work with. You COULD use those answers against the question to figure out which one "matched" all the information in the prompt.

If you ignore the answers, you'll be forced to "do math" on every question. Of the various ways to solve any GMAT question, the "math approach" is often the one that takes the longest. Part of dealing with the GMAT in an effective way is to know how to use the alternative approaches AND which is fastest.

GMAT assassins aren't born, they're made,
Rich