Jack and Bill's ages

LulaBrazilia wrote:Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

A) 9
B) 19
C) 21
D) 23
E) 33

We can use either 1 variable or 2 variables to solve this question.
Here's the 1-variable solution:

PRESENTLY
Jack is now 14 years older than Bill.
Let B = Bill's present age
So, B + 14 = Jack's present age

10 YEARS IN THE FUTURE
In 10 years, the both of them are 10 years older. So...
Let B + 10 = Bill's age in 10 years
So, B + 14 + 10 = Jack's age in 10 years


In 10 years Jack will be twice as old as Bill
So, to make their future ages EQUAL, we'll need to double Bill's age.
That is: (Jack's age in 10 years) = 2(Bill's age in 10 years)
So, we get: B + 14 + 10 = 2(B + 10)
Simplify: B + 24 = 2B + 20
Rearrange to get: 4 = B

So, Bill is PRESENTLY 4 years old.
This means that Jack is PRESENTLY 18 years old

How old will Jack be in 5 years?
Jack will be 23 years old

Answer: D

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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

Cheers,
Brent

LulaBrazilia wrote:Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

A) 9
B) 19
C) 21
D) 23
E) 33

Here's a 2-variable solution:

PRESENTLY
Jack is now 14 years older than Bill.
Let B = Bill's present age
Let J = Jack's present age
So, we can write: J - B = 14

10 YEARS IN THE FUTURE
In 10 years, the both of them are 10 years older. So...
Let B + 10 = Bill's age in 10 years
So, J + 10 = Jack's age in 10 years

In 10 years Jack will be twice as old as Bill
So, to make their future ages EQUAL, we'll need to double Bill's age.
That is: (Jack's age in 10 years) = 2(Bill's age in 10 years)
So, we get: J + 10 = 2(B + 10)
Simplify: J + 10 = 2B + 20
Rearrange to get: J - 2B = 10

So, we now have 2 equations with 2 variables:
J - B = 14
J - 2B = 10

Subtract the bottom equation from the top equation to get: B = 4

So, Bill is PRESENTLY 4 years old.
This means that Jack is PRESENTLY 18 years old

How old will Jack be in 5 years?
Jack will be 23 years old

Answer: D

Aside: Looks like the 1-variable solution is probably faster.

Cheers,
Brent

LulaBrazilia wrote:Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

A) 9
B) 19
C) 21
D) 23
E) 33

I should mention that, if we're totally lost on this question, we can always start TESTING THE ANSWER CHOICES and see which satisfies the given information. It wouldn't take that long to locate the correct answer.

Cheers,
Brent

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

Cheers,
Brent

LulaBrazilia wrote:Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

A) 9
B) 19
C) 21
D) 23
E) 33

Solution:

We first want to define variables for Jack’s age today and Bill’s age today.

J =Jack’s age today

B = Bill’s age today

Now we can use these variables to set up two equations.

We are given that Jack is now 14 years older than Bill. This relationship is represented in our first equation.

J = B + 14 [Eq (1)]

Next we are given that in 10 years Jack will be twice as old as Bill. Remember, in setting up this equation we must add 10 years to both Jack's and Bill’s current ages, respectively.

10 + J = 2(B + 10)

10 + J = 2B + 20

J = 2B + 10 [Eq (2)]

Now we can set our two equations (Eq (1) and Eq (2)) equal to each other and determine the value of B.

B + 14 = 2B + 10

B = 4

This means that Bill’s age today is 4.

Thus, we know that Jack’s age today is 14 + 4 = 18.

This means that Jack’s age in 5 years will be 18 + 5 = 23.

Answer: D