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Sara and Bill's ages

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by kobel51 » Sat Feb 01, 2014 2:27 pm
If Sara's age is exactly twice Bill's age, what is Sara's age?

1) Four years ago, Sara's age was exactly 3 times bill's age

2) Eight years from now, Sara's age will be exactly 1.5 times Bill's age
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by Patrick_GMATFix » Sat Feb 01, 2014 2:45 pm
There are just 2 variables. Sara's and Bill's ages. The prompt (Sara's age is exactly twice Bill's) gives us one simple relationship between the two (a linear equation). Note that each of the answer choices also gives us a simple relationship between the variables. So from each answer choice we'll be able to write a linear equation. As a result, each answer choice, when combined with the prompt, results in two independent linear equations. Whenever you have as many independent linear equations as you have variables, you have sufficient info to solve for the variables. Each of the statements is sufficient and the answer is D. The solution below is taken from the GMATFix App.

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by [email protected] » Sat Feb 01, 2014 3:22 pm
Hi kobel51,

This DS question requires some algebra translation, system math and includes a special rule for "time shifts"

The prompt tells us that Sara's age is exactly twice Bill's age. This translates into...

S = 2B

We're asked for the value of S.

Fact 1: Four years ago, Sara's age was exactly 3 times Bill's age.

This Fact involves a "time shift" to the past. The translation is...

(S - 4) = 3(B - 4)

S = 3B - 8

Combined with the original equation (S = 2B), we now have a "system" of unique equations, which we COULD solve and get the value of S.
Fact 1 is SUFFICIENT

Fact 2: Eight years from now, Sara's age will be exactly 1.5 times Bill's age.

This Fact also involves a "time shift" (this time to the future). The translation is....

(S + 8) = 1.5(B + 8)

S = 1.5B + 4

Combined with the original equation (S = 2B), we also end up with a "system" of unique equations, and we COULD solve and get the value of S.
Fact 2 is SUFFICIENT

Final Answer: D

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by Brent@GMATPrepNow » Mon Oct 21, 2019 8:14 am
kobel51 wrote:If Sara's age is exactly twice Bill's age, what is Sara's age?

1) Four years ago, Sara's age was exactly 3 times bill's age

2) Eight years from now, Sara's age will be exactly 1.5 times Bill's age
Target question: What is Sara's age?

Given: Sara's age is exactly twice Bill's age
Let x = Bill's PRESENT age
So, 2x = Sara's PRESENT age

Statement 1: Four years ago, Sara's age was exactly 3 times Bill's age.
x - 4 = Bill's age FOUR YEARS AGO
2x - 4 = Sara's age FOUR YEARS AGO

We're told that: (Sarah's age 4 years ago) = 3(Bill's age 4 years ago)
We can write: 2x - 4 = 3(x - 4)
Expand: 2x - 4 = 3x - 12
Solve: x = 8
This means Bill's PRESENT age is 8 years old.
So, Sara's PRESENT age is 16
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Eight years from now, Sara's age will be exactly 1.5 times Bill's age.
x + 8 = Bill's age EIGHT YEARS FROM NOW
2x + 8 = Sara's age EIGHT YEARS FROM NOW

We're told that: (Sarah's age 8 years from now) = 1.5(Bill's age 8 years from now)
We can write: 2x + 8 = 1.5(x + 8)
Expand: 2x + 8 = 1.5x + 12
Rearrange to get: 0.5x = 4
Solve: x = 8
This means Bill's PRESENT age is 8 years old.
So, Sara's PRESENT age is 16
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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