Vincen wrote: ↑

Thu Mar 18, 2021 12:09 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.

Answer: D

Source: Official Guide

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