Vincen wrote:In four years, Andy will be twice as old as Betsy. How old is Betsy?
(1) Four years ago, Andy was twice as old as Betsy is now.
(2) Four years ago, Andy was four times as old as Betsy.
Given: In four years, Andy will be twice as old as Betsy.
Let A = Andy's PRESENT age
Let B = Betsy's PRESENT age
So, A+4 = Andy's age IN 4 YEARS
And so, B+4 = Betsy's age IN 4 YEARS
If Andy will be twice as old as Betsy IN 4 YEARS, we can write: A+4 = 2(B+4)
Expand: A + 4 = 2B + 8
Rearrange to get:
A - 2B = 4
Target question: How old is Betsy (i.e., what is the value of B)?
Statement 1: Four years ago, Andy was twice as old as Betsy is now.
A-4 = Andy's age 4 YEARS AGO
B is Betsy's PRESENT age
We can write: A - 4 = 2B
Rearrange to get: A - 2B = 4
IMPORTANT: This is equations is the SAME as the equation we derived from the given information (
A - 2B = 4)
So, statement 1 does NOT provide any new information.
As such, this information is not sufficient to answer the
target question.
Statement 1 is NOT SUFFICIENT
Statement 2: Four years ago, Andy was four times as old as Betsy.
A-4 = Andy's age 4 YEARS AGO
B-4 = Betsy's age 4 YEARS AGO
We can write: A - 4 = 4(B - 4)
Expand: A - 4 = 4B - 16
Rearrange to get:
A - 4B = -12
We also know that
A - 2B = 4
Since we have two DIFFERENT linear equations with 2 variables, we can DEFINITELY solve this system for A and B (but we won't actually do so, since that would be a waste of time)
Since we COULD answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
