In four years, Andy will be twice as old as Betsy. How old is Betsy?

Looks like we have 2 variables (A - Andy's present age and B - Betsy's present age)
The question stem gives an equation: 4 + A = 2 (B + 4)
A = 2B + 4
We see that we will get another equation from each statement. So you might feel that since it is a DS question and you don't really need to solve to get the answer, you should mark D and move on. But this is a DS pitfall. You have to ensure that the two equations are distinct for you to get a unique solution.

(1) Four years ago, Andy was twice as old as Betsy is now.
A - 4 = 2B
Note that this is same as A = 2B + 4
Hence, we do not have 2 distinct equations and hence we will not be able to solve for A and B.

(2) Four years ago, Andy was four times as old as Betsy.
A - 4 = 4*(B - 4)
A = 4B - 12
This does give us a different equation and hence we will be able to solve for A and B.

Answer (B)

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 equation 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

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