Bunuel wrote:

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

(2) 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 = 4Target 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 = -12We also know that

A - 2B = 4Since 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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