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

tagged by: Vincen

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

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.

The OA is B .

How can I conlcude that statement (1) is not sufficient and statement (2) is sufficient? Experts, may you help me?

### GMAT/MBA Expert

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Vincen 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.
The prompt should clarify the intended meaning, as follows:
In four years, Andy will be twice as old as Betsy will be in four years.
Translated into math:
A + 4 = 2(B + 4)
A + 4 = 2B + 8
A = 2B + 4

Statement 1: Four years ago, Andy was twice as old as Betsy is now.
A - 4 = 2B
A = 2B + 4.
Same equation as in the prompt.
INSUFFICIENT.

Statement 2 should clarify the intended meaning, as follows:
Four years ago, Andy was four times as old as Betsy was four years ago.
Translated into math:
A - 4 = 4(B - 4)
A - 4 = 4B - 16
A = 4B - 12.
Since we have two variables (A and B) and two distinct linear equations (A = 2B + 4 and A = 4B - 12), we can solve for the two variables.
Thus, the value of B can be determined.
SUFFICIENT.

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### GMAT/MBA Expert

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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

Cheers,
Brent

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