Brent@GMATPrepNow wrote:How old will Fred be in 3 years?
(1) Presently, Fred is 4 times as old as Gary.
(2) In 10 years, Fred will be 3 times as old as Gary.
Let's solve the question using 2 variables
Let F = Fred's PRESENT age
Let G = Gary's PRESENT age
Target question: What is the value of F+3 ?
Statement 1: Presently, Fred is 4 times as old as Gary.
In other words,
F = 4G
There are several values of F and G that satisfy the equation
F = 4G. Here are two:
Case a: F = 4 and G = 1. In this case, the answer to the target question is
F+3 = 4+3 = 7
Case b: F = 8 and G = 2. In this case, the answer to the target question is
F+3 = 8+3 = 11
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: In 10 years, Fred will be 3 times as old as Gary.
IN 10 YEARS, Fred's age = F + 10
IN 10 YEARS, Gary's age = G + 10
If Fred will be 3 times as old as Gary, we can write: F + 10 = 3(G + 10)
Expand: F + 10 = 3G + 30
Rearrange to get:
F = 3G + 20
There are several values of F and G that satisfy the equation
F = 3G + 20. Here are two:
Case a: F = 23 and G = 1. In this case, the answer to the target question is
F+3 = 23+3 = 26
Case b: F = 26 and G = 2. In this case, the answer to the target question is
F+3 = 26+3 = 29
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that
F = 4G
Statement 2 tells us that
F = 3G + 20
At this point, we should recognize that we have a system of 2 linear equations with 2 variables. As such, we COULD solve this system for G and F, which means we COULD answer the
target question.
ASIDE: Although we COULD solve the system of equations, we would never waste valuable time on test day doing so. We need only determine that we COULD answer the target question.
Since we COULD answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
ASIDE: If we were to solve the system, we'd get: G = 20 and F = 80, which means Fred will be 83 years old in 3 years.
Cheers,
Brent
