Data Sufficiency

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Mon Aug 02, 2021 3:50 am

Manhattan Prep

If Farai is twice as old as Dmitry, how old is Farai?

1) Samantha if 4 years younger than Dmitry
2) Samantha will be 11 years old in 5 years

OA C

Given: Farai is twice as old as Dmitry
Let D = Dmitry's PRESENT AGE
Let F = Farai's PRESENT AGE
So, we can write: F = 2D

Target question: How old is Farai?

Statement 1: Samantha is 4 years younger than Dmitry.
Let S = Samantha's PRESENT AGE
We can write: S = D - 4

We now have the following:
F = 2D
S = D - 4
We have a system of 2 equations and 3 variables.
In order to solve a system with 3 variables, we need at least 3 different linear equations.
Since we only have two equations, we can be certain that statement 1 is NOT SUFFICIENT

Statement 2: Samantha will be 11 years old in 5 years.
This statement is indirectly telling us that Samantha is PRESENTLY 6 years old.
In other words S = 6

We now have the following:
F = 2D
S = 6

Once again, we have a system of 2 equations and 3 variables.
Since we only have two equations, we can be certain that statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the two statements we have:
F = 2D
S = D - 4
S = 6

Since we have 3 different linear equations and 3 variables, we CAN/COULD solve the system for F, D and S (although we would never waste valuable time on test day doing so).
The combined statements are SUFFICIENT

Answer: C

Cheers,
Brent