Megacorp International spent a total of $90,000,000 on television

Question

Megacorp International spent a total of $90,000,000 on television, magazine, and billboard advertising combined. How much of the total was spent on television advertising?

(1) The total spending for billboard and magazine advertising was 20% less than the amount spent on television advertising.

(2) The company spent 50% more on magazine advertising than on billboard advertising.

This is a  Data Sufficiency Butler Question

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SparkRest · Answer

We are given 
T+M+B = 90,000,000 and we have to find the value of T.

S1 tells us M+B= T- 0.2T = 0.8T
So, T+ (M+B)= 90,000,000
T+ 0.8T=90,000,000
So we can find the value of T from this equation, hence  S1 is Sufficient .

S2 tells us M=1.5B. 
So the equation becomes: T+ 1.5B+ B = 90,000,000.
We have two variables and one equation. Hence,  S2 is insufficient .

Therefore, our answer is A.

MarkGMATMentor · Answer

This question is designed to trap you if you aren't careful.  Always make sure you're answering the right question, especially on Data Sufficiency problems.

From the prompt, you get the following equation and question (dropping the "million" for simplicity):
t + m + b = 90
What is t?

Statement 1: 
This tells you that the combined advertising for billboards and magazines was 20% less than television. Since you already know that the total is $90M, there is only one value for television that can work (any other value would scale the billboards and magazines proportionally, throwing the total off of $90M).  Sufficient.

Alternatively, you can look at it algebraically:
b + m = 0.80t

Substitute 0.8t for m + b in the original equation:
t + 0.8t = 90

From this you can solve for t. Note that you can't solve for b and m individually. But the question only asks for t.  Sufficient.

Statement 2: 
This tells you the proportion between magazine and billboard advertising, but multiple answers for television are possible. Together, magazine and billboard ads could take up almost the entire $90M, or they could only take up a tiny fraction of the $90M, leaving different possible values for television.  Insufficient.

Or, algebraically:
m = 1.50b

Substitute into the original equation:
t + 1.5b + b = 90

With two variables, the equation is unsolvable; multiple values for t are possible.  Insufficient.

The   answer is A.

The trap answer is C, because only with both statements together can you solve for all 3 variables. You could easily pick C if you lost track of the question and thought you needed to solve the whole system. Make sure you identify what the question is asking before you try the statements, and confirm that you answered the right question before finalizing your answer.

Megacorp International spent a total of $90,000,000 on television

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­­Megacorp International spent a total of $90,000,000 on television

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Megacorp International spent a total of $90,000,000 on television