Of all the computers owned by Company X, 1/3 were manufactured before

Question

Of all the computers owned by Company X, \(\frac{1}{3}\) were manufactured before 1995. If \(\frac{1}{4}\) of the computers manufactured before 1995 were replaced with new computers, the percent of Company X's computer's manufactured before 1995 would be?

A. \(8\frac{1}{3}\)%

B. \(12.5\)%

C. \(20\)%

D. \(25\)%

E. \(27\frac{1}{3}\)

Show Answer

Official Answer

D

A.  8\frac{1}{3} %

B.  12.5 %

C.  20 %

D.  25 %

E.  27\frac{1}{3}

IanStewart · Answer

You can just imagine having 36 computers in total. Then 12 were made before 1995. We replace 1/4, or three, of those with new computers. That leaves us with 9 old computers, and the total remains 36, so the answer is 9/36 = 25%.

K5 · Answer

How did people get answer A?

AllisonBell · Answer

Good question! One way to arrive at (incorrect) answer choice (A) is to multiply 1⁄3 x 1⁄4. This is actually a common wrong answer pattern on the GMAT, and a good one to be aware for situations when you need to guess. Often, at least one wrong answer choice will reflect the result of a simple arithmetic operation between the numbers in the problem (for example, multiplying the numbers together or adding them). That tends to be wrong, since most GMAT Quant problems involve multiple steps.

For more GMAT practice problems and explanations, check out ManhattanPrep’s   Free GMAT Starter Kit & QBank  .

egmat · Answer

Hi K5,

Good instinct to reverse-engineer the wrong answer, because  A is the classic trap here  and seeing how it's built protects you from it.

Use Ian's setup of  36  computers. Made before 1995 =  12 . We replace  1/4  of those, which is  3  old computers swapped out for new ones. The total stays at  36 .

Where A (8 1/3%) comes from:  those  3  replaced computers are exactly  3/36 = 1/12 = 8 1/3% . So anyone who lands on A has answered  "what percent got replaced?"  instead of  "what percent are still pre-1995?"  They reported the computers that  left  rather than the ones that  remain .

There's a second route to the same wrong number, and it's worth knowing:

-  1/3  (pre-1995 fraction) =  4/12 
-  1/4  (fraction replaced) =  3/12 
- Subtracting them directly: 4/12 - 3/12 =  1/12 = 8 1/3%

That looks tidy, but it's wrong because you can't subtract  1/4  straight from  1/3 . The  1/4  applies  only to the pre-1995 group , not to the whole company. You must take  1/4 OF 1/3 :

- Removed = 1/4 × 1/3 =  1/12 
- Remaining pre-1995 = 1/3 - 1/12 = 4/12 - 1/12 =  3/12 = 25%  -  D

So both paths to A share the same slip: treating the  1/4  as if it acted on the total, and/or answering for the group that was taken away. The question asks for the pre-1995 computers that are  left  -  9  out of  36 , which is  25% .

Answer: D

Of all the computers owned by Company X, 1/3 were manufactured before

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