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15 Dec 2023, 07:00
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Difficulty:
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46% (02:37) correct
54%
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
After completing typing 3/4 of a document, Lana recognizes that at her present speed, she'll finish the entire document in just 2/3 of the allocated time. By what percentage should she decrease her typing speed to ensure she finishes precisely when intended?
A. \(33 \frac{1}{3}\%\)
B. \(50\%\)
C. \(66 \frac{2}{3}\%\)
D. \(75\%\)
D. \(80\%\)
After completing typing 3/4 of a document, Lana recognizes that at her present speed, she'll finish the entire document in just 2/3 of the allocated time. By what percentage should she decrease her typing speed to ensure she finishes precisely when intended?
A. \(33 \frac{1}{3}\%\)
B. \(50\%\)
C. \(66 \frac{2}{3}\%\)
D. \(75\%\)
D. \(80\%\)
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16 Dec 2023, 11:48
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GMAT Club Official Explanation:
After completing typing 3/4 of a document, Lana recognizes that at her present speed, she'll finish the entire document in just 2/3 of the allocated time. By what percentage should she decrease her typing speed to ensure she finishes precisely when intended?
A. \(33 \frac{1}{3}\%\)
B. \(50\%\)
C. \(66 \frac{2}{3}\%\)
D. \(75\%\)
D. \(80\%\)
This question can be solved using pure algebra, but an easier approach is to assume numbers. Let's say the document consists of 12 pages (this number is chosen as it is the least common multiple of the denominators 4 and 3 given in the question) and the allocated time is 12 minutes.
Thus, Lana typed 12*3/4 = 9 pages and realized that instead of taking 12 minutes, she would complete the entire document in only 12*2/3 = 8 minutes, meaning she spent 8*9/12 = 6 minutes typing those 9 pages. Her current typing rate is then 9/6 = 1.5 pages per minute.
She has 3 pages of the document left to finish and wants to do this in the remaining 12 - 6 = 6 minutes. Therefore, she needs to reduce her typing rate to 3/6 = 0.5 pages per minute.
A reduction to a third, from 1.5 to 0.5, is equivalent to a \(66 \frac{2}{3}\%\) decrease. Alternatively, using a formula, we calculate \(\frac{1.5 - 0.5}{1.5}*100\% = \frac{1}{1.5}*100\% = \frac{2}{3}*100\% = 66 \frac{2}{3}\%\).
Answer: C.
General Discussion
Let's say total words required to type the complete doc = w
Lana's initial typing speed = p words/hr
Now she has already completed \(\frac{3}{4}\) th doc => \(\frac{3}{4}\)w is completed and \(\frac{w}{4}\) is pending for typing.
=> Now it's given that \(\frac{w}{p}\) = \(\frac{2}{3}\) T' where T' is the allotted time.
=> T' = \(\frac{3w}{2p}\)
=> time elapsed in completing the 3/4th doc = \(\frac{3w}{4p}\)
Now, let's say new typing speed = p'
=> \(\frac{w}{4p'}\) = \(\frac{3w}{2p}\) - \(\frac{3w}{4p}\) =\(\frac{3w}{4p}\)
=> p' = \(\frac{p}{3}\)
=> % decrease = \([\frac{(p-p')}{p}\) = 66.66%
Option C
Lana's initial typing speed = p words/hr
Now she has already completed \(\frac{3}{4}\) th doc => \(\frac{3}{4}\)w is completed and \(\frac{w}{4}\) is pending for typing.
=> Now it's given that \(\frac{w}{p}\) = \(\frac{2}{3}\) T' where T' is the allotted time.
=> T' = \(\frac{3w}{2p}\)
=> time elapsed in completing the 3/4th doc = \(\frac{3w}{4p}\)
Now, let's say new typing speed = p'
=> \(\frac{w}{4p'}\) = \(\frac{3w}{2p}\) - \(\frac{3w}{4p}\) =\(\frac{3w}{4p}\)
=> p' = \(\frac{p}{3}\)
=> % decrease = \([\frac{(p-p')}{p}\) = 66.66%
Option C
