12 Days of Christmas GMAT Competition - Day 5: After completing typing

Question

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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\%

Bunuel · Accepted Answer

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.

sj296 · Answer

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 =    = 66.66%

Option C

pooh.2304 · Answer

Present rate = 1/(2/3) = 3/2

Time taken to type 3/4 doc = 3/2 * 3/4 = 1/2

Remaining work = 1 - 3/4 = 1/4
Remaining time = 1 - 1/2 = 1/2
Remaining work Rate = 1/2

% decrease = (3/2 - 1/2)/(3/2) * 100 = 66 2/3% (C)

missionmba2025 · Answer

Assume Lana had to type in 1200 pages in 3 hours. She should have typed in 1200/3 = 400 pages per hour.

But she typed 1200 / 2 = 600 pages instead.

After completing 3/4 of 1200 i.e. 900 pages she wants to reduce her speed.

Time to complete 900 pages at her speed = 900 / 600 = 1.5 hours

So she needs to complete 300 pages in 1.5 hours, i.e. 200 pages per hour

200 = 600*x/100

x = 33.33%

Hence, she must reduce her speed by 66.66%

IMO C

DG1989 · Answer

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}{2} %
B. 50%
C. 66 \frac{2}{3} %
D. 75%
E. 80%

Solution:  Let original speed be x and original intended time of completion of the document be T
complete document = x * T
say 100 = x * T

Lana realizes that at current speed say y, work will be completed in  \frac{2}{3} T
i.e. 100 = y *  \frac{2}{3} T
this gives y =  \frac{3}{2} x
or y = 1.5x

Time taken to complete  \frac{3}{4}  of the document say T'
75 = 1.5x * T'
or T' = 50/x

For remaining  \frac{1}{4}  of the document, the speed needs to be reduced from say y to y' and the time taken should be = T - T'
i.e. 25 = y' * (T - T')
25 = y' * ( \frac{100}{x}  -  \frac{50}{x} )
25 = y' *  \frac{50}{x}

Thus y' =  \frac{x}{2} 
or y' = 0.5x

Now, Percentage reduction in the speeds required to finish the work in original intended time
=  \frac{(y - y')}{y}  * 100

=  \frac{(1.5x - 0.5x)}{1.5x}  * 100

=  \frac{x}{1.5x}  * 100

=  \frac{2}{3}  * 100
Percentage reduction = 66 \frac{2}{3} %

Option C   is the right answer

Lalykys · Answer

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?

Let's there be : 
- w: the work of typing an entire document
- Phase 1 where work done is (3/4)*w and T1 the time it takes
- Phase 2 where work to be done is (1/4)*w and T2 the time it will take if Lana keeps the same speed
- T: the time allocated for the entire document
we know that T1+T2 = 2T/3
furthermore as the rate for those 2 phases is the same => 3/4T1 = 1/4T2 => T1=3T2 so 4T2=2T/3 => T2=T/6 and T1=T/2.

so after phase 1, Lana should decrease her speed so that she spend T/2 time to finish w/4:
So her new speed will be R=1/4*2/T=1/2T 
knowinf that initial rate was 3/4T1=3/4*2/T=3/2T it means that Lana should decrease her speed by 3/2T-1/2T=1/T =>which represent a (1/T)/(3/2T)=> (1/T)*(2T/3) => 66-2/3%

So answer C

ChiranjeevSingh · Answer

Here's how I solved it.

At her current speed, Lana would finish the entire document in two-thirds of the allocated time. She has already completed three-fourths of the document.
This means she has used (3/4) × (2/3) = 1/2 of the allocated time to complete three-fourths of the document.

Now, she has the remaining half of the time left, and she needs to complete the remaining one-fourth of the document.
In the first half of the time, she completed three-fourths of the document. In the next half, she needs to complete only one-fourth.

Attachment:

cj_1.png [ 1.03 MiB | Viewed 1810 times ]

This means her typing speed must reduce to one-third of her original speed (because earlier she was doing 3 parts in the same time, now only 1 part).
Thus, her speed must decrease by two-thirds.

A decrease of two-thirds corresponds to 66 2/3%.
Therefore, the answer is 66 2/3%.

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