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# Rate (m09q05)

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Manager
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04 Dec 2008, 20:49
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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

It takes Jack 2 more hours than Tom to type 20 pages. Working together, Jack and Tom can type 25 pages in 3 hours. How long will it take Jack to type 40 pages?

(A) 5 hours
(B) 6 hours
(C) 8 hours
(D) 10 hours
(E) 12 hours

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Can we setup equation like this ?

20/t+2 + 20/t = 25/3 , where t is time taken by tom., so jack is t+2 hrs

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04 Dec 2008, 21:48
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together in one hour they can do
(20/t + 20/t+2) pages

and by the second statement that is equal to 25/3

solving we get t = 4 hours.

john can type 20 pages in 6 hours and forty pages in 12 hours

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05 Dec 2008, 08:32
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Hi ..
OE goes like this.

first step cross multiplication .
For 25 pages -------------- 3 hours
Hence for 20 pages --------------- 20*3/25 = 60/25 hrs.

Now let tom alone take t hours for 20 pages
as the question states jack takes t+2 hours

Now formula says 1/t + 1/(t+2) = 25/60
Solving we get t= 4 hours. So tom takes 4 hours to print 20 pages. ==> Jack takes 6 hours
Definitely he has to take double the time for 40 pages.

Pls post the OA. Some one comment if i am wrong

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18 Aug 2009, 04:40
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Here is how I solved it:

20/(2+T) + 20/T = 25/3

Simply to:

-5*T^2 + 14*T + 24 = 0

T = 4

Rate is 20 / (2+4)

40 * (6/20) = 12

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05 Oct 2009, 22:19
Can anyone explain why the following approach comes close, but doesn't exactly match the answer?

Jack spends 2 more hours than Tom to type 20 pages. Jack and Tom together spend 3 hours to type 25 pages. To equate both statements, we can adjust the 25 pages over 3 hours to 20 pages over 2.4 hours (20% decrease on both pages and time).

Knowing that it takes 2.4 hours for two people to complete a task, and assuming that each works at par for simplicity, you know that each would have take 4.8 hours independently to yield 2.4 hours together (1/4.8 + 1/4.8 = 1/2.4)

Since we know that they aren't at par with Jack taking 2 more hours, you can adjust the 4.8 hours of individual work to 3.8 and 5.8 for Tom and Jack respetively. This means it takes 5.8 hours alone for Jack to type 20 pages. Multiply this rate by 2 for 40 pages and we get 11.6, which is close to 12, but not 12.

What did I do wrong?

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Manager
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07 Oct 2009, 06:40
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dpgxxx wrote:
Can anyone explain why the following approach comes close, but doesn't exactly match the answer?

Jack spends 2 more hours than Tom to type 20 pages. Jack and Tom together spend 3 hours to type 25 pages. To equate both statements, we can adjust the 25 pages over 3 hours to 20 pages over 2.4 hours (20% decrease on both pages and time).

Knowing that it takes 2.4 hours for two people to complete a task, and assuming that each works at par for simplicity, you know that each would have take 4.8 hours independently to yield 2.4 hours together (1/4.8 + 1/4.8 = 1/2.4)

Since we know that they aren't at par with Jack taking 2 more hours, you can adjust the 4.8 hours of individual work to 3.8 and 5.8 for Tom and Jack respetively. This means it takes 5.8 hours alone for Jack to type 20 pages. Multiply this rate by 2 for 40 pages and we get 11.6, which is close to 12, but not 12.

What did I do wrong?

You did nothing wrong. You approximated the solution, and got a good enough approximated value. Although on some exercises this may not work.

20/t+2 + 20/t = 25/3
=> 20/t+2 + 20/t = 20/2.4
=> 1/t+2 + 1/t = 1/2.4
=> 1/6 + 1/4 = 0.16 + 0.25 = 0.416 = 1/2.4 ... (1/3.8 + 1/5.8 not= 1/2.4)
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16 Oct 2009, 16:35
Is there an easier way to get the answer?
I can get the formula. But when I find the root it really takes too much time. How do i solve this in 2 min?
Should I back solve by dividing all the answers by 2?

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21 Jan 2010, 19:30
Ok so I must need some serious help. I get all the way to 1/t + 1/(t+2) = 25/60 but then I'm not seeing how everyone is solving this to get t=4 so quickly. Help please.

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Manager
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18 Jan 2011, 06:40
Hellooo ... Can somobody exolain how to solve -5T^2 + 14T + 24 = 0 ? or similar equations? (not the simple ones, they are easily solvable)
with quadratic formula? or any shortcut?
thanks

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21 Jan 2011, 08:12
You got it correct man , factors are 20 & 6 .

Output will be t = 4 hrs,

Tom's Speed = 5 pages/hr
Jack's Speed = 3.33 pages/hr

For 40 pages for Jack,

40/3.33 = 12 hrs

Answer is 'E' = 12 hrs

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21 Jan 2011, 10:29
emailsector wrote:
together in one hour they can do
(20/t + 20/t+2) pages

and by the second statement that is equal to 25/3

solving we get t = 4 hours.

john can type 20 pages in 6 hours and forty pages in 12 hours

I got the equation but how the heck do you guys solve it within 3 minutes?

There has to be a faster way. Can someone please enlighten me?
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I'm trying to not just answer the problem but to explain how I came up with my answer. If I am incorrect or you have a better method please PM me your thoughts. Thanks!

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Manager
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21 Jan 2011, 17:19
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I think you can just substitute the answers:

40 qns - 5 hrs
20 qns - 5/2 hrs

tom -> 20 qns - 5/2-1=1/2 hrs
1 hr -> 40 pgs...
eliminate A

similarly, you can eliminate B, C

In E:

3 hrs :
Jack =
12 hrs -> 40 qns
3 hrs -> 10 qns

Tom -> 12/2-2=4hrs -> 20 qns
3 hrs -> 20/4*3=15 qns

10+15 = 25

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21 Jan 2011, 17:25
A better soution:

Let t be the time taken by Jack to type 40 qns.

3*40/t+3*20/(t/2-2)=25

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23 Jan 2011, 02:25
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Expert's post
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This problem was also posted in PS subforum. Below is my solution from there.

It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?
A. 5
B. 6
C. 8
D. 10
E. 12

Let the time needed for Jack to type 20 pages by $$j$$ hours, then for Tom it would be $$j-2$$ hours. So the rate of Jack is $$rate=\frac{job}{time}=\frac{20}{j}$$ pages per hour and the rate of Tom $$rate=\frac{job}{time}=\frac{20}{j-2}$$ pages per hour.

Their combined rate would be $$\frac{20}{j}+\frac{20}{j-2}$$ pages per hour and this equal to $$\frac{25}{3}$$ pages per hour --> $$\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}$$ --> $$\frac{60}{j}+\frac{60}{j-2}=25$$. At this point we can either try to substitute the values from the answer choices or solve quadratic equation. Remember as we are asked to find time needed for Jack to type $$40$$ pages, then the answer would be $$2j$$ (as $$j$$ is the time needed to type $$20$$ pages). Answer E works: $$2j=12$$ --> $$j=6$$ --> $$\frac{60}{6}+\frac{60}{6-2}=10+15=25$$.

Some work problems with solutions:
time-n-work-problem-82718.html?hilit=reciprocal%20rate
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal
gmat-prep-ps-93365.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate
solution-required-100221.html?hilit=work%20rate%20done
work-problem-98599.html?hilit=work%20rate%20done

Hope it helps.
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24 Jan 2011, 00:56
take 10 min to solve

Ans:E-12 hours,
for 20 page ,time =12/5
now , 1/t + 1/(t+2) = 25/60
solving for t=4 So tom takes 4 hours to print 20 pages. so, Jack takes 6 hours

Hence answer is 12 hours for 40 pags
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24 Jan 2011, 10:47
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First statement ==> rate jack + rate Tom = 25pages/ 3h ==> 1/J + 1/T = 25/3
Second statement ==> 1/J= 20/(x+2) AND 1/T=20/x
substitute in first statement ==> 20/(x+2) + 20/x = 25/3
simplify by 5 and add up on the left to (8x+8)/(x^2+2x)=5/3
cross multiply ==> 24x+24=5x^2+10x
2nd degree equation ==> 5x^2-14x-24=0
Use formula x= (-b +- (b^2-4ac)^0,5)/2a
x= (14 +- (14^2+4*5*24)^0,5)/10
14^2+4*5*24=2^2*(7^2+120)=2^2*169=2^2*13^2
so x= (14+-26)/10 only positive x ==> x=4
tom needs 4 h for 20 pages
jack needs 4+2=6h for 20 pages.
==> jack needs 12h for 40 pages!

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Manager
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09 Jun 2011, 23:31
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+1 for Bunuel. Plugging midway is an awesome method rather than solving the quadratic. Excellent stuff Man.
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Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

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25 Jan 2012, 13:28
20/t + 20/(t+2) = 25/3 Data Given --- equation 1

Question is what is the value of 2t+4 ?
We know 2t+4 is one among 5,6,8,10,12

Hit and Trial

if 2t+4 = 5 then t = 0.5 does not satisfy equation

if 2t+4 = 6 then t = 2 does not satisfy equation

if 2t+4=12 then t=12 satisfy the equation got the answer.

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25 Jan 2012, 14:57
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Expert's post
neophytehemant wrote:
20/t + 20/(t+2) = 25/3 Data Given --- equation 1

Question is what is the value of 2t+4 ?
We know 2t+4 is one among 5,6,8,10,12

Hit and Trial

if 2t+4 = 5 then t = 0.5 does not satisfy equation

if 2t+4 = 6 then t = 2 does not satisfy equation

if 2t+4=12 then t=12 satisfy the equation got the answer.

Approach is correct, math is not:
If 2t+4 = 6 then t = 1, not 2;
If 2t+4 = 12 then t = 4, which satisfies 20/t + 20/(t+2) = 25/3 (where t is the time needed for Tom to type 20 pages).

If you refer to my solution above, you'll see that it's basically the same as yours except I took j to be the time needed for Jack to type 20 pages. As we are asked about the time needed for Jack to type 40 pages then this notation will simplify a little bit the final stage of calculation.

Hope it helps.
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26 Jan 2012, 11:33
if they need 3 h for 25pages, then for 20 pages they will need 20*3/25=12/5

so,

1/(t+2)+1/t=5/12
5t^2-14-24=0
t=4

Jack's time 4+2=6
if Jack need 6 h for 20 pages, then for 40 pages he will need 40*6/20=12
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Re: Rate (m09q05)   [#permalink] 26 Jan 2012, 11:33

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# Rate (m09q05)

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