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When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy

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When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy [#permalink]

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New post 30 May 2015, 04:24
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Question Stats:

69% (02:03) correct 31% (02:47) wrong based on 143 sessions

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When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 65 lb., the salad quantity chopped by Tammy is what percent greater than the quantity chopped by Tom?

A. 44%
B. 100%
C. 125%
D. 225%
E. 400%


[Reveal] Spoiler:
Trap Answer D:
This is the right answer for the wrong question. If the question were phrased as follows:

The quantity chopped by Tammy is what percent of the quantity chopped by Tom?", then 9 is indeed 225% of 4. However, the presence of the word "greater" means that the question asks about the difference between the two, as a percent of Tom's quantity.
[Reveal] Spoiler: OA

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Re: When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy [#permalink]

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New post 30 May 2015, 12:03
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Get the same time for both:

Tom chops 4 lbs in 6 minutes
Tammy chops 9 lbs in 6 minutes

So in the same amount of time, Tammy chops 125% more than Tom, since 9 is 125% greater than 4. So 125% is the answer.

Note that the actual time doesn't matter. If you multiply the time each work by x, you'll multiply the work each does by x, and 9x is still 125% greater than 4x.
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Re: When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy [#permalink]

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New post 30 May 2015, 22:10
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Hello reto

rate of Tom = \(\frac{2}{3}\) lb per min
rate of Tammy = \(\frac{3}{2}\) lb per min

Fitting it into the given equation

\(\frac{2}{3} * t + \frac{3}{2} * t = 65\)

\(t = 30\)

Tom makes \(\frac{2}{3} * 30 = 20\) lb
Tammy makes \(\frac{3}{2} * 30 = 45\) lb

% \(difference\) \(=\) \(\frac{(45-20)}{20} * 100\) \(=\) \(125\)%

That's option \(C\)
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Re: When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy [#permalink]

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New post 30 May 2015, 22:19
reto wrote:
When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 65 lb., the salad quantity chopped by Tammy is what percent greater than the quantity chopped by Tom?

A. 44%
B. 100%
C. 125%
D. 225%
E. 400%


[Reveal] Spoiler:
Trap Answer D:
This is the right answer for the wrong question. If the question were phrased as follows:

The quantity chopped by Tammy is what percent of the quantity chopped by Tom?", then 9 is indeed 225% of 4. However, the presence of the word "greater" means that the question asks about the difference between the two, as a percent of Tom's quantity.


hi,
we dont require to worry about 65 lbs as we have been given the speed of both and we can work out answer from it..
take LCM of tme 2,3=6 mins
in 6 tammy would do 3*3=9..
in 6 min, tom would do 2*2=4.
difference / speed=5/4=125%..
you are correct that the wordings does not give us D as the ans
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Re: When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy [#permalink]

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New post 31 May 2015, 04:58
Tom = Chops 2 lb in 3 mins or it can be written as 4 lb in 6 min

Tim = Chops 3 lb in 2 mins or it can be written as 9 lb in 6 mins

So, Tim chops (9-4 = 5 lb ) more in 6 mins or (5/4)*100 =125 %
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Re: When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy [#permalink]

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New post 22 Jun 2015, 01:20
I also calcuated their combined rate:

2/3 + 3/2 = 4/6 + 9/6 = 13/6.
So, (to find the % difference) if we take 13 as the whole then (9-4/4) * 100 = 1.25 * 100 = 125%.
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Re: When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy [#permalink]

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New post 09 May 2016, 18:27
reto wrote:
When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 65 lb., the salad quantity chopped by Tammy is what percent greater than the quantity chopped by Tom?

A. 44%
B. 100%
C. 125%
D. 225%
E. 400%


my approach..though took some extra time to double check.
Tom's rate 2/3
Tammy's rate 3/2

rate together: 2/3+3/2 = 13/6
they chopped 65 lb.
they chopped 65 lb in 65*6/13 = 5*6 = 30 minutes.
we know Tom's rate, we have his time, so we can solve for the work done.
2/3 * 30 = 20 lb chopped.
therefore, Tammy must have chopped 45 lb.

we are asked PERCENT GREATER
45-20 = 25
25/20 = 100%+ smth.
all out except for C.
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When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy [#permalink]

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New post 09 May 2016, 21:15
When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 65 lb., the salad quantity chopped by Tammy is what percent greater than the quantity chopped by Tom?

A. 44%
B. 100%
C. 125%
D. 225%
E. 400%

Tammy's rate/Tom's rate=(3/2)/(2/3)=9/4
9/4=2.25=125% increase in Tammy's rate over Tom's
C

Last edited by gracie on 22 Jan 2018, 09:52, edited 1 time in total.
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Re: When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy [#permalink]

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New post 21 Jan 2018, 19:04
reto wrote:
When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 65 lb., the salad quantity chopped by Tammy is what percent greater than the quantity chopped by Tom?

A. 44%
B. 100%
C. 125%
D. 225%
E. 400%


We use the “percent greater than” formula: (Tammy’s rate - Tom’s rate)/Tom’s rate x 100%.

Since Tom’s rate is 2/3 and Tammy’s rate is 3/2, when they work together, Tammy’s work will always be:

(3/2 - 2/3)/2/3 x 100

(9/6 - 4/6)/2/3 x 100

(5/6)/(2/3) x 100 = 5/6 x 3/2 x 100 = 15/12 x 100 = 5/4 x 100 = 125% greater than Tom’s.

Answer: C
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Re: When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy   [#permalink] 21 Jan 2018, 19:04
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