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# When Jack picks olives for two hours at three times his regu

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Manager
Joined: 10 Sep 2012
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When Jack picks olives for two hours at three times his regu [#permalink]

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20 Nov 2012, 18:05
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Difficulty:

55% (hard)

Question Stats:

66% (02:25) correct 34% (02:41) wrong based on 143 sessions

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When Jack picks olives for two hours at three times his regular speed, he picks 10 pounds of olives more than Mac working for five hours at 80% of his regular speed. Therefore, if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed, then

A. Jack picks double the amount of olives Mac picks
B. Mac picks 10 pounds more than Jack
C. Jack picks 10 pounds more than Mac
D. Mac picks 5 more pounds than Jack
E. Jack picks 5 more pounds than Mac

Does anyone have an elegant solution for this?

The solution presents a algebraic brute forcer, but I think some of you guys could do this better. I will post the solution if there are inquiries.
[Reveal] Spoiler: OA

Last edited by reto on 27 Aug 2015, 13:08, edited 1 time in total.
added source and format

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Re: When Jack picks olives for two hours at three times his regu [#permalink]

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20 Nov 2012, 21:15
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anon1 wrote:
When Jack picks olives for two hours at three times his regular speed, he picks 10 pounds of olives more than Mac working for five hours at 80% of his regular speed. Therefore, if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed, then

Jack picks double the amount of olives Mac picks
Mac picks 10 pounds more than Jack
Jack picks 10 pounds more than Mac
Mac picks 5 more pounds than Jack
Jack picks 5 more pounds than Mac

Does anyone have an elegant solution for this?

The solution presents a algebraic brute forcer, but I think some of you guys could do this better. I will post the solution if there are inquiries.

Let's say Jack's regular speed is J olives/hr and Mac's regular speed is M olives/hr

Given:
2*3J = 10 + 5*(4/5)M
3J = 5 + 2M

Question: " if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed"

Mac picks 2M and Jack picks 4*(3/4)J = 3J
They are asking you for the relation between 3J and 2M. You already know 3J = 5 + 2M
So Jack picks 5 pounds more olives than Mac.
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Manager
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Re: When Jack picks olives for two hours at three times his regu [#permalink]

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20 Nov 2012, 22:00
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I understand everything you did and that was pretty easy.

I just wish I'll be able to do that on the test.....

When you first see that, what exactly is your plan? Do you just start writing everything out in terms of numbers and variables, simplify and hope something fits? (especially the last part of simplying to get 2m = 5 +3J , and then changing the second part of the question into 2m and 4*3/4 J and getting 3J, then you reveal the 5) It seems like that's what you did, which is oversimplifying the method but it worked here.

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Re: When Jack picks olives for two hours at three times his regu [#permalink]

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21 Nov 2012, 04:26
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Expert's post
anon1 wrote:
I understand everything you did and that was pretty easy.

I just wish I'll be able to do that on the test.....

When you first see that, what exactly is your plan? Do you just start writing everything out in terms of numbers and variables, simplify and hope something fits? (especially the last part of simplying to get 2m = 5 +3J , and then changing the second part of the question into 2m and 4*3/4 J and getting 3J, then you reveal the 5) It seems like that's what you did, which is oversimplifying the method but it worked here.

Before the test starts there is only one thought in my mind - one can answer every question they ask using the data they give. The question is - how much time do you take?
My plan is to never use variables and never write anything(I solved this question without writing anything though I admit I was doing nothing more than making these equations in my mind). The trouble is that the plan doesn't work sometimes. I read the question and I wanted to pick variables because 2 hrs, 3 times, 80% etc were too complicated to handle without variables though it was obvious that they will all fit in neatly (notice 5 hrs at 80% - we know 80% is 4/5 so we are left with 4 etc)

As for simplifying the equation, it is but a natural step. If you see 2x + 4y = 8, you simplify it to x + 2y = 4 whether you see an immediate need or not. In the next part, when I saw the 2M, it was obvious that a 3J was on the way. Had there been a 6M, I would have expected to see a 9J. Remember, in GMAT things always fit in together.
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Re: When Jack picks olives for two hours at three times his regu [#permalink]

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28 Sep 2013, 02:10
We know form the question and diagram that :

6x = 4y + 10 .....(1)

And from the diagram we need to have a relation between 3x and 2y.

Dividing (1) by 2

We have

3x = 2y + 5

Hence (E) !
Attachments

sol.JPG [ 20.1 KiB | Viewed 1683 times ]

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Re: When Jack picks olives for two hours at three times his regu [#permalink]

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27 Aug 2015, 13:04
anon1 wrote:
When Jack picks olives for two hours at three times his regular speed, he picks 10 pounds of olives more than Mac working for five hours at 80% of his regular speed. Therefore, if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed, then

Jack picks double the amount of olives Mac picks
Mac picks 10 pounds more than Jack
Jack picks 10 pounds more than Mac
Mac picks 5 more pounds than Jack
Jack picks 5 more pounds than Mac

Does anyone have an elegant solution for this?

The solution presents a algebraic brute forcer, but I think some of you guys could do this better. I will post the solution if there are inquiries.

Why do you use variables at all? I just plugged in Values like this:

Jack picks olives for two hours at three times his regular speed, he picks 10 pounds of olives more than Mac working for five hours at 80% of his regular speed. So, look at this;

Jack picks 30 olives and Mac picks 20 olives. Therefore Jacks regular rate is 5 olives per hour (30/2=15 divided with 3 = 5) and Mac's original rate is 5 (20/5 = 4 / 4/5 = 5). Wow they even have the same rate!!! Now what does the question ask?

Mac works for one hour at double his rate? Okay, then 2*5*1 = 10 olives for Mac.
Jack works for four hours at 3/4 his rate? Okay that is 3/4*5*4 = 15

Therefore Jack picks 5 more than Mac does.
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Re: When Jack picks olives for two hours at three times his regu [#permalink]

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When Jack picks olives for two hours at three times his regu [#permalink]

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14 Jan 2017, 11:30
anon1 wrote:
When Jack picks olives for two hours at three times his regular speed, he picks 10 pounds of olives more than Mac working for five hours at 80% of his regular speed. Therefore, if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed, then

A. Jack picks double the amount of olives Mac picks
B. Mac picks 10 pounds more than Jack
C. Jack picks 10 pounds more than Mac
D. Mac picks 5 more pounds than Jack
E. Jack picks 5 more pounds than Mac

Does anyone have an elegant solution for this?

The solution presents a algebraic brute forcer, but I think some of you guys could do this better. I will post the solution if there are inquiries.

let j=Jack's rate; m=Mac's rate
3j*2-10=(4m/5)*5
m=(3j-5)/2
substituting, ratio between Jack's and Mac's outputs=
[(3j/4)*4]/[2*(3j-5)/2]=3j/(3j-5)
J picks 5 more pounds than M
E

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When Jack picks olives for two hours at three times his regu   [#permalink] 14 Jan 2017, 11:30
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