When Jack picks olives for two hours...

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

When Jack picks olives for two hours...

by swerve » Thu Jan 04, 2018 8:05 am

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 Jack
D. Mac picks 5 more pounds than Jack
E. Jack picks 5 more pounds than Mac

The OA is E.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Thu Jan 04, 2018 8:05 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 am; Location: Boston, MA; Thanked: 1153 times; Followed by:128 members; GMAT Score:770

by DavidG@VeritasPrep » Thu Jan 04, 2018 9:50 am

swerve 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 Jack
D. Mac picks 5 more pounds than Jack
E. Jack picks 5 more pounds than Mac

The OA is E.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Say Jack's regular rate = J and Mac's regular rate = M.
If Jack works for two hours at three times his regular speed (3J) then he'll pick 2 * 3J = 6J pounds
If Mac works for five hours at 80% of his regular speed (.8M) he'll pick 5*.8M = 4M pounds.
We've told that the first quantity is 10 more than the second so 6J = 4M + 10, or 6J - 4M = 10

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

If Mac picks for one hour at double his regular speed (2M) he'll pick 2M pounds.
If Jack picks for four hours at 75% of his regular speed, he'll pick 4*.75J = 3J pounds.
Effectively, we're looking for the difference, or 3J - 2M. Well, if 6J - 4M = 10, and we divide both sides by 2, we'll get 3J - 2M = 5, or 3J = 2M + 5. So Jack is picking 5 pounds more than Mac. The answer is E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Aug 12, 2019 5:43 pm

swerve 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 Jack
D. Mac picks 5 more pounds than Jack
E. Jack picks 5 more pounds than Mac

The OA is E.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

Let x = the number of pounds of olives Jack picks per hour regularly, and y = the number of pounds of olives Mac picks per hour regularly.

If Jack works for two hours at three times his regular speed, he will pick 2 * 3x = 6x pounds of olives. If Mac works for five hours at 80% = 4/5 of his regular speed, he will pick 5 * (4/5)y = 4y pounds of olives. Thus, we have:

6x = 4y + 10

3x = 2y + 5

If Mac picks olives for one hour at double his regular speed, he will pick 2y pounds of olives. If Jack picks olives for four hours at 75% = 3/4 of his regular speed, he will pick 4 * (3/4)x = 3x olives. Since 3x is 5 more than 2y, Jack will pick 5 more pounds of olives than Mac.

Answer: E

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