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# Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q

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Math Expert
Joined: 02 Sep 2009
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Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q  [#permalink]

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01 Nov 2019, 03:45
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Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q bought 3 sandwiches and R bought none. Both P and Q shared their sandwiches with R such that each got the same amount. If R paid a total of $8 to P and Q, how much of$8 should P get? Assume both sandwiches and Dollars can be split.

(A) $3 (B)$4
(C) $5 (D)$5.5
(E) $7 Are You Up For the Challenge: 700 Level Questions: 700 Level Questions _________________ GMAT Club Legend Joined: 18 Aug 2017 Posts: 5911 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q [#permalink] ### Show Tags Updated on: 01 Nov 2019, 06:36 1 2 Bunuel wrote: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q bought 3 sandwiches and R bought none. Both P and Q shared their sandwiches with R such that each got the same amount. If R paid a total of$8 to P and Q, how much of $8 should P get? Assume both sandwiches and Dollars can be split. (A)$3
(B) $4 (C)$5
(D) $5.5 (E)$7

total sandwiches ; 8
when shared equally each must have had 8/3 each
R paid ; 8/8/3 ; 3$for sandwich sandwiches which P ate ; 8/3 so he should get money of 5-8/3 ; 7/3 7/3*3 = 7$
IMO E

Originally posted by Archit3110 on 01 Nov 2019, 04:05.
Last edited by Archit3110 on 01 Nov 2019, 06:36, edited 1 time in total.
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Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q  [#permalink]

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01 Nov 2019, 06:28

Each of them ate $$\frac{8}{3}$$ sandwiches.

Since R paid $8 for \frac{8}{3} sandwiches , price of 1 sandwich is $$8*\frac{3}{8}= 3$$ P should get back from R what P did not eat i.e $$5-\frac{8}{3} = \frac{7}{3} of sandwich$$ Therefore Money P should get back is $$\frac{7}{3}*3 = 7$$ Math Expert Joined: 02 Aug 2009 Posts: 8254 Re: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q [#permalink] ### Show Tags 01 Nov 2019, 07:43 1 Bunuel wrote: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q bought 3 sandwiches and R bought none. Both P and Q shared their sandwiches with R such that each got the same amount. If R paid a total of$8 to P and Q, how much of $8 should P get? Assume both sandwiches and Dollars can be split. (A)$3
(B) $4 (C)$5
(D) $5.5 (E)$7

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

P, Q and R can equally share 8 sandwiches by getting $$\frac{8}{3}$$

Cost of $$\frac{8}{3}$$ is 8$, so cost of 1 sandwich = $$8*\frac{3}{8}=3$$$

P gives 5-$$\frac{8}{3} =\frac{7}{3}$$ to R, and price of $$\frac{7}{3}=3*\frac{7}{3}=7$$$E _________________ VP Joined: 20 Jul 2017 Posts: 1331 Location: India Concentration: Entrepreneurship, Marketing WE: Education (Education) Re: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q [#permalink] ### Show Tags 01 Nov 2019, 23:31 Bunuel wrote: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q bought 3 sandwiches and R bought none. Both P and Q shared their sandwiches with R such that each got the same amount. If R paid a total of$8 to P and Q, how much of $8 should P get? Assume both sandwiches and Dollars can be split. (A)$3
(B) $4 (C)$5
(D) $5.5 (E)$7

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

Total sandwiches = 8
Each got same number = 8/3

R paid $8 for 8/3 sandwiches —> Ratio of share of P:Q = (5-8/3) : (3-8/3) = 7/3 : 1/3 = 7 : 1 —> Share of P in$ = 7/(7+1)*8 = $7 IMO Option E Posted from my mobile device SVP Joined: 03 Jun 2019 Posts: 2019 Location: India GMAT 1: 690 Q50 V34 WE: Engineering (Transportation) Re: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q [#permalink] ### Show Tags 25 Nov 2019, 08:38 Bunuel wrote: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q bought 3 sandwiches and R bought none. Both P and Q shared their sandwiches with R such that each got the same amount. If R paid a total of$8 to P and Q, how much of $8 should P get? Assume both sandwiches and Dollars can be split. (A)$3
(B) $4 (C)$5
(D) $5.5 (E)$7

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

Total sandwiches = 5+ 3 = 8
Sandwich for each P, Q & R = 8/3

P bought extra sandwich = 5 - 8/3 = 7/3
Q bought extra sandwich = 3 - 8/3 = 1/3

Total money paid to P & Q = $8 Ratio of money to P : money to Q = 7/3 : 1/3 = 7:1 Money that P should get =$7

IMO E
Intern
Joined: 07 Apr 2019
Posts: 31
Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q  [#permalink]

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26 Nov 2019, 20:06
Hi experts,

I came across a strange concept (tied with a question below) written somewhere not official. Wanted to check with you if that is a correct way to calculating.

We have ratios of History:geography scores for 5 students: GMATNinja (0.8) , nightblade354 (0.35) , VeritasKarishma (0.9) chetan2u (1.25) and Bunuel (0.9). By what percentage did Bunuel score more than @Nightblae354 in History?

Solution: Assuming Nightblade's score as 35:100 and Bunuel's as 90:100 [based on ratios], Bunuel scored : 55/35 * 100 = 57.14% more.
This solution comes from an unofficial GMAT tutor. However, I wanted to see its validity, coz it was quite fascinating to me.

Is this a correct way to compute?
Math Expert
Joined: 02 Aug 2009
Posts: 8254
Re: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q  [#permalink]

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26 Nov 2019, 20:30
deeeuce wrote:
Hi experts,

I came across a strange concept (tied with a question below) written somewhere not official. Wanted to check with you if that is a correct way to calculating.

We have ratios of History:geography scores for 5 students: GMATNinja (0.8) , nightblade354 (0.35) , VeritasKarishma (0.9) chetan2u (1.25) and Bunuel (0.9). By what percentage did Bunuel score more than @Nightblae354 in History?

Solution: Assuming Nightblade's score as 35:100 and Bunuel's as 90:100 [based on ratios], Bunuel scored : 55/35 * 100 = 57.14% more.
This solution comes from an unofficial GMAT tutor. However, I wanted to see its validity, coz it was quite fascinating to me.

Is this a correct way to compute?

No, this would not be correct.
Yes if they have got same score in geography then ok.
B got 81 and 90 in geography, while N got 31.5 and 90 in geography.
So % more =(81-31.5)/31.5*100=5000/31.5=157%.
But say B got 9 in history and 10 in geography, while N got 35 and 100 respectively.
Here B has got lesser marks than N in history.
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Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q  [#permalink]

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26 Nov 2019, 21:09
chetan2u wrote:
deeeuce wrote:
Hi experts,

I came across a strange concept (tied with a question below) written somewhere not official. Wanted to check with you if that is a correct way to calculating.

We have ratios of History:geography scores for 5 students: GMATNinja (0.8) , nightblade354 (0.35) , VeritasKarishma (0.9) chetan2u (1.25) and Bunuel (0.9). By what percentage did Bunuel score more than @Nightblae354 in History?

Solution: Assuming Nightblade's score as 35:100 and Bunuel's as 90:100 [based on ratios], Bunuel scored : 55/35 * 100 = 57.14% more.
This solution comes from an unofficial GMAT tutor. However, I wanted to see its validity, coz it was quite fascinating to me.

Is this a correct way to compute?

No, this would not be correct.
Yes if they have got same score in geography then ok.
B got 81 and 90 in geography, while N got 31.5 and 90 in geography.
So % more =(81-31.5)/31.5*100=5000/31.5=157%.
But say B got 9 in history and 10 in geography, while N got 35 and 100 respectively.
Here B has got lesser marks than N in history.

Hi chetan2u : thanks for the prompt response. Got your point. So can we generalize that if only ratio is provided there is no way to calculate percentage increase or the absolute value it self just by the ratio?

Thanks.
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Posts: 10113
Location: Pune, India
Re: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q  [#permalink]

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26 Nov 2019, 21:16
deeeuce wrote:
Hi experts,

I came across a strange concept (tied with a question below) written somewhere not official. Wanted to check with you if that is a correct way to calculating.

We have ratios of History:geography scores for 5 students: GMATNinja (0.8) , nightblade354 (0.35) , VeritasKarishma (0.9) chetan2u (1.25) and Bunuel (0.9). By what percentage did Bunuel score more than @Nightblae354 in History?

Solution: Assuming Nightblade's score as 35:100 and Bunuel's as 90:100 [based on ratios], Bunuel scored : 55/35 * 100 = 57.14% more.
This solution comes from an unofficial GMAT tutor. However, I wanted to see its validity, coz it was quite fascinating to me.

Is this a correct way to compute?

Remember that different ratios have different multipliers. Whenever in doubt, assign multipliers to the ratios and check.

N's ratio = .35 = 35:100
So N's History marks = 35a
N's Geography marks = 100a

B's ratio = 0.9 = 90:100
So B's History marks = 90b
B's Geography marks = 100b

By what % did B score more than N in History?

= (90b - 35a)/35a * 100

Now, since you cannot get rid of the variables, you cannot get a unique value for this.
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Re: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q  [#permalink]

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27 Nov 2019, 06:04
Although this question is one on Word problems, it also has strong undercurrents of Ratio concepts based on which you need to solve this question. Instead of solving it the usual way of dividing the total of 8 sandwiches among 3 people and dealing with fractions, I’d like to take an approach where I can use integer values and the concept of money- because both these concepts can be easily understood and it will make you more confident with such questions.

The total number of sandwiches is 8; we need to divide this among 3 persons. It’s very clear that this involves uneven division by 3. So, to make it simple, let us take the cost of one sandwich to be $3. This means that the total value of the 8 sandwiches is$24, of which $15 was contributed by P and$9 was contributed by Q. R did not contribute anything but still ended up getting an equal share. What does this mean? It means that he got an equal share of the total value $24 which comes to$8.

This also means that the other two persons P and Q saw their respective shares being reduced to $8 since they were magnanimous enough to share their sandwiches with R. Q’s share was 9 and it went down to 8. This means, he should have given$1 to R (or in other words, $$\frac{1}{3}$$rd of a sandwich to R).

P’s share was 15 and it went down to 8. This means, he should have given $7 to R (or in other words, $$\frac{7}{3}$$rd of a sandwich to R). See how the sum of 7/3 and 1/3 gives you 8/3 which is the value you would have obtained even if you took the traditional approach of dividing 8 by 3. Since R paid$8 to P and Q and the money needs to be split in the ratio of the sandwiches they shared with R, it only means that P got $7 and Q got$1.
The correct answer option is E.

A point to note is that it’s wrong to assume that the money given by R to P and Q was divided uniformly among them. Do not make this mistake, or option B is waiting for you.

Hope that helps!
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Re: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q  [#permalink]

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01 Dec 2019, 06:47
Quote:
P, Q and R can equally share 8 sandwiches by getting $$\frac{8}{3}$$

Cost of $$\frac{8}{3}$$ is 8$, so cost of 1 sandwich = $$8*\frac{3}{8}=3$$$

P gives 5-$$\frac{8}{3} =\frac{7}{3}$$ to R, and price of $$\frac{7}{3}=3*\frac{7}{3}=7$$$E chetan2u I still have a doubt. "Both P and Q shared their sandwiches with R such that each got the same amount" From this we deduce R gets 8/3. That's fine. P gives (5-8/3) and Q gives (3-8/3) but then at the end all 3 don't have the same amount. _________________ The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic You are missing on great learning if you don't know what this is: Project SC Butler Math Expert Joined: 02 Aug 2009 Posts: 8254 Re: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q [#permalink] ### Show Tags 01 Dec 2019, 08:11 1 TheNightKing wrote: Quote: P, Q and R can equally share 8 sandwiches by getting $$\frac{8}{3}$$ Cost of $$\frac{8}{3}$$ is 8$, so cost of 1 sandwich = $$8*\frac{3}{8}=3$$$P gives 5-$$\frac{8}{3} =\frac{7}{3}$$ to R, and price of $$\frac{7}{3}=3*\frac{7}{3}=7$$$

E

chetan2u

I still have a doubt.
"Both P and Q shared their sandwiches with R such that each got the same amount"

From this we deduce R gets 8/3. That's fine.
P gives (5-8/3) and Q gives (3-8/3) but then at the end all 3 don't have the same amount.

P gives R 5-8/3 or 7/3 and he has 8/3 after giving 7/3
Q gives R 3-8/3 or 1/3 and he has 8/3 after giving 1/3
R now has 7/3+1/3=8/3
So all three get 8/3
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Re: Three coworkers P, Q, and R met for a dinner. P bought 5 sandwiches, Q   [#permalink] 01 Dec 2019, 08:11
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