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

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
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The answer is E.

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 \(\frac{7}{3}*3 = 7$\)

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

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

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

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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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.

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.

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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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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R ate 8/3 sandwiches and paid 8 dollars. cost of 8/3 sandwiches = 8
cost of 1 sandwich =3

P bought 5 sandwiches = 15 dollars. P ate 8/3 sandwiches = 8 dollars. So 15-8=7 dollars is what he should get.
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We know that there were 8 sandwiches total, which means that each person must have gotten (8 sandwiches)/(3 people) = 8/3 sandwiches. If we look at what P and Q started with, we see that Q must have contributed 1/3 and P must have contributed 7/3. Since 7 of the 8 thirds were contributed by P, he should get 7/8 of the money, or $7.

ANSWER: E

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.

P = 5
Q = 3
They made total 24 pieces ...15 + 9. R ate 1 piece from Q as Q has total 9 pieces among which he had 8. And R ate 7 from P who has total 15, P got 8 and he gave R the remaining 7.

So, P will get 7$ and Q will get $1 .

E is the answer.

Posted from my mobile device

P, Q and R can share 8 sandwiches by each having 8/3

Cost of 8/3 is 8$, so cost of 1 sandwich = 3/8*8= 3$

P gives 5-8/3=7/3 to R, therefore amount due = 7/3 * 3 = 7
hence E

So I split the total 8 sandwiches in three parts making it 8/3
total cost of sandwiches is 8*3 = 24 (because 8/3 is equal to 8 $ )
as P bought 5 sandwiches he paid 15 $ off with he had sandwiches worth 8 $ so he should get back 15$-8$=7$ from R and as Q spent 3*3=9$ he himself ate sandwiches worth 8$ so he should get balance 1$
Hope it makes sense

Reason through it:
P Q and R bought a sum total of 8 sandwiches.
If they are split evenly, this implies that each received 8/3 each.
We know that P purchased 5, and Q purchased 3.
P therefore has 15 thirds to split, and Q has 9 thirds to split.
Assume P and Q both give R 4 thirds.
R will now have 4 thirds, Q will have 5 thirds, and P will have 11 thirds.
P must then transfer an extra 3 thirds to Q, then they will all have 8 thirds as previously stated.
P transferred a total of 7 thirds.
R paid 8 dollars for 8 thirds.
(7/3)/(8/3)=7/8. This is the proportion that P should get, based on the total transfers.
7/8*8 is 7, which is the correct answer.

The answer to this should be 5. As the share given by P to R should be 5/3 and not 7/3, so when 1 sandwich costs 3$, 5/3 sandwich should cost 5$

I would please request to provide an explanation for this.
Thank you