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Ratio Question

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Ratio Question

by jain0069 » Thu May 01, 2008 9:05 pm
Sorry if this has already been posted before, but I made a search for it and could'nt find any topic relating to the same question.

Tom, Dick and Harry went for lunch to a restaurant. Tom had $100 with him, Dick had $60 and Harry had $409. They got a bill for $104 and decided to give a tip of $16. They further decided to share the total expenses in the ratio of the amounts of money each carried. The amount of money which Tom paid more than what Harry paid is

A) 120
B) 200
C) 60
D) 24
E) 36


The Answer: E

This might be one of those really easy questions but I really could'nt do it. Someone please help me out here... Thanks......
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by codesnooker » Thu May 01, 2008 9:55 pm
I doubt that whether this is question even correct or not?

Reasons:

1) If they to pay the expense according the ratio of money they have then must pay maximum amount as compare to his friend. However, in the end question asked to give the extra amount paid by Tom as compare to Harry. How Tom can pay more than Harry?

2) On first look, one can know that 409 has no common factor with either 100 or 60. So, some of the answer should be in fraction, However, there is none of the answer is in fraction. (This is just my basic instinct that I feel on looking the question).

My approach to solve this question:

Tom' Money + Dick's money + Harry's money = 104 + 16
100x + 60x + 409x = 120
x = 120/569
x = .2109

Tom's share = 100 * .2109 = 21.09$
Dick's share = 60 * .2109 = 12.65$
Harry's share = 409 * .2109 = 86.26$


I guess you have picked up this question from this url: https://www.bestsamplequestions.com/gmat ... tions.html

I don't know how much reliable is this source?

Experts comment required.
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by jain0069 » Thu May 01, 2008 10:00 pm
Hey thanks for the quick reply. Yeah I got this from the same site that you mentioned. Sorry for the stupid question :( ... But thanks anyways for telling me the approach to solve such questions....
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by II » Fri May 02, 2008 2:07 am
Guys ... there might even be a typo here ... I think that Harry's amount "409" should read "40" ... that would certainly make more sense.

The way the question is also phrased ... you would expect the last amount to be the least:
Original statement:
"Tom, Dick and Harry went for lunch to a restaurant. Tom had $100 with him, Dick had $60 and Harry had $409"
What I think it should read as:
"Tom, Dick and Harry went for lunch to a restaurant. Tom had $100 with him, Dick had $60 and Harry had $40"

So if we answer the question using this information:
we have the following ratio: Tom:Dick:Harry => 100:60:40 => 5:3:2
The total bill was for 104+16 = $120

We can write this as: 5x + 3x + 2x = 120 => 10x = 120 => x = 12
So we can now find out how much each person contributed towards the final total bill.
So Tom paid: 5 * 12 = 60
Dick paid 3 & 12 = 36
Harry paid 2 * 12 = 24

Therefore Tom paid (60 - 24) $36 more than Harry. Answer is E.[/u]
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by jain0069 » Fri May 02, 2008 2:11 am
Hey II... now that makes so much more sense... Ofcourse I got my equation all screwed up because of the incorrect value and hence the confusion.... Thanks :)
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by II » Fri May 02, 2008 2:13 am
No problem at all.
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by VP_RedSoxFan » Fri May 02, 2008 8:45 am
Its also worth mentioning that usually the answer choices in PS problems are listed sequentially, either in ascending or descending order.

Good catch on the typo. Given the answer (E) and assuming Harry was a typo, I backed into the typo as follows:

D=0.6*T (since I thought Harry's pocket money was wrong, I just used T and D's ratios as safe)

T + H + D = 120 (they all paid)

T - H = 36 (assumed E was right answer in order to solve the typo)

substituting for H and D:

T + (T-36) + 0.6T = 120, combine like terms, isolate the variable: 2.6T = 156

Solving for T, T = 60

Therefore T = 60, D = 36, H = 24.

That fits the ratio of T:D:H of 60:36:24 or 5:3:2 and scaled up to fit the pocket money we were trusting: 100:60:40. Harry must have had 40, not 409.
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