Help needed with OG question 135

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sanaa.rizwan: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Wed Aug 08, 2012 9:00 amFollowed by: 1 member

by sanaa.rizwan » Sat Nov 10, 2012 1:21 pm

The price for lunch for 15 people is $207, including 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?

a. $11.73
b. $12
c. $13.80
d. $14
e. $15.87

This is how I am solving this question

Finding 15% of 207

15/100 x 207 = $31.05

207 - 31.05 = $175.95 <= price for 15 people without gratuity

price per person = 175.95/15 = 11.73 (this is option A)

but the OG says that correct answer is $12, if there were no option for $11.73 then i can understand that its $12 by rounding it off.

the method that the OG uses brings the result to be $12, but my method is not wrong too, the result should be the same no matter what method you apply

someone help please

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Source: Beat The GMAT — Problem Solving | Sat Nov 10, 2012 1:21 pm

FLUID: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Thu Nov 01, 2012 7:52 pm; Thanked: 7 times

by FLUID » Sat Nov 10, 2012 8:53 pm

sanaa.rizwan wrote:The price for lunch for 15 people is $207, including 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?

a. $11.73
b. $12
c. $13.80
d. $14
e. $15.87

This is how I am solving this question

Finding 15% of 207

15/100 x 207 = $31.05

207 - 31.05 = $175.95 <= price for 15 people without gratuity

price per person = 175.95/15 = 11.73 (this is option A)

but the OG says that correct answer is $12, if there were no option for $11.73 then i can understand that its $12 by rounding it off.

the method that the OG uses brings the result to be $12, but my method is not wrong too, the result should be the same no matter what method you apply

someone help please

Yes, 12 is correct answer.

There are 15 people and let's suppose it cost $x for each.
It costed them 207 including Tips

=> X * 15 + 15/100 (x * 15) = 207
=> x * 15( 1+3/20) = 207
=> x = 12

Since we are excluding Tips it is just 12 $ per person.

Thanks,

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If you Win, you can Lead!
If you Loose, you can Guide!".

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jkaustubh: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Mon Aug 13, 2012 11:53 pm; Location: Mumbai; Thanked: 1 times

by jkaustubh » Mon Nov 12, 2012 2:01 am

FLUID wrote:
sanaa.rizwan wrote:The price for lunch for 15 people is $207, including 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?

a. $11.73
b. $12
c. $13.80
d. $14
e. $15.87

This is how I am solving this question

Finding 15% of 207

15/100 x 207 = $31.05

207 - 31.05 = $175.95 <= price for 15 people without gratuity

price per person = 175.95/15 = 11.73 (this is option A)

but the OG says that correct answer is $12, if there were no option for $11.73 then i can understand that its $12 by rounding it off.

the method that the OG uses brings the result to be $12, but my method is not wrong too, the result should be the same no matter what method you apply

someone help please
Yes, 12 is correct answer.

There are 15 people and let's suppose it cost $x for each.
It costed them 207 including Tips

=> X * 15 + 15/100 (x * 15) = 207
=> x * 15( 1+3/20) = 207
=> x = 12

Since we are excluding Tips it is just 12 $ per person.

Yes. 12 is the correct answer. Sanaa, in your approach you are reducing 15% of the total bill i.e. $207
where as according to the question the 15% gratuity is on the per head cost and not on the total bill.
hence the correct approach is as shown by FLUID.

Hope this helps.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Nov 12, 2012 4:01 am

The price of lunch for 15 people was $207.00,
including a 15 percent gratuity for service. What was
the average price per person, EXCLUDING the
gratuity?

(A) $11.73
(B) $12.00
(C) $13.80
(D) $14.00
(E) $15.87

We can plug in the answers, which represent the cost per person.
Given that the total cost is an INTEGER, the correct answer is almost certainly an integer itself.
Answer choice D is too great, since 15 people paying $14 each = 15*14 = 210 -- a value beyond the total cost of 207.

Answer choice B: $12 per person without gratuity
Total price for 15 people = 15*12 = 180.
Price + gratuity = 180 + .15(180) = 180+27 = 207.
Success!

The correct answer is B.

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shurale: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sat Apr 06, 2013 1:33 am

by shurale » Fri Apr 12, 2013 7:48 am

I have the same question and I don't really get it, why can't we just 207*0,85 instead of 207/1,15 when we are looking for 15%? Shouldn't it be the same?

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Apr 12, 2013 8:03 am

shurale wrote:I have the same question and I don't really get it, why can't we just 207*0,85 instead of 207/1,15 when we are looking for 15%? Shouldn't it be the same?

X is 15% greater than Y does NOT imply that Y is 15% less than X or that Y is 85% of X.

In the problem above, let P = the final price with gratuity and C = the total cost for 15 people without gratuity.

Since the final price is 15% greater than the cost without gratuity, we get:
P = (115/100)C
P = (23/20)C
C = (20/23)P.

Thus, the cost without gratuity is equal to 20/23 -- not 85% -- of the final price with gratuity.

Since P = 207, we get:
C = (20/23)(207) = 180.
Since there are 15 people, the cost per person without gratuity = 180/15 = 12.

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rintoo22: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Sun May 06, 2012 2:19 am; Location: Cape Town; Thanked: 6 times

by rintoo22 » Sat Apr 13, 2013 3:56 am

One more way.

x + 15x/100 = 207
115x = 20700
x = 12

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varun289: Master | Next Rank: 500 Posts; Posts: 298; Joined: Sun Jun 03, 2012 6:42 amFollowed by: 7 members; Location: New delhi; Thanked: 10 times; GMAT Score:590

by varun289 » Sat Apr 13, 2013 5:56 am

dears

try to understand the approach for such question

putting 15% for 207 is wrong it's 15% of X + X = 207

so calculate in such manner that 207/1.15 = actual value

now divide actual value by 15

= 12

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