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Of the 50 guests at a party, 10 percent are smokers. How

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Of the 50 guests at a party, 10 percent are smokers. How [#permalink] New post 09 Aug 2012, 14:48
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77% (01:37) correct 23% (01:06) wrong based on 149 sessions
Of the 50 guests at a party, 10 percent are smokers. How many non-smokers must leave in order to bring the number of smokers up to 50 percent of the guests?

A. 5
B. 10
C. 20
D. 35
E. 40

Kaplan's explanation:

Given 50 guests at a party, of whom 10% are smokers, how many nonsmokers would need to leave in order to have an equal number of smokers and nonsmokers?

Straight math is the best approach to this problem. If 10% of the 50 people are smokers, then there are 10% × 50 = 5 smokers and 50 – 5 = 45 nonsmokers. Smokers will represent 50% — or one-half — of the party guests when there are equal numbers of smokers and nonsmokers; that is, when there are 5 nonsmokers remaining. This means that 40 of the 45 nonsmokers must leave. Answer Choice (E) is correct.

Can someone please explain in a better way the logic to the answer of this problem? I got down:

50 guests @ party:
.10 ---> 5 are smokers
.90 ---> 45 are non smokers

I don't understand why 40 have to leave? It's probably easy but I don't see it.
[Reveal] Spoiler: OA

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Re: Of the 50 guests at a party, 10 percent are smokers. How [#permalink] New post 09 Aug 2012, 14:56
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Of the 50 guests at a party, 10 percent are smokers. How many non-smokers must leave in order to bring the number of smokers up to 50 percent of the guests?

A. 5
B. 10
C. 20
D. 35
E. 40

Now, there are 5 smokers (10% of 50) and 50-5=45 non-smokers at a party. We need there to be 5 smokers and 5 non-smokers, in this case there will be 50% smokers and 50% non-smokers.

Therefore 45-5=40 non-smokers must leave.

Answer: E.
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Re: Of the 50 guests at a party, 10 percent are smokers. How [#permalink] New post 10 Aug 2012, 07:31
Bunuel wrote:
[b]We need there to be 5 smokers and 5 non-smokers, in this case there will be 50% smokers and 50% non-smokers.

Therefore 45-5=40 non-smokers must leave.

Answer: E.




Ahh that makes sense, thanks much!
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Re: Of the 50 guests at a party, 10 percent are smokers. How [#permalink] New post 10 Nov 2012, 02:03
See it as a ratio problem. Let X be number of smokers and Y that of non-smokers (X = 5, Y = 45)
For X to be 50% of the total that mean X shld be = to new nber of Y (let that be Y-a). Thus
X/Y-a = 1 ==> 5= 45-a ==> a = 40
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Re: Of the 50 guests at a party, 10 percent are smokers. How [#permalink] New post 16 Jan 2015, 05:51
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Re: Of the 50 guests at a party, 10 percent are smokers. How [#permalink] New post 16 Jan 2015, 13:27
Expert's post
Hi All,

The math behind this question is pretty simple, as the other explanations have pointed out. If you can't see the "math" approach to this question, then you can use the ANSWERS to your advantage and "brute force" the solution.

We're told that 50 people are at a party and 10% of them are smokers:

Total = 50
Smokers = 5
Non-Smokers = 45

We're then asked how many smokers would need to leave the party to make it so the total party guests are 50% smokers. This means that we will SUBTRACT a number from 45.....since the answer choices are numbers, we can TEST THE ANSWERS until we get a match.

A: 5 --> remove 5 non-smokers....
Smokers = 5
Non-Smokers = 40
5/45 is NOT 50% smokers

B: 10 --> remove 10 non-smokers..
Smokers = 5
Non-Smokers = 35
5/40 is NOT 50% smokers

C:A: 20 --> remove 20 non-smokers....
Smokers = 5
Non-Smokers = 25
5/30 is NOT 50% smokers

D: 35 --> remove 35 non-smokers..
Smokers = 5
Non-Smokers = 10
5/15 is NOT 50% smokers

E: 40 --> remove 40 non-smokers..
Smokers = 5
Non-Smokers = 5
5/10 IS 50% smokers
This MUST be the answer.

Final Answer:
[Reveal] Spoiler:
E


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Re: Of the 50 guests at a party, 10 percent are smokers. How   [#permalink] 16 Jan 2015, 13:27
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