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On a certain tour, half of the men are married, and the

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On a certain tour, half of the men are married, and the [#permalink] New post 18 Jun 2008, 11:52
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On a certain tour, half of the men are married, and the wives of 9/10 of them are also on the tour.
If there are 3 more women on the tour than men, what is the least possible number of people who could be on the tour?

(A) 19
(B) 22
(C) 23
(D) 43
(E) 52
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Re: PS: Tour [#permalink] New post 18 Jun 2008, 12:35
Quote:
On a certain tour, half of the men are married, and the wives of 9/10 of them are also on the tour.
If there are 3 more women on the tour than men, what is the least possible number of people who could be on the tour?


It’s D.

The key to solution is the fact that the number of man (m) on the tour must be an integer :)

So, m/2 should be an integer and also m/2*(1/10) should be an integer. The latter translates to condition that m/20 is an integer. The least possible number that satisfies this condition is 20. So, the number of women is 20+3 = 23 and the total number of people on the tour is 20+23=43.
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Re: PS: Tour [#permalink] New post 18 Jun 2008, 13:48
gmatcrook wrote:
On a certain tour, half of the men are married, and the wives of 9/10 of them are also on the tour.
If there are 3 more women on the tour than men, what is the least possible number of people who could be on the tour?

(A) 19
(B) 22
(C) 23
(D) 43
(E) 52


I get D.

M/2. Then we have 9M/20 for number of wives.

M has to be 20.

Thus W = M+3 --> 23.

23+20 =43.
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Re: PS: Tour [#permalink] New post 18 Jun 2008, 14:01
I also get D for similar reason to the BJ Penn fan ;)

if 50% of the men are married and 9/10 [of those, or 45% of the total] are with their wives, that leaves 5% of the men that are alone. If that 5% has to represent an integer, then 5% = 1 would be the lowest. So then the 100% of the men would be 100%/5% = 20. And if there are 3 more women there than men, then there has to be 23 women, so 20+23 = 43.

SIDE NOTE: This was my 400th post!

gmatcrook wrote:
On a certain tour, half of the men are married, and the wives of 9/10 of them are also on the tour.
If there are 3 more women on the tour than men, what is the least possible number of people who could be on the tour?

(A) 19
(B) 22
(C) 23
(D) 43
(E) 52

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Re: PS: Tour [#permalink] New post 18 Jun 2008, 23:15
I'm a little confused. Can someone help me understand the reasoning? The consensus is that the answer is D and there are 20 men. But if there are 20 men, then half are married --> 10 are married. of those, 9/10 of them are with their wives, so there are 9 wives. Wouldn't that be 20 men and 9 women = 29 people total??

Actually, I don't understand how there could be more women than men at all if only a fraction of the men have their wives along with them.
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Re: PS: Tour [#permalink] New post 19 Jun 2008, 02:05
The Q stem doesnt limit the number of women - re read the stem!!
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Re: PS: Tour [#permalink] New post 19 Jun 2008, 03:00
gmatcrook wrote:
On a certain tour, half of the men are married, and the wives of 9/10 of them are also on the tour. If there are 3 more women on the tour than men, what is the least possible number of people who could be on the tour?

(A) 19
(B) 22
(C) 23
(D) 43
(E) 52


let 2x be the total number of men and y be the number of women that comprises the total group. Now as per the question : y = 2x+3
also we know that x *90% of men are with their wives...so 5 % of men are alone. now the least possible number of men without their wives will be 1
accordinly if 5% of the men are represented by 1 then total number of men would be 20
accordingly the number of women will be 20+3 =23

therefore the least number of people on tour will be 20+23 = 43
so D should be the answer
what is the OA for this
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Re: PS: Tour [#permalink] New post 19 Jun 2008, 04:50
iamcartic wrote:
The Q stem doesnt limit the number of women - re read the stem!!


Actually, the question stem does limit the number of women on the tour. "...there are 3 more women on the tour than men..." Besides, we're not concerned with how many women there could be on the tour, the question specifically asks for the least possible so the fact that we don't know the exact total, or what the possibilities are for the maximum number, is irrelevant.

gmatcrook wrote:
On a certain tour, half of the men are married, and the wives of 9/10 of them are also on the tour. If there are 3 more women on the tour than men, what is the least possible number of people who could be on the tour?

(A) 19
(B) 22
(C) 23
(D) 43
(E) 52

_________________

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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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Re: PS: Tour [#permalink] New post 19 Jun 2008, 04:56
timothyhuang wrote:
I'm a little confused. Can someone help me understand the reasoning? The consensus is that the answer is D and there are 20 men. But if there are 20 men, then half are married --> 10 are married. of those, 9/10 of them are with their wives, so there are 9 wives. Wouldn't that be 20 men and 9 women = 29 people total??

Actually, I don't understand how there could be more women than men at all if only a fraction of the men have their wives along with them.


Some women choose not to marry!
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Re: PS: Tour [#permalink] New post 19 Jun 2008, 05:04
kevincan wrote:
timothyhuang wrote:
I'm a little confused. Can someone help me understand the reasoning? The consensus is that the answer is D and there are 20 men. But if there are 20 men, then half are married --> 10 are married. of those, 9/10 of them are with their wives, so there are 9 wives. Wouldn't that be 20 men and 9 women = 29 people total??

Actually, I don't understand how there could be more women than men at all if only a fraction of the men have their wives along with them.


Some women choose not to marry!


Single women can go on trips too!
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Re: PS: Tour   [#permalink] 19 Jun 2008, 05:04
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