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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]

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08 Aug 2008, 03:35
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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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08 Aug 2008, 05:14
Lets say total men = 300x
Married men = 150x
Married Women on tour = 135x
Total Women = 300x+3
Women not married = 300x+3-135x = 165x + 3

165x needs to be an integer. If x=1/15 then 165x=11

So women = 23, Men = 20

Total = 43 (D)
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08 Aug 2008, 05:34
I used POE.

Answer is 23. In this case 10 men and 13 women. 9/10 of 10 men is 9 women.
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08 Aug 2008, 05:51
scthakur wrote:
I used POE.

Answer is 23. In this case 10 men and 13 women. 9/10 of 10 men is 9 women.

Can't be 23. 10 men would mean 5 men are married. 9/10 of 5 is 4.5 men bring their wives. Not possible.
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08 Aug 2008, 07:28
men = m
women = m+3

number of people on the trip = 2m+3

this will ne minimum when m is minimum...

condtion for m = m/2 * 9/10 is an interger, so m will be minimum when m = 20,

total people = 43 --- D
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08 Aug 2008, 08:09
arjtryarjtry 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 used answer choices to solve
split (Married Men, Unmarried men, women-3 , 3 women )
A) 19 --> 4 4 8 3 [ 8*9/10 -- not integer ]
B) 22 --> 4.25 4.25 9.5 3
C) 23 --> 5 5 10 3 [ 5*9/10 not an integer
]
C) 43 --> 10 10 20 3 [10*9/10 Integer].
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09 Aug 2008, 05:55
suppose number of men = 2M
So the women number will be =2M+3
Total 4M+3
half married have 90% wife with them
9M/10 have to be a lowest integer
So for lowest value of M the fraction has to be an integer
So M =10
so total number of people 4M+3 (4*10+3) =43
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Re: married people   [#permalink] 09 Aug 2008, 05:55
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