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On a certain sight-seeing tour, the ratio of the number of [#permalink]

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09 Aug 2008, 01:09

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On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?

(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11. (2) The number of women on the sight-seeing tour was less than 30.

On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?

(1) On the sight-seeing tour, the ratio of the number of chilren to the number of men was 5 to 11. (2) The number of women on the sight-seeing tour was less than 30.

Thanks!

C.

w:c = 5:2

1) c:m = 5:11

w:c:m = 25:10:22

But this does not give us exact number of men

2) this itself does not tell anything about number of men.

Toegther, since number of women is less than 30 and since the number of ppl will always be an integer and also that 25:10:22 can not be reduced further => there will be 25 women => there will be 22 men. thus suff

could someone explain this differently please _________________

But there’s something in me that just keeps going on. I think it has something to do with tomorrow, that there is always one, and that everything can change when it comes. http://aimingformba.blogspot.com

On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?

Given: \(\frac{w}{c}=\frac{5}{2}\) --> \(w=5x\) and \(c=2x\) for some integer \(x\). Q: \(m=?\)

(1) on the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11 --> \(\frac{c}{m}=\frac{5}{11}\) --> \(c=5y\) and \(m=11y\), for some integer \(y\). Not sufficient to calculate \(m\).

(2) the number of women on the sight-seeing tour was less than 30 --> \(w<30\). Not sufficient to calculate \(m\).

(1)+(2) \(w=5x<30\) --> \(x<6\). \(c=2x\) and as \(c=5y\), \(c\) is a multiple of 5 --> \(x=5\) --> \(c=10=5y\) --> \(y=2\) --> \(m=11y=22\). Sufficient.

Answer: C.

OR: \(\frac{\frac{w}{c}}{m}=\frac{\frac{25}{10}}{22}\) --> \(\frac{w}{m}=\frac{25}{22}\) and as \(w<30\), then \(w=25\) because for other values of \(w<30\), \(m\) (and \(c\)) are not integers --> \(m=22\).

My answer is C from 1 statement we can find out the whole ratio W to Child and Men alone insuf because we need not ratio but number from statement 2 alone we dn't get anything

1 and 2 together do the job!My approuch to DS may be wrong but why to solve further if you already know that from 1 and 2 we can figure out the answer!IMHO

Further calculations may be needed because the lowest number of women needed to satisfy the ratio may be > 30, in which case the answer would've been E. So just changing the ratios a bit can change the answer.

Another specific way of answering: Given w/c= 5/2, c = 2/5(w) (1) c/m = 5/11, m = 11/5(c) insufficient (2) w < 30, no information about men, insufficient.

Considering C: m = 11/5c = 11/5 * 2/5(w) = 22/25(w) and w < 30 here only 25 is a multiple of 25. so w = 5 = 22 Ans. C. _________________

Another specific way of answering: Given w/c= 5/2, c = 2/5(w) (1) c/m = 5/11, m = 11/5(c) insufficient (2) w < 30, no information about men, insufficient.

Considering C: m = 11/5c = 11/5 * 2/5(w) = 22/25(w) and w < 30 here only 25 is a multiple of 25. so w = 5 = 22 Ans. C.

Hi

Sorry I got a bit lost in the logic. Also, i completely do understand the significance of the sentence below in this Q

2. The number of women on the sightseeing tour was less than 30.

Would appreciate your help.

I get how m = 22/25(w)

but then you have mentioned only 25 is a multiple of 25. so w = 5. If we replace 5 with w in this eq -> m = 22/25(w) then m would be 22/5 and not 22? Did you mean to say w = 25 (and mistyped 5)?

Re: On a certain sightseeing tour, the ratio of the number of [#permalink]

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15 Jan 2012, 16:24

This is how I solved it :

Given - W/C = 5/2

From statement 1 we get C/M = 5/11

with this we can get W/M = 25/22

Since we dont the number it wont help so insiffucient.

Statement 2 - we get Women less than 30. wont help So insufficnet.

Combining.

We know that W/M = 25/22 and women # is less that 30 it will be possible only if men are 22 in number based on the ratio we derived from statement 1. so answer C

Re: On a certain sight-seeing tour, the ratio of the number of [#permalink]

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20 Jun 2014, 18:16

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Re: On a certain sight-seeing tour, the ratio of the number of [#permalink]

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11 Jul 2014, 11:33

Expert's post

LTN99 wrote:

Brunel, why can the number not of women not be 0. 25x:10x:22x with x=0 both statements would still told true.

That's not true. If x=0, then w = m = c = 0. But in this case none of the ratios given is true because 0/0 is undefined and not 5:2 or 5:11. _________________

Re: On a certain sight-seeing tour, the ratio of the number of [#permalink]

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19 Oct 2014, 03:29

One small doubt regarding this. When it says that the number of women is less than 30, wouldn't 0 be a valid scenario? In that case number of men would be 0 too .. so it could either be 22 men or 0 men.

Hence option E.

I know 0 sounds a bit illogical but in mathematical terms, it is possible I guess. Please advise.

Re: On a certain sight-seeing tour, the ratio of the number of [#permalink]

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19 Oct 2014, 04:10

Expert's post

rakhauri wrote:

One small doubt regarding this. When it says that the number of women is less than 30, wouldn't 0 be a valid scenario? In that case number of men would be 0 too .. so it could either be 22 men or 0 men.

Hence option E.

I know 0 sounds a bit illogical but in mathematical terms, it is possible I guess. Please advise.

Re: On a certain sight-seeing tour, the ratio of the number of [#permalink]

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27 Sep 2015, 20:37

I got this question wrong because based on the givens, the number of women could have been 5, 10, 15 or any number under 30, which would leave to an indeterminate amount of children and further an indeterminate amount of men.

An answer choice of C is based on an assumption that was not specified in the question. Must we always make assumptions like this? This is frustrating. Sometimes I think the language on some of these questions is a little too vague (not necessarily saying that is true of this one).

gmatclubot

Re: On a certain sight-seeing tour, the ratio of the number of
[#permalink]
27 Sep 2015, 20:37

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