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

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

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Updated on: 29 Oct 2012, 14:06
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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.

Originally posted by clubzzang on 09 Aug 2008, 00:09.
Last edited by Bunuel on 29 Oct 2012, 14:06, edited 1 time in total.
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Re: DS - Sight Seeing Tour  [#permalink]

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07 Sep 2010, 11:59
24
1
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aiming4mba wrote:
could someone explain this differently please

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.

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 --> $$m=22$$.

Hope it's clear.
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Re: DS - Sight Seeing Tour  [#permalink]

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09 Aug 2008, 00:31
23
14
clubzzang wrote:
Ppl, pls help me solve this q.

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
##### General Discussion
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06 Apr 2011, 10:02
2
1
W/C = 5/2

(1) M = 11C/5. this means C has to be a multiple of 5 (C = 5 M/11) insuff.

(2) W < 30 , here w/c could be 5/2, 10/4, 20/8, 25/10 insuff.

Combining both, only 25/10 works
M= 11*10/5= 22
Ans. C
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07 Apr 2011, 03:07
Yurik79 wrote:
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.
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29 May 2011, 06:42
5
1
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.
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20 Nov 2011, 22:12
Baten80 wrote:
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.

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)?

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

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15 Jan 2012, 15:24
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.
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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, 06:57
Brunel,
why can the number not of women not be 0.
25x:10x:22x
with x=0 both statements would still told true.
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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, 10:33
1
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.
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On a certain sight-seeing tour, the ratio of the number of  [#permalink]

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24 Jul 2014, 10:09
Is that correct?

from the question, we know $$W/C = 5/2$$ so $$C=2W/5$$

1) <=> $$C/M = 5/2$$ <=> $$M=11C/5$$
we plug C

$$M=22W/25$$ Insufficient

2) clearly insufficient

1+2) from 2) W must be a multiple of 25 inferior to 30. so $$W=25$$
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Re: On a certain sight-seeing tour, the ratio of the number of  [#permalink]

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24 Jul 2014, 10:16
1
oss198 wrote:
Is that correct?

from the question, we know $$W/C = 5/2$$ so $$C=2W/5$$

1) <=> $$C/M = 5/2$$ <=> $$M=11C/5$$
we plug C

$$M=22W/25$$ Insufficient

2) clearly insufficient

1+2) from 2) W must be a multiple of 25 inferior to 30. so $$W=25$$

Yes, that's correct.
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Re: On a certain sight-seeing tour, the ratio of the number of  [#permalink]

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27 Sep 2015, 19:37
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).
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Re: On a certain sight-seeing tour, the ratio of the number of  [#permalink]

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11 Oct 2016, 07:07
Given: w/c=5x/2x -> 2xw=5xc (1)

I. c/m=5y/11y -> c11y=5ym -> c=5/11m (2)

Plug (2) in (1).
Yields m=22/25w. This has multiple solution, as all 22/25w where w is a multiple of 25 apply.

II. Gives you that only one multiple of 25 (25*1) applies.

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

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11 May 2017, 04:27
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.

Solution:
Given: W/C = 5/2

Considering statement (1) alone:
C/M = 5/11
This statement does mention something about M, but just provides a ratio. A ration by itself is not sufficient to provide the actual number.
But, you can now get a relation between W and C.
(W/C) * (C/M) = (5/2)*(5/11)
=> W/M = 25/22
So, you get that M is a multiple of 22, but doesn't help to get to the real value.

Considering Statement (2) alone:
W < 30
INSUFFICIENT. Eliminate B.

Considering both the statements together:
W/M = 25/22 and W < 30

You know that W is a multiple of 25 and it has to be less than 30. The only value that satisfies the two conditions is 25.
If W = 25, then M = 22

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

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Updated on: 03 Mar 2018, 14:13
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Top Contributor
clubzzang wrote:
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.

Let W = # of women
Let M = # of men
Let C = # of children

Target question: What is the value of M?

Given: The ratio of the number of women to the number of children was 5 to 2
In other words, W : C = 5 : 2

Statement 1: On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
In other words, C : M = 5 : 11

Let's combine this ratio with the given ratio (W : C = 5 : 2)
To do so, we'll find some EQUIVALENT RATIOS such that they both share a term.

Take 5 : 2 and multiply both terms by 5 to get 25 : 10
So, W : C = 25 : 10

Now take 5 : 11 and multiply both terms by 2 to get 10 : 22
So, C : M = 10 : 22

At this point, we can combine the ratios to get W : C : M = 25 : 10 : 22
As you can see this just tells us the ratios of the variables, it does not provide enough information to find the exact value of M
Consider these three conflicting possibilities:
Case a: W : C : M = 25 : 10 : 22
Case b: W : C : M = 50 : 20 : 44
Case c: W : C : M = 75 : 30 : 66
etc.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The number of women on the sight-seeing tour was less than 30.
There's no information at all about the men so statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 essentially tells us that W : C : M = 25 : 10 : 22, so with each ratio that's equivalent to 25 : 10 : 22, we can a different value of M
So, we could have W : C : M = 25 : 10 : 22
or W : C : M = 50 : 20 : 44
or W : C : M = 75 : 30 : 66
etc.
Statement 2 reduces the possible number of women (W).
If W < 30, then there's only ONE possible ratio that works. That is W : C : M = 25 : 10 : 22
This means that there MUST be 22 men
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

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

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23 Sep 2018, 01:41
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.
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Re: On a certain sight-seeing tour, the ratio of the number of women  [#permalink]

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23 Sep 2018, 01:54
1

Solution

Given:
• On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2

To find:
• Number of men on the sight-seeing tour

Analysing Statement 1
As per the information given in statement 1, the ratio of children to men was 5:11.

We also know that the ratio of women to children was 5:2.
• Hence, combining them, we can say women: children: men = 25: 10: 22

But, we don’t know the exact number of men or children or women.

Hence, statement 1 is not sufficient.

Analysing Statement 2
As per the information given in statement 2, the number of women is less than 30.
• But we don’t have any information about the number of men.

Hence, statement 2 is not sufficient.

Combining Both Statements
We know that women: children: men = 25: 10: 22 and number of women is less than 30.
• Therefore, the only possible value of number of women = 25
• And, number of men = 22

Hence, the correct answer is option C.

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

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23 Sep 2018, 02:18
ritu1009 wrote:
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.

Merging topics. Please search before posting.
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Re: On a certain sight-seeing tour, the ratio of the number of  [#permalink]

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25 Sep 2018, 03:16
clubzzang wrote:
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.

W/C= 5/2
M=?
Statement 1: C/M=5/11
Simply a ratio. Does not tell you anything.
Insufficient.
Statement 2: W<30
It tells us that number of women can be= 10,11,20,25
And number of children can be= 4,6,8,10
Still Insufficient
Statement 1 and 2 together:
C can only be 10 as C is multiple of 5
So M=22
Sufficient
C
Re: On a certain sight-seeing tour, the ratio of the number of   [#permalink] 25 Sep 2018, 03:16

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