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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 18 Jul 2019, 00:47, edited 2 times in total.
Renamed the topic and edited the question.
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1
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?

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

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

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2
2
2
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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Re: On a certain sight-seeing tour, the ratio of the number of women to th  [#permalink]

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

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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 women to th  [#permalink]

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

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1
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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1
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

Cheers,
Brent
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If you enjoy my solutions, you'll love my GMAT prep course. Originally posted by BrentGMATPrepNow on 11 May 2017, 09:15.
Last edited by BrentGMATPrepNow on 30 Oct 2019, 15:31, edited 2 times in total.
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Re: On a certain sight-seeing tour, the ratio of the number of women to th  [#permalink]

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2

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 women to th  [#permalink]

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Question states women(W) to children(C) are in the ratio of 5:2.

Statement 1: C:M is 5:11(M is for male)

Therefore,
W:C:M
5:2
5:11 => 25:10:22
But nothing about number of men can be found. NOT SATISFIED.

Statement 2: W<30
Again nothing about number of men is given. NOT SATISFIED.

Combining both statements:
W is less than 30, so W would be 25 and M-men will be 22.

Posted from my mobile device

Originally posted by EncounterGMAT on 14 Oct 2018, 05:09.
Last edited by EncounterGMAT on 23 Jan 2019, 05:40, edited 1 time in total.
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Re: On a certain sight-seeing tour, the ratio of the number of women to th  [#permalink]

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alpha_plus_gamma wrote:
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 suf
f

can you please further explain the underlined part? I don't get why there needs to be 25 women and not 26,27,28 or 29?

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

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tsimo1000 wrote:
alpha_plus_gamma wrote:
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 suf
f

can you please further explain the underlined part? I don't get why there needs to be 25 women and not 26,27,28 or 29?

Thanks,

I'll try.
Stat 1 mentions something about M, but it just provides a ratio of W:C:M. A ratio by itself is not sufficient to provide the actual number. That is why it's not sufficient to answer the question because as per the ratio the number of men can be 22 or 44 [50:20:44] or 88[100:40:88] etc.

Statment 2 says W<30 but nothing about number of men is mentioned and from the question stem, we only know that W:C is 5:2. Not satisfied.

Combining 1 and 2, we know the ratio of W:C:M is 25:10:22. As I mentioned in statement 1, the number can be 25:10:22 or 50:20:44 or 100:40:88 etc. But wait. statement 2 says W<30. So we have to stick to 25:10:22 as we can see W is less than 30 indeed. If you double the ratio, W will increase and will not satisfy W<30. So we'll have to take 25:10:22 into consideration and conclude that number of men=22. Satisfied.
Now your question of why there needs to be 25 women and not 26,27,28 or 29? If that happens, it will hamper the ratio of 25:10:22 and that will be absolutely wrong.
Hope you got it!
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Re: On a certain sight-seeing tour, the ratio of the number of women to th  [#permalink]

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BrentGMATPrepNow wrote:
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

Cheers,
Brent

Can you please explain how did you consider the ratio 25:10:22 represents the actual number of people ?

Thanks, Sanchit
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funkyakki wrote:
Can you please explain how did you consider the ratio 25:10:22 represents the actual number of people ?
Thanks, Sanchit

Once we know that W : C : M = 25 : 10 : 22, there are infinitely many scenarios that meet this condition. For example:
- There are 25 women, 10 children, and 22 men
- There are 50 women, 20 children, and 44 men
- There are 75 women, 30 children, and 66 men
- There are 100 women, 40 children, and 88 men
etc

Does that help?
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Re: On a certain sight-seeing tour, the ratio of the number of women to th  [#permalink]

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Bunuel 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?

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.

Bunuel, please could you explain the highlighted portion - how did you derive this?
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JosephStallone wrote:
You comprehensively elaborated the scenario but i also want to know how you drive the equation

Which equation are you referring to?
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If you enjoy my solutions, you'll love my GMAT prep course.  Re: On a certain sight-seeing tour, the ratio of the number of women to th   [#permalink] 07 Jul 2020, 08:05

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