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On a certain sight seeing tour, the ration of the number of

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Joined: 08 Feb 2008
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On a certain sight seeing tour, the ration of the number of [#permalink]

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05 Jun 2010, 11:51
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On a certain sight seeing tour, the ration of the number of women to number of children was 5 to 2, What was the number of men on the sigh seeing tour

(1) On the sight seeing tour, the ratio of 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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05 Jun 2010, 12:12
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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?

Given: $$\frac{w}{c}=\frac{5}{2}$$. Q: $$m=?$$

(1) on the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11 --> $$\frac{c}{m}=\frac{5}{11}=\frac{10}{22}$$ and $$\frac{w}{c}=\frac{5}{2}=\frac{25}{10}$$ --> $$\frac{\frac{w}{c}}{m}=\frac{\frac{25}{10}}{22}$$ --> # of men is multiple of 22: 22, 44, 66, ... --> multiple values are possible for # of men. Not sufficient.

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

(1)+(2) $$\frac{\frac{w}{c}}{m}=\frac{\frac{25}{10}}{22}$$ and as $$w<30$$, then $$w=25$$ (for other values of $$w<30$$, $$m$$ is not an integer) --> $$m=22$$. Sufficient.

Hope it helps.
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08 Jun 2010, 13:27
Good explaination Bunuel.

Divanshuj, another approach to the problem, that is problably quicker, would be to think logically about the information presented and not worry about the math.

The problem gives you the ratio of women to children and asks you how many men there are.

To figure out the number of men you would have to relate the women-children ratio to men and then determine the number of women or children.

(1) Gives you the ratio were looking for, but not a number. Not sufficient.
(2) Gives you one of the numbers we're looking for, but not a ratio that relates men to women or children. Not sufficient.

Put them together and you have the information you need to figure out how many men there are. Thus, C, both together tell us how many men there are.

Hope this helps.

Thanks,

Jared
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08 Jun 2010, 21:04
sk818020, I think this one is a little dangerous to simply use logic. Many people will pick E if they do that, because it seems like there are multiple possible values for w, c, and m. It takes a bit of scratch work to see that, because they must all be integer values, the only possible of m is 22.
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08 Jun 2010, 21:10
TheGmatTutor wrote:
sk818020, I think this one is a little dangerous to simply use logic. Many people will pick E if they do that, because it seems like there are multiple possible values for w, c, and m. It takes a bit of scratch work to see that, because they must all be integer values, the only possible of m is 22.

I'll grant your point, but using the statements I posted above how would my reasoning point you down the wrong path? I appreciate your point, but I'd like to know how I could go wrong with the simple reasoning I used.

Based on my reasoning, I wouldn't have chosen E. Why based on my points above would you chose E? I guess I'm asking you to use my logic above to prove there are multiple solutions to the problem.

Hopefully we can all learn from it, including me .

Jared
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08 Jun 2010, 21:42
I've seen people pick E on this one because they figure that they can't find an exact value of w. Although they know w<30, it requires a little extra work to see that w can only be 25.

I think it's a case of overusing the "Don't solve the problem!" advice that many test prep companies give.
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13 Jun 2010, 05:07
sk818020,
Your approach is correct no doubt but how will you ensure that there are not more than one solution for number of men??
Bunuel,
Can you please explain if there is any short method available to ensure that there is only one solution and all other number of women will not give integer? Because on test we will not have enough time to check all these things... correct? Please explain if you are aware of something like that.
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13 Jun 2010, 05:19
amitjash wrote:
sk818020,
Your approach is correct no doubt but how will you ensure that there are not more than one solution for number of men??
Bunuel,
Can you please explain if there is any short method available to ensure that there is only one solution and all other number of women will not give integer? Because on test we will not have enough time to check all these things... correct? Please explain if you are aware of something like that.

We have that $$\frac{w}{m}=\frac{25}{22}$$ (note that 25/22 is a reduced fraction, we can not reduce it anymore), which means that $$w=25x$$ and $$m=22x$$ for some integer $$x\geq{1}$$. So the possible values of $$w$$ are 25, 50, 75, ... and corresponding possible values of $$m$$ are 22, 44, 66, ... So if $$w<30$$, then $$w=25$$ and $$m=22$$.

Hope it's clear.
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10 Jul 2010, 00:57
On a certain sight seeing tour, the ratio of the number of women to the number of children was 5 is to 2. What was the number of men on the sight seeing tour?

(1) On the sight seeing tour, 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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10 Jul 2010, 02:09
W:C = 5:2 ; M = ?

1. C:M = 5:11

We are still working with ratios so we cannot evaluate the absolute value of M

INSUFFICIENT

2. W < 30

INSUFFICIENT

Both 1 and 2

Let's combine the ratios by making the value of C in both equal

W:C = 5:2 = 25:10
C:M = 5:11 = 10:22

W:C:M = 25 : 10 : 22

Now, all these values must be integers because they represent people. Thus the only possible values would be multiples of the above ratio. i.e. The next highest set would be:

W:C:M = 50:20:44

But here W > 30. Thus the only possible value is for W = 25, C = 10 and M = 22

SUFFICIENT

Pick C.

Can you please confirm OA? I'm pretty sure A cannot be sufficient.
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19 Mar 2011, 09:38
C it is, always be careful with ds especially those who got +40. Questions are sometimes not like it appears
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20 Mar 2011, 02:15
W/C = 5/2

From (1) C/M = 5/11

=> W:M = 5/2 * 5/11 = 25/22

But this is not sufficient to give the exact number of men

From(2) W < 30, but this does not give anything about the number of men, so not sufficient.

Also, W/C = 5/2 can mean w = 5, C = 2 or W = 10, C = 4, hence the number of men is not a definitive from this.

From(1) and (2), W:M:C = 25:22:10

which satisifes all the ratios and also, this is a reduced ratio in the sense that if we reduce the number of women < 25, the ratio 25:22 will not hold good, so the answer is (C).
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30 Apr 2011, 09:46
1. insuff
2. insuff

combined ratio becomes 25:10:55
hence women < 30 can be only 25
then sufficient C
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Re: On a certain sight seeing tour, the ration of the number of [#permalink]

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29 Apr 2017, 07:10
Top Contributor
divanshuj wrote:
On a certain sight seeing tour, the ration of the number of women to number of children was 5 to 2, What was the number of men on the sigh seeing tour

(1) On the sight seeing tour, the ratio of 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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Re: On a certain sight seeing tour, the ration of the number of   [#permalink] 29 Apr 2017, 07:10
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