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On a certain sight-seeing tour, the ratio of the number of women to th
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Updated on: 18 Jul 2019, 01:47

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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 th
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07 Sep 2010, 12:59

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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: \(\frac{w}{c}=\frac{5}{2}\) --> \(w=5x\) 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 --> \(m=22\).

Re: On a certain sight-seeing tour, the ratio of the number of women to th
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09 Aug 2008, 01:31

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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

Status: No dream is too large, no dreamer is too small

Joined: 14 Jul 2010

Posts: 424

Re: On a certain sight-seeing tour, the ratio of the number of women to th
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29 May 2011, 07:42

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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.
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Re: On a certain sight-seeing tour, the ratio of the number of women to th
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11 Jul 2014, 11:33

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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
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11 May 2017, 05:27

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 Asked: M = ? Make sure to mark your AD/BCE

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. INSUFFICIENT. Eliminate AD.

Considering Statement (2) alone: W < 30 Doesn't even talk about M. 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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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

Re: On a certain sight-seeing tour, the ratio of the number of women to th
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22 Jan 2019, 19:37

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 suff

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?

Re: On a certain sight-seeing tour, the ratio of the number of women to th
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23 Jan 2019, 06:57

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 suff

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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