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On a certain sightseeing tour, the ratio of the number of women to th
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On a certain sightseeing 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 sightseeing tour? (1) On the sightseeing tour, the ratio of the number of children to the number of men was 5 to 11. (2) The number of women on the sightseeing tour was less than 30.
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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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On a certain sightseeing tour, the ratio of the number of women to th
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07 Sep 2010, 11:59
On a certain sightseeing 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 sightseeing tour?Given: \(\frac{w}{c}=\frac{5}{2}\) > \(w=5x\) and \(c=2x\) for some integer \(x\). Q: \(m=?\) (1) on the sightseeing 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 sightseeing 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 > \(m=22\). Hope it's clear.
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Re: On a certain sightseeing tour, the ratio of the number of women to th
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09 Aug 2008, 00:31
clubzzang wrote: Ppl, pls help me solve this q.
On a certain sightseeing 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 sightseeing tour?
(1) On the sightseeing tour, the ratio of the number of chilren to the number of men was 5 to 11. (2) The number of women on the sightseeing 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




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Re: On a certain sightseeing tour, the ratio of the number of women to th
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06 Apr 2011, 10:02
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 sightseeing tour, the ratio of the number of women to th
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29 May 2011, 06:42
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 sightseeing tour, the ratio of the number of women to th
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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 sightseeing tour, the ratio of the number of women to th
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11 Jul 2014, 10:33
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 sightseeing tour, the ratio of the number of women to th
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11 May 2017, 04:27
On a certain sightseeing 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 sightseeing tour? (1) On the sightseeing tour, the ratio of the number of children to the number of men was 5 to 11. (2) The number of women on the sightseeing 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
The answer is (C).
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On a certain sightseeing tour, the ratio of the number of women to th
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Updated on: 30 Oct 2019, 15:31
clubzzang wrote: On a certain sightseeing 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 sightseeing tour?
(1) On the sightseeing tour, the ratio of the number of children to the number of men was 5 to 11. (2) The number of women on the sightseeing 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 sightseeing tour, the ratio of the number of children to the number of men was 5 to 11. In other words, C : M = 5 : 11Let'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 : 22As you can see this just tells us the ratios of the variables, it does not provide enough information to find the exact value of MConsider these three conflicting possibilities: Case a: W : C : M = 25 : 10 : 22Case b: W : C : M = 50 : 20 : 44Case c: W : C : M = 75 : 30 : 66etc. Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: The number of women on the sightseeing 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 : 22or W : C : M = 50 : 20 : 44or W : C : M = 75 : 30 : 66etc. 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 : 22This means that there MUST be 22 menSince we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C Cheers, Brent
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Re: On a certain sightseeing tour, the ratio of the number of women to th
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23 Sep 2018, 01:54
Solution Given:• On a certain sightseeing tour, the ratio of the number of women to the number of children was 5 to 2 To find:• Number of men on the sightseeing tour Analysing Statement 1As 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 2As 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 StatementsWe 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. Answer: C
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Re: On a certain sightseeing tour, the ratio of the number of women to th
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Updated on: 23 Jan 2019, 05:40
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 Mmen will be 22.
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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 sightseeing tour, the ratio of the number of women to th
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22 Jan 2019, 18:37
alpha_plus_gamma wrote: clubzzang wrote: Ppl, pls help me solve this q.
On a certain sightseeing 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 sightseeing tour?
(1) On the sightseeing tour, the ratio of the number of chilren to the number of men was 5 to 11. (2) The number of women on the sightseeing 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,



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Re: On a certain sightseeing tour, the ratio of the number of women to th
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23 Jan 2019, 05:57
tsimo1000 wrote: alpha_plus_gamma wrote: clubzzang wrote: Ppl, pls help me solve this q.
On a certain sightseeing 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 sightseeing tour?
(1) On the sightseeing tour, the ratio of the number of chilren to the number of men was 5 to 11. (2) The number of women on the sightseeing 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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Re: On a certain sightseeing tour, the ratio of the number of women to th
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16 Jun 2020, 05:36
BrentGMATPrepNow wrote: clubzzang wrote: On a certain sightseeing 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 sightseeing tour?
(1) On the sightseeing tour, the ratio of the number of children to the number of men was 5 to 11. (2) The number of women on the sightseeing 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 sightseeing tour, the ratio of the number of children to the number of men was 5 to 11. In other words, C : M = 5 : 11Let'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 : 22As you can see this just tells us the ratios of the variables, it does not provide enough information to find the exact value of MConsider these three conflicting possibilities: Case a: W : C : M = 25 : 10 : 22Case b: W : C : M = 50 : 20 : 44Case c: W : C : M = 75 : 30 : 66etc. Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: The number of women on the sightseeing 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 : 22or W : C : M = 50 : 20 : 44or W : C : M = 75 : 30 : 66etc. 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 : 22This means that there MUST be 22 menSince we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C 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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Re: On a certain sightseeing tour, the ratio of the number of women to th
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16 Jun 2020, 05:44
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 sightseeing tour, the ratio of the number of women to th
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07 Jul 2020, 06:40
Bunuel wrote: On a certain sightseeing 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 sightseeing tour?
Given: \(\frac{w}{c}=\frac{5}{2}\) > \(w=5x\) and \(c=2x\) for some integer \(x\). Q: \(m=?\)
(1) on the sightseeing 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 sightseeing 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 > \(m=22\).
Hope it's clear. Bunuel, please could you explain the highlighted portion  how did you derive this?



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Re: On a certain sightseeing tour, the ratio of the number of women to th
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07 Jul 2020, 08:05
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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