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What is the ratio of a to b to c ? [#permalink]
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28 Apr 2013, 12:05
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What is the ratio of a to b to c ? (1) \(\frac{c}{a} =\frac{5}{2}\) and \(b=4a\) (2) \(ac = 40\) and \(b=16\)
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Re: What is the ratio of a to b to c ? [#permalink]
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28 Apr 2013, 12:25
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(1) Sufficient. we know that \(c=5x\) and \(a=2x\) for some number \(x\). Therefore \(b=8x\) and the ratio \(a:b:c=2x:8x:5x=2:8:5\). (2) Insufficient. We don't know the ratio \(a:c\). For example \(a=4\), \(c=10\) or it could be in reverse order \(a=10\), \(c=4\). The answer is A.
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Re: What is the ratio of a to b to c ? [#permalink]
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28 Apr 2013, 12:32
What is the ratio of a to b to c ?\(a/b/c=\frac{a}{bc}\) (1) \(\frac{c}{a} =\frac{5}{2}\) and \(b=4a\)\(c=5/2a\), \(b=4a\) Substitute \(\frac{a}{4a*2.5a}=\frac{1}{10a}\). It depends on a. Not sufficient (2) \(ac = 40\) and \(b=16\)a and c can have many values (2,20 or 4,10) so the ratio in not determined. Not sufficient 1+2)b=16 a=4 c=10. We know all the numbers, we know also a/b/c Sufficient A is not the answer take c=50 a=20 and b= 80 ratio 1/200 take a=8 c=20 b=32 ratio 1/80. I disagree with the OA...
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Re: What is the ratio of a to b to c ? [#permalink]
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28 Apr 2013, 12:37
Zarrolou wrote: What is the ratio of a to b to c ?
\(a/b/c=\frac{a}{bc}\)
I don't think that this is correct ?! all we know is the ratio of a to b is a/b .. that's why you must assign a new variable x and refer to it as smyarga did It is the correct way to do this
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Re: What is the ratio of a to b to c ? [#permalink]
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28 Apr 2013, 12:48
Rock750 wrote: I don't think that this is correct ?! all we know is the ratio of a to b is a/b .. that's why you must assign a new variable x and refer to it as smyarga did
It is the correct way to do this My point is : the ratio a to b is a division a/b The ration a to b is 2 means a/b=2 the ration (a to b) to c is also a division (I don't see why it sould not be). That's why I do not agree, maybe I have to review ratios Look at the real numbers , all respect A. a=20 , b= 80 c=50 a:b:c=1/200 a=8 , b=32 c=20 a:b:c=1/80
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Re: What is the ratio of a to b to c ? [#permalink]
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28 Apr 2013, 12:54
Zarrolou wrote: Rock750 wrote: I don't think that this is correct ?! all we know is the ratio of a to b is a/b .. that's why you must assign a new variable x and refer to it as smyarga did
It is the correct way to do this My point is : the ratio a to b is a division a/b The ration a to b is 2 means a/b=2 the ration (a to b) to c is also a division (I don't see why it sould not be). That's why I do not agree, maybe I have to review ratios Look at the real numbers , all respect A. a=20 , b= 80 c=50 a:b:c=1/200 a=8 , b=32 c=20 a:b:c=1/80 in your opinion, why should ratio of a to b to c equal to (a to b) to c and not equal to a to (b to c) ? we don't know if the operation "to" is transitive ..
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Re: What is the ratio of a to b to c ? [#permalink]
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28 Apr 2013, 12:59
Rock750 wrote: in your opinion, why should ratio of a to b to c equal to (a to b) to c and not equal to a to (b to c) ? we don't know if the operation "to" is commutative .. I think we are going nowhere here but in my opinion we should not forget the meaning of ratio: it's a division 5:5:5=0.2 is equal to (5:5):5=0,2 and not to 5:(5:5)=5
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Re: What is the ratio of a to b to c ? [#permalink]
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28 Apr 2013, 13:00
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Zarrolou, in your examples the ratio is the same. a=20 , b= 80 c=50 a:b:c=20:80:50=2:8:5 a=8 , b=32 c=20 a:b:c=8:32:20=2:8:5 You shouldn't mix them. Here is relative ratio of three numbers together. The ratio of three numbers a:b:c=n:m:k just means that there some integer x such that a=nx, b=mx, c=kx.
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Re: What is the ratio of a to b to c ? [#permalink]
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28 Apr 2013, 13:02
Zarrolou wrote: Rock750 wrote: in your opinion, why should ratio of a to b to c equal to (a to b) to c and not equal to a to (b to c) ? we don't know if the operation "to" is commutative .. I think we are going nowhere here but in my opinion we should not forget the meaning of ratio: it's a division 5:5:5=0.2 is equal to (5:5):5=0,2 and not to 5:(5:5)=5 the ratio of 5:5:5 is equal to 1:1:1
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Re: What is the ratio of a to b to c ? [#permalink]
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28 Apr 2013, 13:03
Oh yeah guys I see your point Program of my day tomorrow: REVIEW RATIOS!
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Re: What is the ratio of a to b to c ? [#permalink]
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28 Apr 2013, 13:04
For example, the ratio of the number of women to the number of men to the number of children is 1 to 2 to 3. Your ratio as 1 to 80 is meaningless, because you compare 3 objects and as result have comparison of two objects.
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Re: What is the ratio of a to b to c ? [#permalink]
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27 Jun 2013, 06:03
Hi I am also having difficulty understanding this one, expressing all in terms of a we get b=4a \(c=\frac{5}{2} a\) then a:b:c \(\frac{\frac {a}{4a}}{\frac{5a}{2}}\) \(so if a =1 \to a:b:c = \frac{\frac {1}{4}}{\frac{5}{2}}\) \(if a = 2 \to a:b:c = \frac{\frac {2}{8}}{5}\) \(if a=3 \to a:b:c = \frac{\frac {3}{12}}{\frac{15}{2}\) \(if a=4 \to a:b:c = \frac{\frac {4}{16}}{{10}}\) so a:b:c differs each time, does it not? B alone is also insuff. 1+2 a:b:c 4:16:10 similar sum whatistheratioofxyz56282.html#p400899Can anybody clear this confusion? Thanks.
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Re: What is the ratio of a to b to c ? [#permalink]
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27 Jun 2013, 06:49
Rock750 wrote: What is the ratio of a to b to c ?
(1) \(\frac{c}{a} =\frac{5}{2}\) and \(b=4a\)
(2) \(ac = 40\) and \(b=16\) st.1 a/c = 2/5, a/b = 1/4. to put these 3 in ratio we've to equate the common thing i.e. a. it'll become a/c=2/5 and a/b=2/8. << I equated a in both the expression by multiplying and dividing 2 a:b:c=2:8:5. simple. st.2 It will clearly wont give the desired rsult.
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Re: What is the ratio of a to b to c ? [#permalink]
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27 Jun 2013, 07:39
stne wrote: Hi I am also having difficulty understanding this one, expressing all in terms of a we get b=4a \(c=\frac{5}{2} a\) then a:b:c \(\frac{\frac {a}{4a}}{\frac{5a}{2}}\) \(so if a =1 \to a:b:c = \frac{\frac {1}{4}}{\frac{5}{2}}\) \(if a = 2 \to a:b:c = \frac{\frac {2}{8}}{5}\) \(if a=3 \to a:b:c = \frac{\frac {3}{12}}{\frac{15}{2}\) \(if a=4 \to a:b:c = \frac{\frac {4}{16}}{{10}}\) so a:b:c differs each time, does it not?B alone is also insuff. 1+2 a:b:c 4:16:10 similar sum whatistheratioofxyz56282.html#p400899Can anybody clear this confusion? Thanks. What is the ratio of a to b to c ?(1) \(\frac{c}{a} =\frac{5}{2}\) and \(b=4a\). From \(b=4a\), we have the \(\frac{a}{b}=\frac{1}{4}=\frac{2}{8}\). So, we have that a:c=2:5 and a:b=2:8 > a:b:c=2:8:5. Sufficient. (2) \(ac = 40\) and \(b=16\). Not sufficient. Answer: A. As for your solution: the ratio is the same! You have a:b:c = a:4a:(2.5a) > a reduces: a:b:c = 1:4:(2.5), which is the same ratio as a:b:c = 2:8:5 = 4:16:10 = 8:32:20 ... Hope it's clear.
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Re: What is the ratio of a to b to c ? [#permalink]
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27 Jun 2013, 09:19
First of all thank you members, But little confusion still remains, as long as I see this sum in isolation everything is clear but when I try and relate this sum to this sum given below I get a bit confused. What is the ratio of x:y:z? ( whatistheratioofxyz56282.html#p400899 ) (1) xy = 14 (2) yz = 21 now in this sum individually obviously both are insufficient but when we take them together, expressing everything in terms of y \(x = \frac {14}{y}\) \(z =\frac {21}{y}\) \(so \,x:y:z = \frac {\frac{\frac{14}{y}}{y}}{\frac{21}{y}}\) \(so \, for \, Y=1 \to x:y:z =\frac {\frac{14}{1}}{21}\) and \(for \, Y=7 \to x:y:z =\frac {\frac{2}{7}}{3}\) now using the same logic as above where we said "a reduces" and said that the ratio remains the same, can't we say in this sum too that ( x:y:z ) "Y reduces" hence 1+2 is sufficient to answer the ratio of x:y:z ? if in a:b:c sum we say " as a:b:c = 2:8:5 = 4:16:10 = 8:32:20 ... " meaning in all the cases ratio is same why in x:y:z = 14:1:21 and x:y:z = 2:7:3 , we are taking ratio to be different? shouldn't the ratio be same whether x:y:z= 14:1:21 or x:y:z = 2:7:3 we can say Y can be reduced and that 14:1:21 is the same as 2:7:3 answer should be C in this x:y:z sum, still here the answer is E. ?? Am I messing up something? Thanks. Edit: my bad didn't see that 14:1:21 cannot be reduced to 2:7:3 so of course the answer is E
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Re: What is the ratio of a to b to c ? [#permalink]
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27 Jun 2013, 09:29
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stne wrote: First of all thank you members, But little confusion still remains, as long as I see this sum in isolation everything is clear but when I try and relate this sum to this sum given below I get a bit confused. What is the ratio of x:y:z? ( whatistheratioofxyz56282.html#p400899 ) (1) xy = 14 (2) yz = 21 now in this sum individually obviously both are insufficient but when we take them together, expressing everything in terms of y \(x = \frac {14}{y}\) \(z =\frac {21}{y}\) \(so \,x:y:z = \frac {\frac{\frac{14}{y}}{y}}{\frac{21}{y}}\) \(so \, for \, Y=1 \to x:y:z =\frac {\frac{14}{1}}{21}\) and \(for \, Y=7 \to x:y:z =\frac {\frac{2}{7}}{3}\) now using the same logic as above where we said "a reduces" and said that the ratio remains the same, can't we say in this sum too that ( x:y:z ) "Y reduces" hence 1+2 is sufficient to answer the ratio of x:y:z ? if in a:b:c sum we say " as a:b:c = 2:8:5 = 4:16:10 = 8:32:20 ... " meaning in all the cases ratio is same why in x:y:z = 14:1:21 and x:y:z = 2:7:3 , we are taking ratio to be different? shouldn't the ratio be same whether x:y:z= 14:1:21 or x:y:z = 2:7:3 we say say Y can be reduced and that 14:1:21 is the same as 2:7:3 answer should be C in this x:y:z sum, still here the answer is E. ?? Am I messing up something? Thanks. Hey, if you havent checked my post .. check it .. just above bunuel's post >> whatistheratioofatobtoc151800.html#p1240411we have to equate the common term in two ratios to get a three no. ratio ... like a/b=1/2 and a/c=3/2 . here common term is a. After equating a .. the expressions will be a/b=3/6 and a/c=3/2 .. here I made a equal in both the expressions. hence a:b:c=3:6:2. In the question you posted there is no way you can do this. Hence answer is E. got it ?
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Re: What is the ratio of a to b to c ? [#permalink]
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27 Jun 2013, 09:51
@stunn3r Thank you, equating the common variable seems to make sense , doing it my way where I was expressing everything in terms of a single variable , does not seem to work here. Thank you
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