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# If 5a=9b=15c, what is the value of a+b+c? 1. 3c-a=5c-3b 2.

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If 5a=9b=15c, what is the value of a+b+c? 1. 3c-a=5c-3b 2. [#permalink]  08 Oct 2006, 07:09
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100% (01:44) correct 0% (00:00) wrong based on 3 sessions
If 5a=9b=15c, what is the value of a+b+c?

1. 3c-a=5c-3b
2. 6cb=10a
Intern
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Question gives us the following:
a=3c
3b=5c
5a=9b

Let's see what we can do with 1:

3c-a=5c-3b => 3b-a=2c , if we substitute a with 3c, we find 5c=3b, nothing new...

Now 2:

Substitute a with 3c, the equation becomes;

6cb=30c, divide each side by 6c, we find b=5

=> c=3 and a=9

Hence, a+b+c=9+5+3=17

SVP
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i agree b this is the only way to solve it.
Senior Manager
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It is B............

Look at this

Given that 5a=9b=15c
Let 5a=9b=15c= k

So a:b:c = 1/5:1/9:1/15
i.e. a:b:c = 9: 5: 3
So a=9x b=5x and c=3x

Statement 1:
if u substitute these values in statment 1 we get nothing..........., I mean the information given in 1 is obvious from the above values...........

Statement 2:

6cb=10a
ie 90x^2 = 90x
ie 90x(x-1) = 0
Clearly x cannot be zero, so x=1
ie a=9 b=5 and c=3
So 2 is sufficient

Hence B
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Current Student
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Well guys, according to the OA/OE, (B) isn't the answer. Any other guesses?
Director
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B

Statement 1: Seems to be insufficient

Statement 2:
a = 6bc/10

But, a = 9b/5

c = 3. Other values can be solved for.
Director
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cicerone wrote:
It is B............

Look at this

Given that 5a=9b=15c
Let 5a=9b=15c= k

So a:b:c = 1/5:1/9:1/15
i.e. a:b:c = 9: 5: 3
So a=9x b=5x and c=3x

Statement 1:
if u substitute these values in statment 1 we get nothing..........., I mean the information given in 1 is obvious from the above values...........

Statement 2:

6cb=10a
ie 90x^2 = 90x
ie 90x(x-1) = 0
Clearly x cannot be zero, so x=1
ie a=9 b=5 and c=3
So 2 is sufficient

Hence B

ie 90x(x-1) = 0
Clearly x cannot be zero, so x=1

Why x can not be 0? x has two values doesnt it make B Unsufficient?
Senior Manager
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GMATT73 wrote:
Well guys, according to the OA/OE, (B) isn't the answer. Any other guesses?

Was doublting B , I think its E

b can be 0 or 5
c can be 0 or 3

Example: (Taken from Hong Hu's Math principles in this forum)

x(x-2)=x
You can't cancel out the x on both side and say x=3 is the solution. You must move the x on the right side to the left side.
x(x-2)-x=0
x(x-2-1)=0
The solutions are: x=0 and x=3
The reason why you can't divided both sides by x is that when x is zero, you can't divide anything by zero.
Senior Manager
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Re: DS Ratios [#permalink]  09 Oct 2006, 08:04
1. repeats the samething i.e,a:b:c::5:9:15
2.solving we get c=3
hence a=9
b=5

hence,choice b
Senior Manager
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Re: DS Ratios [#permalink]  09 Oct 2006, 08:23
want to make ammendment

while solving for c,i got 10c^2=30c
so 10c(c-3)=0..hence there are two values of namely 0 and 3 for which the above equation holds.
hence there are two value for each of a nad b
and hence there are two values for a+b+c i.e., 17 and zero.
so choice b is not true.
hence choice e is the right answer.
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Re: DS Ratios [#permalink]  09 Oct 2006, 09:58
GMATT73 wrote:
If 5a=9b=15c, what is the value of a+b+c?

1. 3c-a=5c-3b
2. 6cb=10a

This is a very good question. Tests quite a few skills and traps.

From 1: a-3b+2c=0
You can stop here if you have a feel about the following: Since a,b,c are all related in a fix ratio, this equation tells us that they are all equal to zero.
If you can't see it, do some further analysis:
5a=9b, thus 3b=(5/3)a
5a=15c thus 2c=(2/3)a
In other words a-(5/3)a+(2/3)a=0
a=0
therefore b=0,c=0 and a+b+c=0. Sufficient.

You will waste a little time if you try to make sure the fractions are correct, which is not crucial to get the correct answer. So try to stop as soon as you get the feeling that they are all the same thing and thus are all going to be zero.

(b)6cb=10a, or 3cb=5a.
Substitute back into 5a=9b=15c
3cb=9b
3cb=15c
c=3, b=5, or c=0,b=0
Therefore we cannot uniquely determine what a+b+c is.

Looks like A to me then.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

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ivymba wrote:
GMATT73 wrote:
Well guys, according to the OA/OE, (B) isn't the answer. Any other guesses?

Was doublting B , I think its E

b can be 0 or 5
c can be 0 or 3

Example: (Taken from Hong Hu's Math principles in this forum)

x(x-2)=x
You can't cancel out the x on both side and say x=3 is the solution. You must move the x on the right side to the left side.
x(x-2)-x=0
x(x-2-1)=0
The solutions are: x=0 and x=3
The reason why you can't divided both sides by x is that when x is zero, you can't divide anything by zero.

Yeah, I think I made a mistake by dividing each side of 6cb=30c by 6c. This could have been:

6cb-30c=0 => 6c(b-5)=0 => c=0 or b=5

Senior Manager
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Re: DS Ratios [#permalink]  09 Oct 2006, 15:20
HongHu wrote:
GMATT73 wrote:
If 5a=9b=15c, what is the value of a+b+c?

1. 3c-a=5c-3b
2. 6cb=10a

This is a very good question. Tests quite a few skills and traps.

From 1: a-3b+2c=0
You can stop here if you have a feel about the following: Since a,b,c are all related in a fix ratio, this equation tells us that they are all equal to zero.
If you can't see it, do some further analysis:
5a=9b, thus 3b=(5/3)a
5a=15c thus 2c=(2/3)a
In other words a-(5/3)a+(2/3)a=0
a=0
therefore b=0,c=0 and a+b+c=0. Sufficient.

You will waste a little time if you try to make sure the fractions are correct, which is not crucial to get the correct answer. So try to stop as soon as you get the feeling that they are all the same thing and thus are all going to be zero.

(b)6cb=10a, or 3cb=5a.
Substitute back into 5a=9b=15c
3cb=9b
3cb=15c
c=3, b=5, or c=0,b=0
Therefore we cannot uniquely determine what a+b+c is.

Looks like A to me then.

HongHu excellent approach but isn't a-(5/3)a+(2/3)a=0 true for any value of a ? a doesn't necessarily have to be 0 to satisfy the equation .
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Hmmm you are very right. I should have looked at the fractions after all. One does get rusty if one doesn't practise a lot. E it is then.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Senior Manager
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Re: DS Ratios [#permalink]  09 Oct 2006, 21:13
CHOICE B SEEMED a more lucrative offer which it was not.
tx for ur tip on choice a.will keep this in mind.
Current Student
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Good work guys, OA is (E). The last few posts do a good job of proving why either statement alone or together is insuff.
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