Question: Find the Ratio a:b:c

Comment on Find the Ratio a:b:c

in regards to statement 1. how was '6c' concluded?
gmat-admin's picture

Once we know that the a:b:c ratio is equal to c/3 : c/2 : c, we can create an equivalent ratio that eliminates the fractions. We create that equivalent ratio by multiplying all three values by 6 (the least common multiple of 2 and 3) to get 2c : 3c : 6c

This is no different than taking the ratio 1 : 2 and multiplying both values by 5 to get the equivalent ratio 5 : 10

Does that help?

i don't understand the second one why you put a=1 in number 2) ab=c and c=6
and how can i say insufficient
gmat-admin's picture

For statement 2, we're told that c = 6 AND ab = c
In other words, ab = 6
So, when we test certain values of a, b and c, those values must meet the given conditions.

NOTE: The values I used are not the only values meet the given conditions. We COULD have used other values. Here are some examples:

a = 1, b = 6, c = 6 (a:b:c = 1:6:6)
a = 0.5, b = 12, c = 6 (a:b:c = 0.5:12:6)
a = 4, b = 1.5, c = 6 (a:b:c = 4:1.5:6)
a = 3, b = 2, c = 6 (a:b:c = 3:2:6)

Notice that the ratio a:b:c is different each time. So, using the information in statement 2, we cannot answer the target question with certainty.

Does that help?

What is the target question for #2? I understand the explanation but not the question.
gmat-admin's picture

The target question for both statements is "What is the ratio a:b:c?

Thank you gmat-admin, your explanations are clear, for statement 2 the numbers you used has yield two different relationships, therefore the statement 2 alone is not sufficient. I hope it's clear for others as well.
gmat-admin's picture

That's correct.

for statement 1, you can also get result 4:6:12, you got more than one possible answer, so I think statement 1 alone is not Sufficient. I believe this question is 1&2 combine sufficient. Each of them alone wont be sufficient.
gmat-admin's picture

The ratios 2:3:6 and 4:6:12 are equivalent. So, there is still only one answer to the target question.

For 1), How do we know c is just c.
gmat-admin's picture

For statement 1, we are trying to rewrite the variable in terms of c.

So, for example, we rewrote a as a = c/3

Likewise, we rewrote b as b = c/2

Now comes c. What do we do with that? Well, since our goal is to rewrite each variable in terms of c, we can see that c is ALREADY written in terms of c. That is, c = c.

So, we're done!

Does that help?

I can't believe I got this correct, I did a simple chart and found two overlapping answers and knew A was sufficient. Then I knew that B didn't give enough info! Thanks so much for this awesome prep material, with Veritas Prep alone I never would have even known where to begin with a question like this, but thanks to your course I not only had a chance but figured the correct answer out. :D
gmat-admin's picture

That's great to hear! Thanks for saying that.


why doesn't this method work?

c/a = 3/1 (cross multiply) to get 3a = C ie, ratio of 3;1???

gmat-admin's picture

What relationship do you feel has a ratio of 3:1?
If you feel that, since 3a = c, then the ratio a:c = 3:1, this is not correct.

We can verify this by examining some values of a and c that satisfy the equation 3a = c

One such solution is a = 1 and c = 3, in which case a : c = 1 : 3
Another such solution is a = 2 and c = 6, in which case a : c = 2 : 6 = 1 : 3

Does that help?

Hi Brent,

Is this solution for the question in the video correct, my concern is Statement1 only:
c/a = 3, --> c:a =3:1
c/b=2 --> c:b = 2:1
c is the common, so let's make it equal in both rations
multiply by 2, c:a = 6:2 and c:b = 6:3
so a : b : c = 2 : 3: : 6
Statement 1 is Suff.

Statement 2 is not Suff.

gmat-admin's picture

That's a perfect solution, Aladdin!

Is there anything wrong with my logic on statement one by doing:
C/A = 3/1 and C/B = 2/1 so you have C:A 3:1 and C:B 2:1 convert to common C and get C:A = 6:2 C:B = 6:3 so your ratio is 2:3:6.

I guess my question is, am i wrong in assuming in the original that:
C = 3 and C = 2
A = 1 and B = 1

Does that make sense?
gmat-admin's picture

That approach totally works with this question.

The only thing I'd add is that, if C/A = 3/1, then it's quite possible that C = 3 and A = 1.
So, using those values in your solution will yield the correct answer.

That said, if C/A = 3/1, then it's ALSO quite possible that C = 6 and A = 2.
So, using those values in your solution will ALSO yield the correct answer (as will C = 12 and A = 4, etc)


hi Brent,
Could you help me with the below question?

The monthly savings of a person is two fifths of his monthly salary. If his monthly salary is increased by 7/13th and his expenditure remains unchanged, then what will be ratio of new savings to old savings?
gmat-admin's picture

Let M = ORIGINAL monthly salary.
Since he saves 2/5 of his salary, the amount saved = 2/5 of M
= 2M/5

ASIDE: this also tells us that he SPENDS 3/5 of his salary (M).
So his monthly EXPENDITURES = 3M/5

If his monthly salary increased by 7/13, then the NEW salary = M + (7/13 of M)
= M + (7M/13)
= 13M/13 + 7M/13
= 20M/13

Since his expenditures remain at 3M/5, the NEW amount saved = 20M/13 - 3M/5
= 100M/65 - 39M/65
= 61M/65

Ratio of NEW savings to OLD savings = (61M/65)/(2M/5)
= (61M/65)(5/2M)
= 305M/130M
= 61/26

Answer: 61/26

hi Brent, thank you for helping me out with this question, but the answer is not among the given options.
the options i have are :

a) 26:61
b) 23:41
c) 26:41
d) 27:34
e) 61:26
gmat-admin's picture

Ahhh. I was wondering what "expenditure remains unchanged" meant.
I read it as still spending 3/5 of his salary (i.e., still saving 2/5 of his salary), whereas the answer choices tell me that he saves the same AMOUNT of money as he did previously (as opposed to the same FRACTION)

I have revised my above response accordingly.

thank you!

Here i made a slight mistake..

S-1: I have considered c=3a. and written as a:b:c = c/3:c/2:3a.. so insufficient.

S-2: I missed out 6*1=6 concept and chose B as sufficient.

Cant we consider c=3a in statement 1?
gmat-admin's picture

For statement 1, you did everything correctly to get c/3 : c/2 : 3a
From here, since we know c = 3a, we can take the last term above and replace 3a with c
When we do this we get c/3 : c/2 : c
To create an equivalent ratio, multiply all terms by 6 to get 2c : 3c : 6c
Divide all terms by c to get 2 : 3 : 6

For statement 1 is it possible to create an equivalent ratio since c is in both fractions ?
gmat-admin's picture

Partially. We also need the fact that the other two variables (a and b) also appear in both fractions.

Can I understand statement 1 as c:a = 1:3 and c:b= 1:2,
so a to c and c to b is 3:1:2
gmat-admin's picture

That's not quite right.
The necessary property here says that k = k/1.
For example 3 = 3/1.

They've statement 1 says that c/a = 3.
This is the same as saying c/a = 3/1
Similarly, c:a = 3:1 (not 1:3)

The same applies to c/b = 2.
We can rewrite this as c/b = 2:1
In other words c:b = 2:1

Does that help?

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