At a given time, what was the ratio of the number of sailboats to the

hi,
you are correct prior to the coloured portion..
why are you taking ratio of s# and m#.... its not correct
what we require to do is equate both of them due to the statement
If the number of motorboats on Lake X had been 25% greater, the number of sailboats on Lake X would have been 110% of the number of motorboats on Lake X...
so here s#=m#..
or (5/4) s =(11/10) m .... get s and m on one side and you will have s/m and other side you will have the ratio

Ah! did not register the "would have been" clearly!

Thanks a lot for the clarification chetan

(1) If the number of motorboats on Lake X had been 25% greater, the number of sailboats on Lake X would have been 110% of the number of motorboats on Lake X.
S=110/110(M+M/4)
S/M=8/11 ....Suff
(2) The positive difference between the number of motorboats on Lake X and the number of sailboats on Lake X was 30.
...M-S=30 ....Insuff

Ans: A

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

At a given time, what was the ratio of the number of sailboats to the number of motorboats on Lake X?

(1) If the number of motorboats on Lake X had been 25% greater, the number of sailboats on Lake X would have been 110% of the number of motorboats on Lake X.
(2) The positive difference between the number of motorboats on Lake X and the number of sailboats on Lake X was 30.

In the original condition and the question, consider the number of sailboats as ‘s’ and the number of motorboats as ‘m’. Then, you can come up with a question ‘s:m=?.’ However, when a ratio is asked in a question, it is likely that con is the ratio, which is an answer. So, in 1) s=1.1(1.25m), since s:m is unique, it is sufficient. In 2) |s-m|=30, since s:m is not unique, it is not sufficient. Therefore, the answer is A.

we need to find s/m

St.1 increasing m 1.25 times means that s/m ratio became 1.25 times less than original. So, original ratio was 1.25*1.1=1.375. SUFF

St.2 INSUFF.

A

hi chetan2u

I don't understand your explanation.

I deduced x=1.1*1.25*y
(since it says if Y is 25%increased, X is 110% of y - Doesn't that mean 1.1*1.25*Y?)

You are correct rachitshah. As per the given verbiage of statement 1, the equation if you have to set up will be s=1.1*1.25*m and not 1.25s = 1.1 m .

But the main point to note here is that this statement is sufficient to calculate the ratio of s/m at any given time.

Hope this helps.

Can someone please give a detailed explanation to this problem. why 1.25m=1.1s?

The statement says "the number of sailboats on Lake X would have been 110% of the number of motorboats"

Doesnt it mean s=1.1m?

You are only quoting a part of the first statement and ignoring the red part above. This is where 1.25s will come from.