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Tricky wording..........Ratio problem

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by Mo2men » Sun Aug 13, 2017 4:50 am
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.

OA: A
Source: Kaplan

How can Statement 1 be interpreted??? The question stem is about ratio of sailboats (S)/motorboats(M). In statement 1, there is hypothetical situation that create let's say
S1 = 1.25 S
M1 = 1.1 S1 = (1.1) (1.25) S
How can I reach OA? I feel missing something.
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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Aug 13, 2017 6:46 am
If x is equal to 110% = 11/10 of y, then y is equal to 10/11 of x.
Mo2men wrote: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.
Statement 1:
If the number of motorboats on Lake X had been 25% greater.
125% of M = (5/4)M.
Then the number of sailboats on Lake X would have been 110% of the number of motorboats on Lake X.
Put another way:
Then the number of motorboats on Lake X would have been 10/11 of the number of sailboats on Lake X.
Thus, the value in red would have been equal to 10/11 of S:
(5/4)M = (10/11)S.
S/M = (11/10)(5/4) = 11/8.
SUFFICIENT.

Statement 2:
Case 1: S=10 and M=40, with the result that S/M = 10/40 = 1/4.
Case 2: S=40 and M=10, with the result that S/M = 40/10 = 4/1.
Since S/M can be different values, INSUFFICIENT.

The correct answer is A.
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by Mo2men » Sun Aug 13, 2017 7:00 am
GMATGuruNY wrote:If x is equal to 110% = 11/10 of y, then y is equal to 10/11 of x.
Mo2men wrote: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.
Statement 1:
If the number of motorboats on Lake X had been 25% greater.
125% of M = (5/4)M.
Then the number of sailboats on Lake X would have been 110% of the number of motorboats on Lake X.
Put another way:
Then the number of motorboats on Lake X would have been 10/11 of the number of sailboats on Lake X.
Thus, the value in red would have been equal to 10/11 of S:
(5/4)M = (10/11)S.
S/M = (11/10)(5/4) = 11/8.
SUFFICIENT.
I have one question.

does the part in Red above represent number of motorboats after the being greater by 25% or number of motorboats in original condition?

Thanks
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by GMATGuruNY » Sun Aug 13, 2017 7:30 am
Mo2men wrote:I have one question.

does the part in Red above represent number of motorboats after the being greater by 25% or number of motorboats in original condition?

Thanks
The value in red represents the number of motorboats increased by 25%.
According to Statement 1, the actual number of sailboats would have been 110% of the hypothetically increased number of motorboats (the value in red):
S = (11/10)(5/4)M
S/M = (11/10)(5/4) = 11/8.
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by Mo2men » Sun Aug 13, 2017 11:56 am
GMATGuruNY wrote:
Mo2men wrote:I have one question.

does the part in Red above represent number of motorboats after the being greater by 25% or number of motorboats in original condition?

Thanks
The value in red represents the number of motorboats increased by 25%.
According to Statement 1, the actual number of sailboats would have been 110% of the hypothetically increased number of motorboats (the value in red):
S = (11/10)(5/4)M
S/M = (11/10)(5/4) = 11/8.
Thanks a lot of for clear explanation.

What is you take away in DS question with statements that present hypothetical situation especially in DS questions of Speed problems.
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