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Confusing Explanation

by NWSimon2 » Thu Jan 21, 2016 7:43 pm
Lake A has a duck population of 30 females and 36 males. Lake B's duck population consists of the same ratio of females to males. If 6 new female ducks are added to Lake B and no other ducks are added or removed, the new total duck population of Lake B could be which of the following?

A. 144
B. 105
C. 78
D. 51
E. 36

OA: A

Source: MGMAT

The first time I went through this I guess you could say I fell for the "trap". I understand the explanation as it says you must think of the new ratio as 5x+6:6x, so the answer would have to be a multiple of 11 and then you add the 6 in.

However, couldn't the answer technically be D because the questions says COULD BE? If you take it down to the lowest ratio and then add 6 ducks, that COULD be the answer. I was hoping someone could explain this in further detail.

Thanks.
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by GMATGuruNY » Thu Jan 21, 2016 7:55 pm
Lake A has a duck population of 30 females and 36 males. Lake B's duck population consists of the same ratio of females to males. If 6 new female ducks are added to Lake B and no other ducks are added or removed, the new total duck population of Lake B could be which of the following?

A)144

B)105

C)78

D)51

E)36
Female ducks : male ducks = 30:36 = 5:6.
Since there are 5 females ducks for every 6 male ducks, the total number of ducks must be a MULTIPLE OF 11.

We can PLUG IN THE ANSWERS, which represent the number of ducks AFTER 6 female ducks are added.
Since before the addition of 6 female ducks the total number of ducks is a multiple of 11, subtracting 6 from the correct answer choice must yield a multiple of 11.

A: 144-6 = 138.
Since 138 is not a multiple of 11, eliminate A.

B: 105-6 = 99.
Success!

The correct answer is B.
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by [email protected] » Thu Jan 21, 2016 10:30 pm
Hi NWSimon2,

It sounds like you got to the 'step' in which you determined that the ratio of Females to Males was 5:6, so the TOTAL number of ducks in Lake B could have been....

5 females + 6 males = 11 total
10 females + 12 males = 22 total
15 females + 18 males = 33 total
20 females + 24 males = 44 total
25 females + 30 males = 55 total
Etc.

Unfortunately, you CANNOT get to a total of 51 by adding 6 to any of these options, so Answer D is not a possible solution.

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by Matt@VeritasPrep » Fri Jan 22, 2016 4:34 pm
Let's think of it this way:

Lake A:
Female = 30
Male = 36

Lake B:
Female = 5x
Male = 6x

After we add the females to Lake B, we have

New Lake B:
Female = 5x + 6
Male = 6x

So the total population of Lake B now = 11x + 6. Hence the answer MUST be 6 greater than a multiple of 11. This gives me B, not A.
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