j_shreyans wrote: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.

Hi Guru ,

Thanks for your explanation.

One thing is that why do we take multiple of 11 , we are asked to find the total number of duck from Lake B and multiple of 11 comes from Lake A. Pls advise.

Also can we solve this question through algebra.

j_shreyans wrote:

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

Hi Guru ,

Thanks for your explanation.

One thing is that why do we take multiple of 11 , we are asked to find the total number of duck from Lake B and multiple of 11 comes from Lake A. Pls advise.

According to the prompt:
Lake B's duck population consists of the same ratio of females to males [as Lake A's population].
The words in brackets are omitted, but their presence is implied.
Thus:
(lake B's females : {lake B's males) = (lake A's females) : (lake A's males) = 30:36 = 5:6.
Implication:
In both Lake B and in Lake A, there are 5 females for every 6 males, implying that the total population IN EACH LAKE is a MULTIPLE OF 11.

Also can we solve this question through algebra.

As noted above, the total population in Lake B must be a multiple of 11.
Let the original total population = 11x, where x is an integer greater than 0.
After 6 female ducks are added, we get:
New total population = 11x + 6.
Options for the new total population:
17, 28, 39, 50, 61, 72, 83, 94, 105...

Since it's possible that the new total population = 105, the correct answer is B.

We could also do a little algebra here. We know that at Lake B the ratio of females to males is 5 : 6, which we can write as 5x : 6x. After we add 6 female ducks, our ratio is (5x + 6) : 6x. That means the total number of ducks is (5x + 6) + 6x, or 11x + 6. Any answer of this form (in which x is an integer) will work.

144 = 11x + 6 gives x as a fraction
105 = 11x + 6 gives x = 9
78 = 11x + 6 gives x as a fraction
51 = 11x + 6 gives x as a fraction
36 = 11x + 6 gives x as a fraction

So the answer must be B.

j_shreyans wrote: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

We are given that Lake A has a duck population of 30 females and 36 males. Since Lake B's duck population consists of the same ratio of females to males:

f/m = 30/36 = 5/6

Thus, we can let 5x = the number of female ducks in Lake B and 6x = the number male ducks in Lake B. Therefore, the total number of ducks is 11x. We are also given that 6 new female ducks are added to Lake B. We need to check which answer choice could be the total number of ducks after 6 new female ducks are added to Lake B. Keep in mind that x must be an integer.

A. 144

11x + 6 = 144

11x = 138

x = 138/11 = 12 6/11

Since x is not an integer, 144 can't be the total number of ducks in Lake B.

B. 105

11x + 6 = 105

11x = 99

x = 99/11 = 9

Since x is an integer, 105 could be the total number of ducks in Lake B.

Answer: B