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# Lake A has a duck population of 30 females and 36 males.

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Lake A has a duck population of 30 females and 36 males.  [#permalink]

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25 May 2013, 14:27
3
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45% (medium)

Question Stats:

67% (02:12) correct 33% (02:16) wrong based on 371 sessions

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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
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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25 May 2013, 14:34
11
2
yogirb8801 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

The ratio of females to males in Lake B is 30:36 = 5:6 --> the total number of ducks in Lake B must be a multiple of (5+6)=11.

When 6 new female ducks are added to Lake B, the total number of ducks in Lake B becomes a multiple of 11 plus 6.

Only 105 is a multiple of 11 plus 6: 9*11+6=105.

Hope it's clear.
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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29 May 2013, 08:32
4
1
the ratio is 5:6
So let the female ducks be 5x and male be 6x.
Total duck=11x
Now 11x+6 should divide one of the options.
105-6=99
Therefore ans is B
##### General Discussion
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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25 May 2013, 14:46
2
3
yogirb8801 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

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Hope it helps.
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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27 May 2013, 03:18
Thanks Bunuel for explanation. very helpful.
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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31 May 2013, 12:40
I wrote a table down as following and checked which values could be plugged in

F. M. F+m+6
15 18 38
30 36 71
45 54 105 <--- stopped here
60 72
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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17 Aug 2013, 18:52
Why not a multiple of 17?
5 F to 6 M. If you add 6 F then 11 F to 6 M for a total of 17 ducks. So Lake B must have a multiple of 17 ducks?

How can it be a multiple of 11 if you add only female ducks? Once you add 6 female ducks, the ratio of F and M ducks changes!
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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17 Aug 2013, 19:20
manavkhurana wrote:
Why not a multiple of 17?
5 F to 6 M. If you add 6 F then 11 F to 6 M for a total of 17 ducks. So Lake B must have a multiple of 17 ducks?

How can it be a multiple of 11 if you add only female ducks? Once you add 6 female ducks, the ratio of F and M ducks changes!

Hi,

The female to male population is in the ratio 5:6. So the total duck population is 11x . It could be 11, 22 ,33 and so on. Now 6 female ducks are added to this population . In other words you are adding 6 to a multiple of 11. So the new duck population should be multiple of 11 + 6.

So the only choice that satisfies this requirement is 105 which is 99+6.

It is not a multiple of 17 because we do not have 11 female ducks for every 6 male ducks.
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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17 Aug 2013, 19:37
Got it, thanks a lot!

Basically, as you stated, we are just adding 6 ducks to the original amount of ducks in lake B. If it was a multiple of 17, there would be a lot more than 6 ducks added. We do not have 11 F per 5 M, we just have 6 more ducks overall.

Thanks again.
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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18 Aug 2013, 18:36
Bunuel wrote:
yogirb8801 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

The ratio of females to males in Lake B is 30:36 = 5:6 --> the total number of ducks in Lake B must be a multiple of (5+6)=11.

When 6 new female ducks are added to Lake B, the total number of ducks in Lake B becomes a multiple of 11 plus 6.

Only 105 is a multiple of 11 plus 6: 9*11+6=105.

Hope it's clear.

Hi,

I am not able to understand the question properly.

Q says the Lake population is 30 females and 36 males. and for Lake B population the Ratio of male to female is is same. i.e. 3:3.

its nowhere mentioned as Lake B population is of same ratio as Lake A.

Regards,
Rrsnathan.
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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19 Aug 2013, 00:46
rrsnathan wrote:
Bunuel wrote:
yogirb8801 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

The ratio of females to males in Lake B is 30:36 = 5:6 --> the total number of ducks in Lake B must be a multiple of (5+6)=11.

When 6 new female ducks are added to Lake B, the total number of ducks in Lake B becomes a multiple of 11 plus 6.

Only 105 is a multiple of 11 plus 6: 9*11+6=105.

Hope it's clear.

Hi,

I am not able to understand the question properly.

Q says the Lake population is 30 females and 36 males. and for Lake B population the Ratio of male to female is is same. i.e. 3:3.

its nowhere mentioned as Lake B population is of same ratio as Lake A.

Regards,
Rrsnathan.

Lake A has a duck population of 30 females and 36 males --> the ratio is F:M = 30:36 = 5:6.
Lake B’s duck population consists of the same ratio of females to males --> F:M = 5:6.
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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28 Sep 2014, 23:56
yogirb8801 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

As mentioned in earlier posts, we have to find answer by subtracting 6 from all 5 options & check if the resultant is divisible by 11?

What I did is, instead of subtracting 6, added 5 to all the 5 options

(Addition goes more easy with me; only result remains the same)

A. 144+5 = 149 (Not divisible by 11)

B: 105+5 = 110 (Yes we got it)

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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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11 Oct 2014, 09:41
hix...i thought lake B has the same ratio means 50:50 male and female ducks....blazz
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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14 Apr 2016, 11:13
The best way I can go is drawing a table as below -
Attachment:

Capture.PNG [ 3.91 KiB | Viewed 2725 times ]

Further we are given -

Quote:
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?

So prior to adding female ducks the total number of ducks must be multiple of 11

check the options except (B) none of the option is divisible by 11.

105 - 6 = 99 ( Which is divisible by 11 )

Hence the correct answer is (B)

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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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21 May 2017, 19:11
yogirb8801 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

It's a problem that tests organization and the hidden multiplier.

Lake A is irrelevant, except that it provides the ratio of females:males (30/36 = 5/6).

With that ratio, we can determine that the ratio in lake B is also 5x/6x. The "x" variable here is the hidden multiplier, so it's important to insert it because we want to find the total of the population. The hidden multiplier is the path.

The total population is 11x because it's the sum of the two components: male and female ducks (5x+11x). So we can arrive at the following formula 11x+6 = total duck population.

We must now backsolve using the answer choices. (B) is the only one that provides a multiple of 11 (=99).
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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23 May 2017, 16:20
yogirb8801 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.

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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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23 May 2017, 21:00
yogirb8801 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?

Though I got to the correct answer, I was slightly confused with the wording of the problem. "Lake B’s duck population consists of the same ratio of females to males" can be interpreted as 1:1 ratio and thought Lake A's data is a distraction. Better wording might be "Lake B’s duck population consists of the same ratio of females to males as of Lake A" Not sure if anyone else faced the same trouble
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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23 May 2017, 21:05
workout wrote:
yogirb8801 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?

Though I got to the correct answer, I was slightly confused with the wording of the problem. "Lake B’s duck population consists of the same ratio of females to males" can be interpreted as 1:1 ratio and thought Lake A's data is a distraction. Better wording might be "Lake B’s duck population consists of the same ratio of females to males as of Lake A" Not sure if anyone else faced the same trouble

Your reading is not correct. The same ratio cannot be interpreted as 1:1, it does not and cannot mean that females = males.
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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23 May 2017, 21:08
Bunuel wrote:
workout wrote:
yogirb8801 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?

Though I got to the correct answer, I was slightly confused with the wording of the problem. "Lake B’s duck population consists of the same ratio of females to males" can be interpreted as 1:1 ratio and thought Lake A's data is a distraction. Better wording might be "Lake B’s duck population consists of the same ratio of females to males as of Lake A" Not sure if anyone else faced the same trouble

Your reading is not correct. The same ratio cannot be interpreted as 1:1, it does not and cannot mean that females = males.

I think I understand the problem correctly now. Thanks for the clarification.
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Re: Lake A has a duck population of 30 females and 36 males.  [#permalink]

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24 May 2017, 23:02
Got the right answer and this question made me realize, "The same ratio cannot be interpreted as 1:1". Thanks
Re: Lake A has a duck population of 30 females and 36 males.   [#permalink] 24 May 2017, 23:02

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