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40 percent of the ducks included in a certain side effects study were

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sairam595
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40 percent of the ducks included in a certain side effects study were [#permalink] New post   24 Apr 2016, 07:13
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40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 30 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?

A. 1/4
B. 9/14
C. 2/3
D. 7/8
E. 8/7
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Re: 40 percent of the ducks included in a certain side effects study were [#permalink] New post   19 Jan 2017, 05:52
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Hi sairam595,

Word problems on the GMAT can be really tricky. The best thing to do when you solve word problems is to read the question in parts rather than reading the entire question. Also keep in mind that when you deal with questions related to percentages, it always makes sense to start with an initial value of 100.

So lets work this question out part by part.

40 percent of the ducks included in a certain side effects study were male

Now if we assume the total number of ducks to be 100, then we have 40 male ducks and 60 female ducks

If some of the ducks had side effects

Let the number of ducks who have side effects be 's'.

30 percent of the ducks who had side effects were male

This means that the number of males who had side effects is 0.3s and the number of females who had side effects is 0.7s

What was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?

The side effect rate for male ducks = Number of male ducks with side effects/Total number of males ducks -----> (0.3s)/40

The side effect rate for male ducks = Number of male ducks with side effects/Total number of males ducks -----> (0.7s)/60

Ratio = (0.3s)/40 : (0.7s)/60

Simplifying we get 9/14

Hope this helps!

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Re: 40 percent of the ducks included in a certain side effects study were [#permalink] New post   24 Apr 2016, 08:10
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40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 30 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?
A. 1/4
B. 9/14
C. 2/3
D. 7/8
E. 8/7

Say total male = 40
Total female =60

Required ratio =( .3/40)/ (.7/60) = 9/14 B is the answer

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Re: 40 percent of the ducks included in a certain side effects study were [#permalink] New post   18 Jan 2017, 15:00
This question doesn't sound complete to me. "SOME" of the ducts had side effects and out of these "SOME" ducks, 30% are male, so the other 70% are female.
SOME could be 10 ducks or even 100 ducks. Lets take 10 as example,
0.30 * 10 = 3 male
0.70*10 = 7 female
The answer should be 3/7

I think it has wording issue.
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40 percent of the ducks included in a certain side effects study were [#permalink] New post   25 Mar 2019, 12:21
Bunuel shouldn't the answer be 3/7 ? :?


0.30*40 =12

0.7*60 = 42

\(\frac{12}{42} = \frac{3}{7}\)

Hey Gladi how are you there ? :) Gladiator59
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40 percent of the ducks included in a certain side effects study were [#permalink] New post   Updated on: 26 Mar 2019, 07:16
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dave13 wrote:
Bunuel shouldn't the answer be 3/7 ? :?


0.30*40 =12

0.7*60 = 42

\(\frac{12}{42} = \frac{3}{7}\)

Hey Gladi how are you there ? :) Gladiator59


It should be 9/14.

You are looking for the ratio of the side effects rate between males and females. To get this you have to get the side effects rate of the males and compare with the side effects rate of the females.

If x = total ducks with side effects, then 0.3x = # of male ducks with side effects, and 0.7x = # of female ducks with side effects.

Male side effects rate = \(\frac{males with side effects}{total male population}\). =\(\frac{0.3x}{40}\)

Female side effects rate = \(\frac{females with side effects}{total female population}\) =\(\frac{0.7x}{60}\)

Therefore, ratio of males to females is:

\(\frac{0.3x}{40}\) : \(\frac{0.7x}{60}\). LCM is 120.

= \(\frac{0.9x}{120}\) : \(\frac{1.4x}{120}\)

=9 : 14

Originally posted by rodri102 on 25 Mar 2019, 14:47.
Last edited by rodri102 on 26 Mar 2019, 07:16, edited 2 times in total.
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Re: 40 percent of the ducks included in a certain side effects study were [#permalink] New post   26 Mar 2019, 06:50
how 0.3 / 40 we get 9 ?


Any math professors out there ? :grin:
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40 percent of the ducks included in a certain side effects study were [#permalink] New post   26 Mar 2019, 07:19
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dave13 wrote:
how 0.3 / 40 we get 9 ?


Any math professors out there ? :grin:


Please see above. It is corrected.

Ratio of males to females is:

= \(\frac{0.3x}{40}\) : \(\frac{0.7x}{60}.\). LCM is 120

= \(\frac{0.9x}{120}\) : \(\frac{1.4x}{120}\)

= 9 : 14
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Re: 40 percent of the ducks included in a certain side effects study were [#permalink] New post   26 Mar 2019, 20:56
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Hi there dave13 , hope you're doing great! :-)

Lets try to take a few numbers to begin with.
Study has 40% male ducks. Assuming there are a total of 100 there are 40 male and 60 female ducks.

Let's X ducks be affected. It is given that 30% of X are male and hence remaining (i.e 70%)will be female.

Incidence rate for male ducks will be

# of affected males / # of total males

0.3*X / 40 .... (A)

Similarly from female,
0.7*X / 60 .... (B)

When we divide (A) by (B) we will get-

(0.3* X * 60) / (0.7* X* 40)

Or 18/28

Which is 9/14

Hence (B) is correct.

Hope this helps. :-)


dave13 wrote:
how 0.3 / 40 we get 9 ?


Any math professors out there ? :grin:


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Re: 40 percent of the ducks included in a certain side effects study were [#permalink] New post   19 Sep 2020, 02:23
I faced one similar question in a GMAT prep official mock test. The formula for side effects rate was given in the problem.

Male side effects rate= (males with side effects/total male population).
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40 percent of the ducks included in a certain side effects study were [#permalink] New post   17 Dec 2020, 12:37
Hi!
Is there a way to solve this with the Matrix method?

My matrix looked like the following:
But I cant get over this step! Please help

_______| With | With/O | Total
_______| Side E | _______|____
--------------------------------------
Male | 30%X | _______| 40
--------------------------------------
Female | 70%x | ________| 60
--------------------------------------
Total | ______| ________| 100
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Re: 40 percent of the ducks included in a certain side effects study were [#permalink] New post   17 Jan 2022, 06:45
I solved it with Matrix Method:

Let:
Total ducks = 100
Ducks with side-effects = x
(Kindly refer to the screenshot attached for the Matrix)

Rate for Male ducks = 0.3x/40
Rate for Female ducks = 0.7x/60

Ratio of the side effect rate for the male ducks to the side effect rate for the female ducks = 0.3x/40 * 60/0.7x = 9/14 (B)
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Re: 40 percent of the ducks included in a certain side effects study were [#permalink] New post   20 Jun 2023, 22:11
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Re: 40 percent of the ducks included in a certain side effects study were [#permalink]
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