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Sixty percent of the rats included in an experiment were female rats.

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Sixty percent of the rats included in an experiment were female rats.  [#permalink]

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New post 01 Dec 2014, 04:22
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Tough and Tricky questions: Mixture Problems.



Sixty percent of the rats included in an experiment were female rats. If some of the rats died during an experiment and 70 percent of the rats that died were male rats, what was the ratio of the death rate among the male rats to the death rate among the female rats?

A) 7 : 2
B) 7 : 3
C) 2 : 7
D) 3 : 7
E) Cannot be determined from the information given

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Re: Sixty percent of the rats included in an experiment were female rats.  [#permalink]

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New post 01 Dec 2014, 05:45
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Let x be the total number of rats in the experiment.
Male = 0.4x
Female = 0.6x

Let a be the total number of rats that died during experiment.
Male = 0.7a
Female =0.3a

Death rates
Male = 0.7a/0.4x
Female = 0.3a/0.6x

Ratio of death rates among males and females = 0.7a/0.4x*0.6x/0.3a
=0.7/0.2
=7/2

Ans = A
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Re: Sixty percent of the rats included in an experiment were female rats.  [#permalink]

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New post 01 Dec 2014, 11:16
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As we are asked to find only ratios we can pick numbers to answer this question.

Let the total number of rats be 100
Number of female rats = 60 and number of male rats = 40.

Given , 70% of the dead rats are males . So the other 30% must be females.
Let the total number of dead rats be x.

Death rate = number of dead ones/ total number

Therefore , ratio = (number of dead ones/ total number ) / ( number of dead ones/ total number)

That is , ratio= ( 70x/100 / 40 ) / (30x/100 / 60)
= 7/2
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Re: Sixty percent of the rats included in an experiment were female rats.  [#permalink]

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New post 01 Dec 2014, 17:21
1
I wish I could draw this, but I think this can be easily solved using algebra and/or a double matrix. With the double matrix we have two categories: gender and dead or not. As we're dealing with percentages, let's say the total number of subjects is 100.

So, we have 40 males and 60 females. We also know some number are dead, let's say x and 100-x are alive. From this we know that 0.7x are male and 0.3x are female. Let's compute some ratios.

The male death rate is 0.7x/40 and the female death rate is 0.3x/60. Male:Female --> male/female = 0.7x/40*60/0.3x

Solving yields 7/2 or answer choice A.
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Re: Sixty percent of the rats included in an experiment were female rats.  [#permalink]

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New post Updated on: 01 Dec 2014, 20:33
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Answer = A) 7 : 2

Using Matrix method (Refer diagram)

Attachment:
dead.png
dead.png [ 4.71 KiB | Viewed 3886 times ]


1. Say total number of rats = 100

2. Total Female = 60

3. So, total Male = 100-60 = 40

4. Say total dead = x

5. Males in dead constitute 70% = \(\frac{70x}{100}\)

6. So, dead in female \(= \frac{30x}{100}\)

Death rate in Males \(= \frac{\frac{70x}{100}}{40} = \frac{7x}{400}\)

Death rate in Females \(= \frac{\frac{30x}{100}}{60} = \frac{x}{200}\)


Ratio (Male/Female) death rates \(= \frac{\frac{7x}{400}}{\frac{x}{200}} = \frac{7x}{400} * \frac{200}{x} = \frac{7}{2}\)
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Originally posted by PareshGmat on 01 Dec 2014, 20:30.
Last edited by PareshGmat on 01 Dec 2014, 20:33, edited 1 time in total.
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Re: Sixty percent of the rats included in an experiment were female rats.  [#permalink]

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New post 01 Dec 2014, 20:32
1
Lets total mouse = 100
Male 40 and female 60.
Lets say x mouse are dead. Since 70% dead are male => Dead (Male) = 0.7x and Dead (Female) = 0.3x
Rate of dead(Male) = 0.7x / 40
Rate of dead (Female) = 0.3x /60
Ratio of Death rate (M/F) = (0.7x/40)/(0.3x/60) = 7/2.
Hence answer is A.
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Re: Sixty percent of the rats included in an experiment were female rats.  [#permalink]

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New post 02 Dec 2014, 07:51
Bunuel wrote:

Tough and Tricky questions: Mixture Problems.



Sixty percent of the rats included in an experiment were female rats. If some of the rats died during an experiment and 70 percent of the rats that died were male rats, what was the ratio of the death rate among the male rats to the death rate among the female rats?

A) 7 : 2
B) 7 : 3
C) 2 : 7
D) 3 : 7
E) Cannot be determined from the information given

Kudos for a correct solution.

Source: Chili Hot GMAT


The correct answer is A.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Sixty percent of the rats included in an experiment were female rats.  [#permalink]

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New post 22 Apr 2016, 16:03
(.7/.4)/(.3/.6)=7/2
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Re: Sixty percent of the rats included in an experiment were female rats.  [#permalink]

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New post 07 Jul 2017, 17:16
Bunuel wrote:

Tough and Tricky questions: Mixture Problems.



Sixty percent of the rats included in an experiment were female rats. If some of the rats died during an experiment and 70 percent of the rats that died were male rats, what was the ratio of the death rate among the male rats to the death rate among the female rats?

A) 7 : 2
B) 7 : 3
C) 2 : 7
D) 3 : 7
E) Cannot be determined from the information given

Kudos for a correct solution.

Source: Chili Hot GMAT


Let there be \(100\) rats in total.

No. of female rats = \(60\)
No. of male rats = \(40\)

No. of rats that died = \(x\).

No. of dead male rats = \(0.7x\)
No. of dead female rats = \(0.3x\)

Death rate of male rats = No. of dead male rats/Total male rats.
Death rate of male rats = \(\frac{0.7x}{40}\)

Death rate of female rats = \(\frac{0.3x}{60}\)

Ratio = \(\frac{0.7x*60}{0.3x*40} = \frac{0.7*3}{0.3*2} = \frac{7*3}{3*2} = \frac{7}{2}\). Ans - A.
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Re: Sixty percent of the rats included in an experiment were female rats.  [#permalink]

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Re: Sixty percent of the rats included in an experiment were female rats.   [#permalink] 03 Feb 2019, 01:17
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