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Of 200 surveyed students, 20% of those who read book A [#permalink]

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26 Sep 2013, 22:14

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Of 200 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?

Of 200 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?

A. 20 B. 25 C. 30 D. 35 E. 40

Say the number of students who read book A is A and the number of students who read book B is B.

Given that 20% of those who read book A also read book B and 25% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.25B --> A=1.25B.

Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 200=1.25B+B-0.25B --> B=100, A=1.25B=125 and {Both}=0.25B=25.

The number of students who read only book A is {A}-{Both}=125-25=100; The number of students who read only book B is {B}-{Both}=100-25=75;

Re: Of 200 surveyed students, 20% of those who read book A [#permalink]

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29 Sep 2013, 06:38

Bunuel,

Could you please give an example of a problem where we would use Total= only A+ only B + both. Why aren't we using this formula in this problem? thanks

Re: Of 200 surveyed students, 20% of those who read book A [#permalink]

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29 Sep 2013, 07:05

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LinaNY wrote:

Bunuel,

Could you please give an example of a problem where we would use Total= only A+ only B + both. Why aren't we using this formula in this problem? thanks

It depends on what information you have with you.

If you know the values of TOTAL, ONLY A and ONLY B and you need to calculate the value of BOTH, then you can use the formula: Total= only A+ only B + both

But if you don't know the values of ONLY A and ONLY B (like in this case where we are able to deduce the values of A and B but not of ONLY A and ONLY B), the we should use the following formula: Total= A+ B - BOTH.

So use of formula varies depending on the information available.

I hope I have addressed your query
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Do not forget to hit the Kudos button on your left if you find my post helpful

Could you please give an example of a problem where we would use Total= only A+ only B + both. Why aren't we using this formula in this problem? thanks

Re: Of 200 surveyed students, 20% of those who read book A [#permalink]

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09 Sep 2017, 06:04

Bunuel wrote:

m15 q16

Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 200=1.25B+B-0.25B --> B=100, A=1.25B=125 and {Both}=0.25B=25.

The number of students who read only book A is {A}-{Both}=125-25=100; The number of students who read only book B is {B}-{Both}=100-25=75;

The difference is 100-75=25.

Answer: B.

Hi Bunuel ,I know it must be little silly to ask but how did you get both =0.25 B.. Even I could come upto A(=5/4)B but couldn't understand what to write for "both". Please elaborate.

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