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Re M1516 [#permalink]
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15 Sep 2014, 23:55
Official Solution: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 \(0.2A=0.25B\), and therefore \(A=1.25B\). Since each student read at least one of the books then \(\{Total\}=\{A\}+\{B\}\{Both\}\), hence \(200=1.25B+B0.25B\), which gives \(B=100\), \(A=1.25B=125\) and \(\{Both\}=0.25B=25\). The number of students who read only book \(A\) is \(\{A\}\{Both\}=12525=100\); The number of students who read only book \(B\) is \(\{B\}\{Both\}=10025=75\); The difference is \(10075=25\). Answer: B
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Re: M1516 [#permalink]
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09 Jul 2015, 07:40
Bunuel wrote: Official Solution:
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 \(0.2A=0.25B\), or: \(A=1.25B\). Since each student read at least one of the books then \(\{Total\}=\{A\}+\{B\}\{Both\}\), hence \(200=1.25B+B0.25B\), which gives \(B=100\), \(A=1.25B=125\) and \(\{Both\}=0.25B=25\). The number of students who read only book \(A\) is \(\{A\}\{Both\}=12525=100\); The number of students who read only book \(B\) is \(\{B\}\{Both\}=10025=75\); The difference is \(10075=25\).
Answer: B Hi Bunuel, I got this answer right but it took me almost 5 minutes.... I dont know If I am too slow but I think I did it in a normal pace.... How can this problem be solved faster? Usually I am good with overlapping sets using double matrix, but this problem has different restrictions that makes it a harder... Could you help me? Thanks a lot. Regards Luis Navarro Looking for 700



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Re: M1516 [#permalink]
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19 Jul 2015, 08:03
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The third statement concludes with "or: A=1.25B". "Or" in math isn't quite the same as "or" in english. Indeed, "Or" represents an alternative to the expression, but it's not logical with the noun it modifies. That is, "or: A=1.25B" isn't the number of those who read A and B anymore, but the ratio of A and B. I know what you meant, but the logic could be enhanced. Perhaps you could add " .20A = .25B, and therefore, A=1.25B." Otherwise the meaning isn't as clear as it could be.
Thanks,



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Re: M1516 [#permalink]
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20 Jul 2015, 04:04
mejia401 wrote: The third statement concludes with "or: A=1.25B". "Or" in math isn't quite the same as "or" in english. Indeed, "Or" represents an alternative to the expression, but it's not logical with the noun it modifies. That is, "or: A=1.25B" isn't the number of those who read A and B anymore, but the ratio of A and B. I know what you meant, but the logic could be enhanced. Perhaps you could add " .20A = .25B, and therefore, A=1.25B." Otherwise the meaning isn't as clear as it could be.
Thanks, Edited as suggested. Thank you!
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Re M1516 [#permalink]
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19 Aug 2015, 07:07
I think this is a highquality question and the explanation isn't clear enough, please elaborate. Need help as to how the calculation for both which is 0.25B has been derived?



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Re: M1516 [#permalink]
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19 Aug 2015, 09:05



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Re: M1516 [#permalink]
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20 Aug 2015, 06:24
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Bunuel wrote: 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 After constructing the matrix as attached: From here: 0.2X=0.25Y......> 4x=5Y or the same X=1.25Y Difference between reading only A and only B= 0.8X  0.75Y, simplify and from above equation to 0.2(4X)  0.75Y= 0.2*5Y 0.75 Y = Y0.75Y= 0.25Y.......(1) From the matrix: Y+0.8X=200…..> Y + 0.2 (4X)+Y=200……> 2Y=200…> Y=100. Applying in (1)… Difference=0.25Y=25 Answer is B
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Re M1516 [#permalink]
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06 Sep 2015, 19:55
I think this is a highquality question and the explanation isn't clear enough, please elaborate. I actually thought the question implied that the no of people reading both A and B is 0.2 A + 0.25 B. Can it not be the case upon reading the question? Please throw some light on this.



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Re: M1516 [#permalink]
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31 Oct 2015, 20:27
0.2A = 0.25B, this can be inferred from the question. this can be rewritten as 0.8A = 1B, or total who reads A = 1.25B and those who read only A = B now we have B0.75B = 0.25B the only left to find out is B. we have 0.25B both, 0.75B both, and B  those who read only A. We have 2B=200 or B=100. The difference thus must be 10075 = 25.



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Re: M1516 [#permalink]
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24 Sep 2016, 02:47
Isn't it should be A+B2(both) as both part is common to both A and B?



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Re: M1516 [#permalink]
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25 Sep 2016, 22:37



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Re: M1516 [#permalink]
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06 Dec 2016, 01:43
Twenty percent of A is common with Twenty five percent of B. Rest of A =80% ,Rest of B =75% If we consider the common part as 1 part of A and 1 part of B, 4 parts of A and 3 parts of B are left. therefore the total number of parts is 8 and the difference between only A and only B is 1 part which is equal to 200/8 =25



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Re: M1516 [#permalink]
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18 Jan 2017, 05:13
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The ratio of A to B is 5 to 4. We are given that each student chooses at least one book. The intersection of A & B is 'x' (assuming 5X choose A and 4X choose B). There are a total of 200 students. The number of people reading just A is 4x. The number of people reading just B is 3X. X read both A & B. 8X = 200 > X=25. 4X3X=X=25.
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Re: M1516 [#permalink]
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20 Jan 2017, 09:46
I think this is a highquality question and the explanation is clear enough.



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Re: M1516 [#permalink]
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02 May 2017, 05:43
very simple ! m=ones who just read A , n=ones who just read B 0.2(m+x)=x ... m=4x 0.25(n+x)=x ... n=3x 200=m+x+n=8x ... x=25 mn=x=25



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Re: M1516 [#permalink]
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02 May 2017, 15:14
20% who read A also reads B.....read both(A+B)=0.20A 25% who read B also reads A.....read both(A+B)=0.25B
0.20A=0.25B B=4/5 A
read only A= read A  read both(A+B)=A0.2A=0.8A read only B= read B  read both(A+B)=B0.25B=0.75B=0.75*4/5A=0.6A [B=4/5 A]
Total= read only A + read only B + read both(A+B) 200 =0.8A+0.6A+0.2A A= 125
read only A =0.8A=0.8*125=100 read only B=0.6A=0.6*125=75
read only Aread only B=10075=25
Answer: B










