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# At the beginning of the school year, 50% of all students in Mr. Wells'

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Math Expert
Joined: 02 Sep 2009
Posts: 58396
At the beginning of the school year, 50% of all students in Mr. Wells'  [#permalink]

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31 Mar 2019, 20:52
00:00

Difficulty:

65% (hard)

Question Stats:

50% (02:15) correct 50% (02:12) wrong based on 16 sessions

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At the beginning of the school year, 50% of all students in Mr. Wells' math class answered "Yes" to the question "Do you love math", and 50% answered "No." At the end of the school year, 70% answered "Yes" and 30% answered "No." Altogether, x% of the students gave a different answer at the beginning and end of the school year. What is the difference between the maximum and the minimum possible values of x?

A. 0
B. 20
C. 40
D. 60
E. 80

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Re: At the beginning of the school year, 50% of all students in Mr. Wells'  [#permalink]

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31 Mar 2019, 21:51
1
Bunuel wrote:
At the beginning of the school year, 50% of all students in Mr. Wells' math class answered "Yes" to the question "Do you love math", and 50% answered "No." At the end of the school year, 70% answered "Yes" and 30% answered "No." Altogether, x% of the students gave a different answer at the beginning and end of the school year. What is the difference between the maximum and the minimum possible values of x?

A. 0
B. 20
C. 40
D. 60
E. 80

The minimum value of X = 20%
i.e. only 20% of people who said no at the start, now say yes.

The maximum value of X = 80%
i.e. 50% of the people who said No at the start now say yes
and 30% of the people who said yes at the start now say no.

Difference = 80-20 = 60%
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Re: At the beginning of the school year, 50% of all students in Mr. Wells'  [#permalink]

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01 Apr 2019, 02:15
Bunuel wrote:
At the beginning of the school year, 50% of all students in Mr. Wells' math class answered "Yes" to the question "Do you love math", and 50% answered "No." At the end of the school year, 70% answered "Yes" and 30% answered "No." Altogether, x% of the students gave a different answer at the beginning and end of the school year. What is the difference between the maximum and the minimum possible values of x?

A. 0
B. 20
C. 40
D. 60
E. 80

one of a kinda % question i have ever encountered
let total class ; 100
Beginning yes = 50
beginning no 50
End yes= 70
end no 30
% change ; yes = 70-50/50 ; 40% (+)
and % change ; = 50-30/50 ; 40 % (-)
net 40 students who gave different answer
max possible value of x ; 40+ 40 ; 80 students and min can be 70-50= 20
difference ; 80-20 ; 60 iMO D
Re: At the beginning of the school year, 50% of all students in Mr. Wells'   [#permalink] 01 Apr 2019, 02:15
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