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# In a certain high school, 20 percent of the students in the sophomore

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Joined: 02 Sep 2009
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In a certain high school, 20 percent of the students in the sophomore  [#permalink]

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09 Oct 2019, 22:03
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25% (medium)

Question Stats:

81% (01:51) correct 19% (01:55) wrong based on 31 sessions

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Competition Mode Question

In a certain high school, 20 percent of the students in the sophomore class have obtained a driver's license, and half of those students took a driver's education class. Of the sophomores without a license, 70 percent have taken a driver's education class. What percentage of the class has not taken a driver's education class?

A. 66
B. 50
C. 44
D. 36
E. 34

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Re: In a certain high school, 20 percent of the students in the sophomore  [#permalink]

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09 Oct 2019, 22:30
1
10+ (30/100*80)
10+ 24
=34

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Re: In a certain high school, 20 percent of the students in the sophomore  [#permalink]

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09 Oct 2019, 23:21
1
Let total number of Sophomore class be 100.
The portion of the class who have Driver's License, A, = 20% = 20
The portion of the class without a Driver's License, B, = 80% = 80

We know from the question stem that half of the class with Driver's License took Driver Education Classes. This implies half of A did not take Driver's Education Class.
Hence number out of A, who do not have Driver's Education = 0.5*20 = 10

We also know from the question stem that 70% of those without Driver's License, B, took Driver Education Classes, implying 30% of B did not take the class.
Number out of A without the class = 0.3*80 = 24
Total without the class = 24+10 = 34
Hence 34% did not take the Driver Education Class.

Option E is the answer in my view.
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Re: In a certain high school, 20 percent of the students in the sophomore  [#permalink]

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10 Oct 2019, 01:07
1
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File comment: OA: E

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Re: In a certain high school, 20 percent of the students in the sophomore  [#permalink]

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10 Oct 2019, 03:02
1
In a certain high school, 20 percent of the students in the sophomore class have obtained a driver's license, and half of those students took a driver's education class. Of the sophomores without a license, 70 percent have taken a driver's education class. What percentage of the class has not taken a driver's education class?

assume there are 100 sophomore
20% of sophomore have driver's license: 20
half of those took driver's class: 10
of sophomore w/o license, 70% taken driver's class: .7x(100-20): 56
what percentage of the class(sophomore) has not taken a driver's class: 100-10-56=34

Therefore, E
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Re: In a certain high school, 20 percent of the students in the sophomore  [#permalink]

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10 Oct 2019, 03:27
1
In a certain high school, 20 percent of the students in the sophomore class have obtained a driver's license, and half of those students took a driver's education class. Of the sophomores without a license, 70 percent have taken a driver's education class. What percentage of the class has not taken a driver's education class?

A. 66
B. 50
C. 44
D. 36
E. 34

Half of students with drier's license have taken driver's education class i.e 20%/2 = 10%
Since 80% students are without a license which includes 70% who have taken driver's education class and remaining without it, percentage of students without driver's education class is 30% * 80% = 24%

Hence total students without driver's education class = 24 + 10 = 34%

IMO Answer E.
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Re: In a certain high school, 20 percent of the students in the sophomore  [#permalink]

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10 Oct 2019, 05:18
Quote:
In a certain high school, 20 percent of the students in the sophomore class have obtained a driver's license, and half of those students took a driver's education class. Of the sophomores without a license, 70 percent have taken a driver's education class. What percentage of the class has not taken a driver's education class?

A. 66
B. 50
C. 44
D. 36
E. 34

............drivers:......not:
class…..0.5(1/5)....0.7(4/5)
not…....0.5(1/5)......0.3(4/5)
total.......1/5........4/5

not: 0.5(1/5)+0.3(4/5)=34/100

Answer (E)
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Re: In a certain high school, 20 percent of the students in the sophomore  [#permalink]

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10 Oct 2019, 06:23
solve using 2x2 matrix
-----DL--NDL---Total
Class-10--56-----66
nclas--10--24----34
total--20---80---100

IMO E; 34

In a certain high school, 20 percent of the students in the sophomore class have obtained a driver's license, and half of those students took a driver's education class. Of the sophomores without a license, 70 percent have taken a driver's education class. What percentage of the class has not taken a driver's education class?

A. 66
B. 50
C. 44
D. 36
E. 34
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Posts: 264
Re: In a certain high school, 20 percent of the students in the sophomore  [#permalink]

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10 Oct 2019, 13:16
Let 100 be the number of students in the sophomore class.
—> 20% of them have a driver’s license:
—> 10 of them took driver’s education class
—> the other 10 students didn’t take driver’s education class

80 students don’t have driver’s license:
—> 80*70%= 80*70/100=56 students have taken the driver’s education class.
—> 80– 56= 24 students haven’t taken that class.
In total, there are 10+24=34 students have not taken the driver’s education class
—> that means 34 % of the class have not taken the driver’s education class.

The answer is E

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Re: In a certain high school, 20 percent of the students in the sophomore  [#permalink]

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13 Oct 2019, 18:27
1
Bunuel wrote:

Competition Mode Question

In a certain high school, 20 percent of the students in the sophomore class have obtained a driver's license, and half of those students took a driver's education class. Of the sophomores without a license, 70 percent have taken a driver's education class. What percentage of the class has not taken a driver's education class?

A. 66
B. 50
C. 44
D. 36
E. 34

We can let n = the total number of students in the sophomore class. We know that 0.2n have a license and 0.8n do not have a license.

0.2n * 0.5 = 0.1n took a driver’s education class and have a licence and

0.8n * 0.7 = 0.56n took a driver’s education class but do not have a licence.

Thus, 0.1n + 0.56n = 0.66n students took a driver’s education class, which means 0.34n, or 34% of the students, have not taken a driver’s education class.

Answer: E
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Re: In a certain high school, 20 percent of the students in the sophomore   [#permalink] 13 Oct 2019, 18:27
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