Each student in a class to choose an optional subject. If 1/5

Question

Each student in a class to choose an optional subject. If \(\frac{1}{5}\) chose math, \(\frac{1}{4}\) chose biology, \(\frac{1}{2}\) chose history and the remaining 10 chose psychology. What is the number of students in the class?

A) 80
B) 110
C) 160
D) 200
E) 400

A) 80
B) 110
C) 160
D) 200
E) 400

Lampard42 · Answer

As it is one optional subject per student 10=(1-(1/5+1/4+1/2))*X where x is total number of students. number of students who have chosen psychology as a fraction of the total class. Solving the equation x=200.

Option D

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Option D

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Archit3110 · Answer

let total students = x
so 
x/5+x/4+x/2+10=x
solve for x
x=200
IMO D

LeoN88 · Answer

x/5 + x/4 + x/2 + 10 =x

x= 200

AyushCrackVerbal · Answer

Let the number of students in the class be " x "

Number of students who chose Maths = \frac{x}{5}

Number of students who chose Biology =  \frac{x}{4}

Number of students who chose History =  \frac{x}{2}

Number of students who chose Psychology =  x -  \frac{x}{5}  -  \frac{x}{4} -  \frac{x}{2}  = 10

x  -  \frac{19x}{20}  = 10

\frac{x}{20}  = 10

x = 200

The correct answer is D

Kinshook · Answer

Given:
1. Each student in a class to choose an optional subject. 
2.  \frac{1}{5}  chose math,  \frac{1}{4}  chose biology,  \frac{1}{2}  chose history and the remaining 10 chose psychology.

Asked: What is the number of students in the class?

1. Each student in a class to choose an optional subject. 
2.  \frac{1}{5}  chose math,  \frac{1}{4}  chose biology,  \frac{1}{2}  chose history and the remaining 10 chose psychology. 
Remaining fraction of students who chose psychology = 1 - 1/5 - 1/4 - 1/2 = (20-4-5-10)/20 = 1/20
Let the number of students in the class be x

x/20 = 10
x = 200

IMO D

TheNightKing · Answer

1/5=20%
1/4=25%
1/2=50%

They add upto 95%. The remaining 5% = 10. So 10%=20. 100%=200

Answer D

ScottTargetTestPrep · Answer

Solution:

We can create the equation:

n/5 + n/4 + n/2 + 10 = n

Multiplying by 20, we have:

4n + 5n + 10n + 200 = 20n

200 = n

Alternate Solution:

Adding 20%, 25%, and 50%, we obtain 95%, and this is the percent of students that chose a subject other than psychology. Thus, the remaining 5% chose psychology, and this represents 10 students. We can set up the proportion:

5 percent / 10 students = 100 percent / x students

5x = 1000

x = 200

Answer: D

Each student in a class to choose an optional subject. If 1/5

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Each student in a class to choose an optional subject. If 1/5

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