What a weird class

Number Theory Level 1

In a class, $\frac{1}{5}$ received an A grade, $\frac{1}{4}$ received a B grade, $\frac{1}{3}$ received a C grade and the rest received a D grade. What is the minimum number of people who received a D grade?

Image credit: Wikipedia Nkhiangte

1 11 5 13 10 12 2

3 solutions

Discussions for this problem are now closed

Brian Charlesworth
Jan 27, 2015

If there are $N$ students, then since the numbers of students who receive each of the four grades must be integer-valued, we require that $N$ be divisible by each of $3,4$ and $5$ . The least such value is LCM( $3,4,5) = 60$ , which will in turn yield the minimum possible value for the number of students who receive a D grade. This value will be

$60 - \frac{60}{5} - \frac{60}{4} - \frac{60}{3} = 60 - 12 - 15 - 20 = \boxed{13}.$

I thought it based on number of students in the photo...and the answer is 5 #LOL but if we talk about how fractions work then it must be 13

Elni Verawati - 6 years, 3 months ago

Nope, lets do it like… Assuming there are 5 students in the class, 1 student got an A. And he is separated from the ones who get a B. So, now it is just 4, in which 1 gets a B. As it goes on, the rest receive a D, which is 2. P.S. In the question it is given to find the least no. who received a D!!

Vikram Venkat - 6 years, 4 months ago

That is not how fractions work.

Calvin Lin Staff - 6 years, 4 months ago

The problem in your reasoning is that you are separating people, and that's incorrect.

Roberto Villadangos Carrera - 6 years, 4 months ago

Your answer would work if the problem is rephrased as such:

"In a class, $\frac{1}{5}$ received an A grade. After removing the those A grade students, the remaining $\frac{1}{4}$ of the students received a B grade. After removing the those A grade students and B grade students, the remaining $\frac{1}{3}$ received a C grade. And the rest received a D grade. What is the minimum number of people who received a D grade?"

Do you see the difference?

Pi Han Goh - 6 years, 2 months ago

Gamal Sultan
Jan 31, 2015

Let the number of students in the class = x

Then

The number of student who received a D grade =

x - (1/5 + 1/4 + 1/3)x = (13/60)x

The number (13/60)x to be an integer, x must be a multiple of 60

i.e.

x = 60, 120, 180, ...............

To get the minimum number, x must be 60

The minimum number of student who received a D grade = 13

Junaid Hameed
Feb 1, 2015

You need to find the lowest common multiple of 5, 4, and 3 so you can get whole number solutions for each fraction of the whole class. The LCM of 5, 4 and 3 is 5 x 4 x 3 = 60. (Keep in mind LCM is not always all three numbers multiplied together, but it is in this case)

1/5 of 60 is 12. 1/4 of 60 is 15. 1/3 of 60 is 20.

20 + 15 + 12 = 47 60 - 47 = the rest of the class, people who received a D grade = 13.

What a weird class

Image credit: Wikipedia Nkhiangte

3 solutions

Discussions for this problem are now closed

0 pending reports