A group of n students is divided into two classes in such a way that

Question

A group of n students is divided into two classes in such a way that one class has one more student than the other. In terms of n, which of the following is the number of students in the larger class.

(A)  \frac{n+1}{2}

(B)  \frac{n}{2}+1

(C)  \frac{n}{2}

(D)  \frac{n-1}{2}

(E)  \frac{2n-1}{2}

chetan2u · Accepted Answer

One class has x and other x+1, so total is 2x+1.
n=2x+1…..2x=n-1 or  x=\frac{n-1}{2} 
But the larger class has x+1 or  \frac{n-1}{2}+1=\frac{n+1}{2}

OR
Use options
You could take an odd value of n and use options. 
Let n=21, so the distribution is 10 and 11
Look for option that gives you 11 as answer. 
A) \frac{n+1}{2}=11 
B) \frac{n}{2}+1=11.5 
C) \frac{n}{2}=10.5 
D) \frac{n-1}{2}=10 
E) \frac{2n-1}{2}=20.5

A

isanyamm · Answer

Given: n is the total number of students
The problem states that one class has one more student than the other

Let x be the number of students in the larger class
The number of students in the smaller class is x - 1

Total number of students is the sum of both classes
n = (x - 1) + x

Combine like terms
n = 2x - 1

Solve for x, the number of students in the larger class
2x = n + 1
x = (n + 1) / 2

The number of students in the larger class (x) is (n + 1) / 2

x = (n + 1) / 2

egmat · Answer

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GMATinsight · Answer

n students to be divided into two classes such that one class has one student more than the other class It's possible only when n = ODD Let's keep 1 student aside and divide rest of the (n-1) students equally in two classes Let's start with equal Division Class 1 | Class 2 (n-1)/2 | (n-1)/2 Now one student has to join one class to satisfy the requirement highlighted Division now Class 1 | Class 2 (n-1)/2 | +1 i.e. Student in larger class = +1 = (n+1)/2 Answer: Option A --- GMATinsight | www.GMATinsight.com GMAT FOCUS PREP Expert Youtube: www.Youtube.com/GMATinsight

KarishmaB · Answer

Use the concept of splitting a sum unevenly discussed here: https://youtube.com/shorts/gKyfdSDGIc0

rak08 · Answer

KarishmaB

I have a silly doubt in this,
if i say there are a total 10 students (n)

so n/2 + 1 = 6
which is true for larger group. (option B)

if N were "odd"
n/2 would be a decimal and then the above n/2 + 1 would fail

so say 7, we do (n+1)/2 ~ 4 (larger) (Option A)
however in case its even and we use n+1 / 2 ~ we will have a decimal number. (Option B)

Where is my logic flawed?

KarishmaB · Answer

Total number of students cannot be even if one class has one student more than the other. 
a + (a+1) = 2a + 1 which is necessarily an odd number when a is a positive integer.

MakB · Answer

I followed the same approach but got the answer D.

I took number of students in the larger class as x + 1 
 Total number of students 
 n = (x + 1) + x 
 n = 2x + 1

Solving in terms of x,  
 n - 1 = 2x 
 x = (n - 1) / 2

What went wrong idk.
Can someone pls explain??

Bunuel · Answer

Your setup is correct, but the final step is missing. Check the question:

A group of n students is divided into two classes in such a way that one class has one more student than the other. In terms of n, which of the following is the number of students in the larger class.

(A) \(\frac{n+1}{2}\)

(B) \(\frac{n}{2}+1\)

(C) \(\frac{n}{2}\)

(D) \(\frac{n-1}{2}\)

(E) \(\frac{2n-1}{2}\)

You defined the   larger   class as x + 1 and the smaller class as  x . So when you found:

x = (n - 1)/2

you found the number of students in the smaller class, not the larger class.

The larger class is:

x + 1 = (n - 1)/2 + 1 = (n + 1)/2

So the answer is A, not D.

Hope it's clear.

Rhitib · Answer

I did a trick, I took n=101, one class will have 50, another will hav 51. Then 101+1/2=51
this ia analogoues to option A, so A is the answer

A group of n students is divided into two classes in such a way that

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