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

Watch this solution to see how a seemingly straightforward question can be solved even more efficiently with a crucial inference. By recognizing that n is odd, you can significantly reduce your calculation time.
This video demonstrates the importance of analyzing given information before diving into computations, potentially saving you valuable minutes in the exam.
Are you making the most of such inferences in your problem-solving approach?

https://www.youtube.com/watch?v=7hskuUEVTRw

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.

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

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

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