GMAT Exam > GMAT Questions > A group of n students can be divided into equ...
Start Learning for Free
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?
- a)33
- b)46
- c)49
- d)53
- e)86
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A group of n students can be divided into equal groups of 4 with 1 stu...
When n is divided by 4 it has a remainder of 1, so n = 4x + 1, where x is an integer. Likewise when n is divided by 5 it has a remainder of 3, so n = 5y + 3, where y is an integer. To find the two smallest values for n, we can list possible values for n based on integer values for x and y. To be a possible value for n, the value must show up on both lists:
The first two values for n that work with both the x and y expressions are 13 and 33. Their sum is 46.
The correct answer is B.
The correct answer is B.
Most Upvoted Answer
A group of n students can be divided into equal groups of 4 with 1 stu...
To solve this problem, we need to find the values of n that satisfy the given conditions. Let's break it down step by step.
Step 1: Set up the equations
We are given two conditions:
1) n divided by 4 leaves a remainder of 1
2) n divided by 5 leaves a remainder of 3
We can represent these conditions as equations:
1) n = 4a + 1 (where a is an integer)
2) n = 5b + 3 (where b is an integer)
Step 2: Find the smallest possible values of n
To find the smallest possible values of n, we need to find the smallest values for a and b that satisfy the equations.
Condition 1: n divided by 4 leaves a remainder of 1
We can start by substituting n in equation 1 with the expression from equation 2:
5b + 3 = 4a + 1
Rearranging the equation:
5b - 4a = -2
We can see that the smallest values for a and b that satisfy this equation are a = 2 and b = 2.
Substituting these values back into the equations, we can find the smallest possible values for n:
n = 4a + 1 = 4(2) + 1 = 9
n = 5b + 3 = 5(2) + 3 = 13
So the smallest possible values of n are 9 and 13.
Step 3: Find the sum of the smallest possible values of n
The sum of the smallest possible values of n is 9 + 13 = 22.
However, we need to find the sum of the two smallest possible values of n. Since we already have two values (9 and 13), we can conclude that the sum of the two smallest possible values of n is 9 + 13 = 22.
Therefore, the correct answer is option B) 22.
Step 1: Set up the equations
We are given two conditions:
1) n divided by 4 leaves a remainder of 1
2) n divided by 5 leaves a remainder of 3
We can represent these conditions as equations:
1) n = 4a + 1 (where a is an integer)
2) n = 5b + 3 (where b is an integer)
Step 2: Find the smallest possible values of n
To find the smallest possible values of n, we need to find the smallest values for a and b that satisfy the equations.
Condition 1: n divided by 4 leaves a remainder of 1
We can start by substituting n in equation 1 with the expression from equation 2:
5b + 3 = 4a + 1
Rearranging the equation:
5b - 4a = -2
We can see that the smallest values for a and b that satisfy this equation are a = 2 and b = 2.
Substituting these values back into the equations, we can find the smallest possible values for n:
n = 4a + 1 = 4(2) + 1 = 9
n = 5b + 3 = 5(2) + 3 = 13
So the smallest possible values of n are 9 and 13.
Step 3: Find the sum of the smallest possible values of n
The sum of the smallest possible values of n is 9 + 13 = 22.
However, we need to find the sum of the two smallest possible values of n. Since we already have two values (9 and 13), we can conclude that the sum of the two smallest possible values of n is 9 + 13 = 22.
Therefore, the correct answer is option B) 22.
Attention GMAT Students!
To make sure you are not studying endlessly, EduRev has designed GMAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GMAT.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer?
Question Description
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer?.
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer?.
Solutions for A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?a)33b)46c)49d)53e)86Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup