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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?
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.
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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 2025 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 2025 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 2025 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 2025 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?.
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