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In a certain class, a teacher distributed a few candies and a few bars among the students such that each student got an equal number of candies and an equal number of bars and no candies or bars remained undistributed. How many students were there in the class?
(1) The teacher distributed 180 candies and 40 bars.
(2) The total number of items received by each student was less than or equal 20.
(2) The total number of items received by each student was less than or equal 20.
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
- d)EACH statement ALONE is sufficient to answer the question asked;
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In a certain class, a teacher distributed a few candies and a few bars...
Given: The teacher distributed a few candies and a few bars among the students such that each student got an equal number of candies and an equal number of bars and no candies or bars remained undistributed.
To find: How many students were there in the class?
Solution:
Let the number of candies distributed be C and the number of bars distributed be B. Let the number of students in the class be S. We are looking for the value of S.
From the given information, we know that:
- Each student got an equal number of candies and an equal number of bars.
- No candies or bars remained undistributed.
Therefore, we can say that:
- The number of candies distributed to each student = C/S
- The number of bars distributed to each student = B/S
Since each student got an equal number of candies and an equal number of bars, we can say that:
C/S = B/S
Multiplying both sides by S, we get:
C = B
So, the number of candies and bars distributed is equal.
Now, let's analyze the given statements.
Statement 1: The teacher distributed 180 candies and 40 bars.
This statement alone is not sufficient to answer the question asked. We don't know how many students there are in the class.
Statement 2: The total number of items received by each student was less than or equal 20.
This statement alone is not sufficient to answer the question asked. We don't know the exact number of candies and bars distributed.
Statements 1 and 2 together:
From statement 1, we know that the number of candies and bars distributed is 180 and 40 respectively. From statement 2, we know that the total number of items received by each student is less than or equal to 20.
So, we can write:
- C/S + B/S <=>
- C + B <=>
Substituting C = B (as we found earlier), we get:
2C <=>
C <=>
Therefore, the maximum value of C can be 180 (from statement 1). So, we can write:
C <=>
10S <=>
S <=>
So, we know that there are at most 18 students in the class.
Combining both statements, we know that there are at most 18 students in the class and the number of candies and bars distributed. Therefore, both statements together are sufficient to answer the question asked.
Answer: Option (c) Both statements (1) and (2) together are sufficient to answer the question asked, but neither statement alone is sufficient.
To find: How many students were there in the class?
Solution:
Let the number of candies distributed be C and the number of bars distributed be B. Let the number of students in the class be S. We are looking for the value of S.
From the given information, we know that:
- Each student got an equal number of candies and an equal number of bars.
- No candies or bars remained undistributed.
Therefore, we can say that:
- The number of candies distributed to each student = C/S
- The number of bars distributed to each student = B/S
Since each student got an equal number of candies and an equal number of bars, we can say that:
C/S = B/S
Multiplying both sides by S, we get:
C = B
So, the number of candies and bars distributed is equal.
Now, let's analyze the given statements.
Statement 1: The teacher distributed 180 candies and 40 bars.
This statement alone is not sufficient to answer the question asked. We don't know how many students there are in the class.
Statement 2: The total number of items received by each student was less than or equal 20.
This statement alone is not sufficient to answer the question asked. We don't know the exact number of candies and bars distributed.
Statements 1 and 2 together:
From statement 1, we know that the number of candies and bars distributed is 180 and 40 respectively. From statement 2, we know that the total number of items received by each student is less than or equal to 20.
So, we can write:
- C/S + B/S <=>
- C + B <=>
Substituting C = B (as we found earlier), we get:
2C <=>
C <=>
Therefore, the maximum value of C can be 180 (from statement 1). So, we can write:
C <=>
10S <=>
S <=>
So, we know that there are at most 18 students in the class.
Combining both statements, we know that there are at most 18 students in the class and the number of candies and bars distributed. Therefore, both statements together are sufficient to answer the question asked.
Answer: Option (c) Both statements (1) and (2) together are sufficient to answer the question asked, but neither statement alone is sufficient.
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Community Answer
In a certain class, a teacher distributed a few candies and a few bars...
Given: Each student gets an equal number of candies and an equal number of few bars
Do not assume! Number of candies = Number of bars
To find out: The number of students in the class
Statement 1:
We know that each student received an equal number of candies and an equal number of bars.
Thus, the GCD of the number of candies and the number of bars is the largest possible number of students in the class.
180 = 22 × 32 × 5
40 = 23 × 5
The terms common to both: 22 5 = 20
⇒ GCD of 40 and 180 = 20
⇒ GCD of 40 and 180 = 20
Thus, the number of students could be 20 or a factor of 20 (that is, 1, 2, 4, 5, 10):
Scenario #1
Number of students = 20 (Maximum possible number of students):
Number of candies received by each student: 180 / 20 = 9
Number of bars received by each student: 4 / 20 = 2
Number of bars received by each student: 4 / 20 = 2
Scenario #2
Number of students = 10
Number of candies received by each student: 180 / 10 = 18
Number of bars received by each student: 40 / 10 = 4
Number of bars received by each student: 40 / 10 = 4
Scenario #3
Number of students = 5
Number of candies received by each student: 180 / 5 = 36
Number of bars received by each student: 40 / 5 = 8
Number of bars received by each student: 40 / 5 = 8
There are three more possible cases for the number of students, i.e. 4 or 2 or 1. Of these, the possibility of the number of students being 1 can be rejected because the question explicitly mentions students in the plural.
So, the number of students can be 20, 10, 5, 4, or 2.
Thus, there is no unique answer. – Insufficient
Statement 2:
There is no information about the number of candies and the number of bars distributed. – Insufficient
Statement 1 & 2 together:
Combining both statements, we find that since the total number of items received by each student is less than 20, the only possible scenario is Scenario #1, where:
i. the number of students is 20.
ii. Total number of items received by each student: 9 + 2 = 11< 20.
The total number of items received by each student in other scenarios is more than 20. – Therefore, we’ve arrived at a unique answer: the number of students is 20. Sufficient
i. the number of students is 20.
ii. Total number of items received by each student: 9 + 2 = 11< 20.
The total number of items received by each student in other scenarios is more than 20. – Therefore, we’ve arrived at a unique answer: the number of students is 20. Sufficient
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In a certain class, a teacher distributed a few candies and a few bars among the students such that each student got an equal number of candies and an equal number of bars and no candies or bars remained undistributed. How many students were there in the class?(1) The teacher distributed 180 candies and 40 bars.(2) The total number of items received by each student was less than or equal 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer?
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In a certain class, a teacher distributed a few candies and a few bars among the students such that each student got an equal number of candies and an equal number of bars and no candies or bars remained undistributed. How many students were there in the class?(1) The teacher distributed 180 candies and 40 bars.(2) The total number of items received by each student was less than or equal 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. 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 In a certain class, a teacher distributed a few candies and a few bars among the students such that each student got an equal number of candies and an equal number of bars and no candies or bars remained undistributed. How many students were there in the class?(1) The teacher distributed 180 candies and 40 bars.(2) The total number of items received by each student was less than or equal 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain class, a teacher distributed a few candies and a few bars among the students such that each student got an equal number of candies and an equal number of bars and no candies or bars remained undistributed. How many students were there in the class?(1) The teacher distributed 180 candies and 40 bars.(2) The total number of items received by each student was less than or equal 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer?.
In a certain class, a teacher distributed a few candies and a few bars among the students such that each student got an equal number of candies and an equal number of bars and no candies or bars remained undistributed. How many students were there in the class?(1) The teacher distributed 180 candies and 40 bars.(2) The total number of items received by each student was less than or equal 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. 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 In a certain class, a teacher distributed a few candies and a few bars among the students such that each student got an equal number of candies and an equal number of bars and no candies or bars remained undistributed. How many students were there in the class?(1) The teacher distributed 180 candies and 40 bars.(2) The total number of items received by each student was less than or equal 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain class, a teacher distributed a few candies and a few bars among the students such that each student got an equal number of candies and an equal number of bars and no candies or bars remained undistributed. How many students were there in the class?(1) The teacher distributed 180 candies and 40 bars.(2) The total number of items received by each student was less than or equal 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer?.
Solutions for In a certain class, a teacher distributed a few candies and a few bars among the students such that each student got an equal number of candies and an equal number of bars and no candies or bars remained undistributed. How many students were there in the class?(1) The teacher distributed 180 candies and 40 bars.(2) The total number of items received by each student was less than or equal 20.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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