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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 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?

Answers

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 = 2× 5
The terms common to both: 2 5 = 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
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
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
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

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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 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 2023 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 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 2023 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 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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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 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?, a detailed solution 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 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'. 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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 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? theory, EduRev gives you an ample number of questions to practice 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 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? tests, examples and also practice GMAT tests.
Given: Each student gets an equal number of candies and an equal number of few barsDo not assume! Number of candies = Number of barsTo find out: The number of students in the classStatement 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 × 540 = 23× 5The terms common to both: 225 = 20⇒ GCD of 40 and 180 = 20Thus, the number of students could be 20 or a factor of 20 (that is, 1, 2, 4, 5, 10):Scenario #1Number of students = 20 (Maximum possible number of students):Number of candies received by each student: 180 / 20 = 9Number of bars received by each student: 4 / 20 = 2Scenario #2Number of students = 10Number of candies received by each student: 180 / 10 = 18Number of bars received by each student: 40 / 10 = 4Scenario #3Number of students = 5Number of candies received by each student: 180 / 5 = 36Number of bars received by each student: 40 / 5 = 8There 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. – InsufficientStatement 2:There is no information about the number of candies and the number of bars distributed. – InsufficientStatement 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