In a certain class, a teacher distributed a f...

### Related Test 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)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed. EduRev GMAT
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 View courses related to this question Explore GMAT courses
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