A teacher distributed pens, pencils, and eras...

### Related Test

A teacher distributed pens, pencils, and erasers among the students of his class, such that all students got an equal number of pens, an equal number of pencils, and an equal number of erasers. If no pens, pencils, or erasers remained with the teacher, how many students were in the class?
(1) Each student got pens, pencils, and erasers in the ratio 3:4:5, respectively.
(2) The teacher distributed a total of 27 pens, 36 pencils, and 45 erasers.
• 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.

We are given that a teacher gave an equal number of pens, an equal number of pencils, and an equal number of erasers to each student of this class.
You must NOT assume:
(Number of pens per student) = (Numbers of pencils per student) = (Number of erasers per student)
The number of pens that a student - say Student A - got may be different from the number of pencils and from the number of erasers he got; however, every student in the class got as many pens as Student A gets (and likewise, as many pencils and erasers as Student A gets).
Let the total number of students in the class be n, and each student got x number of pens, y number of pencils, and z number of erasers. We have to find out n.
Statement 1:
Each student got pens, pencils, and erasers in the ratio 3:4:5, respectively.
Thus, we have:
x : y : z = 3 : 4 : 5
⇒ x = 3k, y = 4k, z = 5k,where k is a constant of proportionality.
However, we have no information on n. - Insufficient
Statement 2:
We know that the teacher distributed a total of 27 pens, 36 pencils, and 45 erasers.
Thus, nx = 27,ny = 36,nz = 45
We have no information about x, y, z.
Hence, we cannot determine the value of n. - Insufficient
Statement 1 & 2 together:
Substituting the values of x, or y, or z from Statement 1 in the information from Statement 2, we have:
nx = 27 = 3k
n = 9k
Since k is unknown, we cannot determine n.
The valid values of k can be 1, 3, and 9, rendering the values of n = 9, 3, and 1. (k cannot be greater than 9 because n, the number of students, cannot be a fraction. And, k cannot be a fraction, for example, 1/2 etc., because we know that x = 3k, y = 4k, & z = 5k. Since x, y, & z denote the number of items, they cannot be fractions. For x, y, & z to have integer values, k must be an integer.)
No unique value of n. - Insufficient

 View courses related to this question Explore GMAT courses
 Explore GMAT coursesView courses related to this question
 1 Crore+ students have signed up on EduRev. Have you?