Question 1203905: A music teacher is able to arrange all of the chairs in the practice room into 2 or more rows that contain the same number of chairs.
Which of the following numbers can *not* be the total number of chairs in the practice room?
19
21
25
15
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
Obviously, from the problem, the number of chairs is the product of two integer numbers,
greater than 1, the number of rows and the number of chairs in each row.
The only number in the list, which can not be such a product, is a prime number 19, first in the list.
ANSWER. The number 19 can not the total number of chairs in the practice room.
Solved.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
A music teacher is able to arrange all of the chairs in the practice room into 2 or more rows that contain the same
number of chairs.Which of the following numbers can *not* be the total number of chairs in the practice room?
19
21
25
15
I wonder! 19 seems to be the most appropriate choice, but:
21 chairs yield: 7 rows, each with 3 chairs, or 3 rows, each with 7 chairs
25 chairs yield: 5 rows, each with 5 chairs
15 chairs yield: 5 rows, each with 3 chairs, or 3 rows, each with 5 chairs
For 19 chairs, having 2 or more rows means that we can't have 1 row with 19 chairs, but what about
19 rows, each with just 1 chair? Nothing states that there should be more than 1 chair in a row.
And, how about the others? I'd say: 21 chairs COULD yield 21 rows, each with 1 chair!
25 chairs COULD yield 25 rows, each with 1 chair!
15 chairs COULD yield 15 rows, each with 1 chair!
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