+0  
 
0
63
2
avatar

The number of students in a school is between 500 and 600. If we group them into groups of 12, 20, or 36 each, 7 students are always left over. How many students are in this school?

 Dec 3, 2019
 #1
avatar
0

N mod 12 = 7

N mod 20 = 7

N mod 36 = 7

 

N = 547 - Number of students in the school.

 Dec 4, 2019
 #2
avatar
0

547 was arrived at as follows:

 

The LCM[12, 20, 36] = 180, then smallest N is:

180m + 7 =187, where m=0, 1, 2, 3......etc.

Since the number of students is between 500 and 600 students, then:

180 * 3 + 7 = 547 - Number of students in this school.

Guest Dec 4, 2019

65 Online Users

avatar
avatar
avatar
avatar