Ravi is organizing chairs for a conference. He has a certain number of chairs, denoted by c, such that: c 10, the number of chairs c is divisible by 5 but it is not divisible by 10. Based on this, which of the following total numbers of guests (in integers) can he arrange evenly into rows of 4?
(a) 2c
(b) 3c
(c) 2c + 6
(d) 3c + 1

Question

Ravi is organizing chairs for a conference. He has a certain number of chairs, denoted by c, such that: c > 10, the number of chairs c is divisible by 5 but it is not divisible by 10. Based on this, which of the following total numbers of guests (in integers) can he arrange evenly into rows of 4?
(a) 2c
(b) 3c
(c) 2c + 6
(d) 3c + 1

ONLiNE UPSC · Accepted Answer

Let's find possible values of c:
c > 10
c is divisible by 5 but not by 10 &rarr; So c must be odd multiples of 5 over 10
So possible values: 15, 25, 35, ...
Let's try c = 15
(a) 2c = 2 &times; 15 = 30 &rarr; Not divisible by 4
(b) 3c = 3 &times; 15 = 45 &rarr; Not divisible by 4
(c) 2c + 6 = 30 + 6 = 36 &rarr; Divisible by 4
(d) 3c + 1 = 45 + 1 = 46 &rarr; Not divisible by 4
Try next: c = 25
(a) 2c = 50 &rarr; Not divisible by 4
(b) 3c = 75 &rarr; Not divisible by 4
(c) 2c + 6 = 56 &rarr;Divisible by 4
(d) 3c + 1 = 76 &rarr; Not divisible by 4
Hence, option c is correct.

Number Theory

Divisibility Rules

Website Link

Test Your Knowledge

Student Resources


M Question 1	⏱ 0
Ravi is organizing chairs for a conference. He has a certain number of chairs, denoted by c, such that: c > 10, the number of chairs c is divisible by 5 but it is not divisible by 10. Based on this, which of the following total numbers of guests (in integers) can he arrange evenly into rows of 4? (a) 2c (b) 3c (c) 2c + 6 (d) 3c + 1