Show that exactly one of the numbers n, n + 2 or n + 4 is divisible by 3.
This is a question of CBSE Sample Paper - Class 10 - 2017/18.
You can download the question paper here https://www.teachoo.com/cbse/sample-papers/
Last updated at Sept. 14, 2018 by Teachoo
This is a question of CBSE Sample Paper - Class 10 - 2017/18.
You can download the question paper here https://www.teachoo.com/cbse/sample-papers/
Transcript
Question 13 Show that exactly one of the numbers n, n + 2 or n + 4 is divisible by 3. Theory As per Euclid’s Division Lemma If a and b are 2 positive integers, then a = bq + r where 0 ≤ r < b If b = 3, a = 3q + r where 0 ≤ r < 3 So, r = 0, 1, 2 ∴ Numbers = 3q + 0, 3q + 1, 3q + 2 Let’s assume n = 3q, 3q + 1, 3q + 2 Now, we check whether n, n + 2, n + 4 is divisible by 3 If n = 3q n = 3q Since n can be divided by 3 It is divisible by 3 n + 2 = 3q + 2 Putting q = 1 n + 2 = 3(1) + 2 = 5 Since 5 is not divisible by 3 n + 2 is not divisible by 3 n + 4 = 3q + 4 Putting q = 1 n + 4 = 3(1) + 4 = 7 Since 7 is not divisible by 3 n + 4 is not divisible by 3 If n = 3q + 1 n = 3q + 1 Putting q = 1 n = 3(1) + 1 = 4 Since 4 is not divisible by 3 n is not divisible by 3 n + 2 = 3q + 1 + 2 n + 2 = 3q + 3 n + 2 = 3(q + 1) Since n + 2 can be divided by 3 It is divisible by 3 n + 4 = 3q + 1 + 4 n + 4 = 3q + 5 Putting q = 1 n + 4 = 3(1) + 5 = 8 Since 8 is not divisible by 3 n + 4 is not divisible by 3 n + 4 = 3q + 1 + 4 n + 4 = 3q + 5 Putting q = 1 n + 4 = 3(1) + 5 = 8 Since 8 is not divisible by 3 n + 4 is not divisible by 3 If n = 3q + 2 n = 3q + 2 Putting q = 1 n = 3(1) + 2 = 5 Since 5 is not divisible by 3 n is not divisible by 3 If n = 3q + 1 n = 3q + 1 Putting q = 1 n = 3(1) + 1 = 4 Since 4 is not divisible by 3 n + 2 is not divisible by 3 n + 4 = 3q + 2 + 4 n + 4 = 3q + 6 n + 4 = 3(q + 2) Since n + 4 can be divided by 3 It is divisible by 3 We see that in all 3 cases, Exactly one of the numbers n, n + 2, n + 4 is divisible by 3 Hence proved
CBSE Class 10 Sample Paper for 2018 Boards
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Question 13 You are here
Question 14
Question 15
Question 16
Question 17
Question 18
Question 19
Question 20
Question 21
Question 22
Question 23
Question 24
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Question 26
Question 27
Question 28
Question 29
Question 30
CBSE Class 10 Sample Paper for 2018 Boards
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