Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

GATE | GATE-CS-2005 | Question 44

  • Difficulty Level : Easy
  • Last Updated : 28 Jun, 2021

What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs (a, b) and (c, d) in the chosen set such that “a ≡ c mod 3” and “b ≡ d mod 5”
(A) 4
(B) 6
(C) 16
(D) 24


Answer: (C)

Explanation:
a = c mod 3 (given)
Thus, ‘a’ can be any one of these values : 0, 1, 2

b = d mod 5 (given)
Thus, ‘b’ can be any one of these values : 0, 1, 2, 3, 4

Thus, ordered pair for (a, b) are :
(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4)

Therefore, ordered pair (a, b) has 15 combinations and ordered pair (c, d) has 1 combination.
Total combinations = 15 + 1 = 16

 
Hence, option (C) is correct.

 
Please comment below if you find anything wrong in the above post.


Quiz of this Question

Attention reader! Don’t stop learning now.  Practice GATE exam well before the actual exam with the subject-wise and overall quizzes available in GATE Test Series Course.

Learn all GATE CS concepts with Free Live Classes on our youtube channel.

My Personal Notes arrow_drop_up
Recommended Articles
Page :