The GATE Grind

GATE 2026 DA – Question 7

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20.

Ignoring permutations, the number of ways to pick these five integers is _____

  1. 0
  2. 1
  3. 2
  4. 3

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) 1

Explanation

Write the integers in order as $a \le b \le c \le d \le e$. The mean is 12, so they add up to 60, and the median is $c = 18$. The mode is 20 and it is the only mode, so 20 appears more often than any other value, and only $d$ and $e$ can equal it (as $c = 18$). So $d = e = 20$ and $a + b = 60 - 18 - 40 = 2$. The pairs are $(0, 2)$ and $(1, 1)$. The pair $(1, 1)$ makes 1 appear twice, which would give a second mode, so only $(0, 2)$ works, giving 0, 2, 18, 20, 20. There is exactly 1 way.