JEE Main 2022 · 26 Jun · Shift 2 · Mathematics Q25

MathematicsInteger+4 / -1Question 25 of 90

The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is ______.

Your answer

Answer and worked solution

Official answer: 150

Condition. $\gcd(n,36)=2$ means $n\equiv2\pmod4$ and $3\nmid n$ .

Count. 3-digit $n\equiv2\pmod4$ : 102 to 998, 225 numbers. Of these, those divisible by 3 are $\equiv6\pmod{12}$ : 102 to 990, 75 numbers.

Answer. $225-75=150$ .

Answer: 150

JEE Main 2022 · 26 Jun · Shift 2, Mathematics question 25