Home › UP Board Class 10 › mathematics › numbertheory › How many positive integers less than 1000 are di…
How many positive integers less than 1000 are divisible by neither 2 nor 5?
A300
B500
C450
D400
Answer & Solution
Correct answer: D. 400
From 1 to 999: divisible by 2 → 499, by 5 → 199, by 10 → 99. By inclusion-exclusion, divisible by 2 or 5 $= 499+199-99 = 599$. Neither $= 999 - 599 = 400$.
Related questions
If $3^x = 4^y = 12^z$ with $x,y,z$ nonzero, then $\dfrac{1}{z}$ equalsThe HCF of two consecutive positive integers isTwo positive integers have HCF 9 and LCM 90. If one number is 18, the other isThe remainder when $2^{100}$ is divided by 7 isWhich of the following is an irrational number?If $a = 2^3 \cdot 3^4 \cdot 5^2$ and $b = 2^4 \cdot 3^2 \cdot 7$, then $\dfrac{\text{LCM}(If $n$ is a natural number, then $6^n$ can never end with the digitThe smallest positive integer that is divisible by every integer from 1 to 10 is