Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
First 100 multiples of 10 i.e. 10, 20, 30, 1000 are multiplied together. The number of zeros at the end of the product will be
(a)100
(b)111
(c)124
(d)125
Answer
Answer (as printed): C
Explanation
Let $N=10 \times 20 \times 30 \times$...... $\times 1000=10^{100} \times(1 \times 2 \times 3$ $$\times 4 \times \ldots \ldots \ldots 100)=10^{100} \times 100!$$ Number of zeros in 100 ! = Highest power of 5 in 100 ! $$=\left[\frac{100}{5}\right]+\left[\frac{100}{5^{2}}\right]=20+4=24 .$$ ∴ Number of zeros in $N=100+24=124$.
Explanation as extracted from the printed page; notation may be imperfect.