Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 12
The probability that a randomly chosen positive divisor of $$10^{29}$$ is an integer multiple of $$10^{23}$$ is: $$a^{2} /b^{2} $$, then ‘b - a’ would be:
Solution
Number of factors of $$10^{29} = 2^{29} \times 5^{29}$$
= $$30 \times 30 = 900$$
Factors of $$10^{29}$$ which are multiple of $$10^{23}$$
= $$10^6 = 2^6 \times 5^6$$
= $$7 \times 7 = 49$$
=> Required probability = $$\frac{49}{900} = \frac{a^2}{b^2}$$
=> $$\frac{a}{b} = \frac{7}{30}$$
$$\therefore b - a = 30 - 7 = 23$$
Video Solution
XAT Quant Questions | XAT Quantitative Ability
XAT Number Systems QuestionsXAT Time, Distance and Work QuestionsXAT Venn Diagrams QuestionsXAT Logarithms, Surds and Indices QuestionsXAT Inequalities Questions
XAT DILR Questions | LRDI Questions For XAT
XAT Special Charts QuestionsXAT Quant Based DI QuestionsXAT Arrangement QuestionsXAT Data Interpretation Basics QuestionsXAT Games and Tournamnents Questions
