Question 95
Let x and y be positive real numbers such that
$$\log_{5}{(x + y)} + \log_{5}{(x - y)} = 3,$$ and $$\log_{2}{y} - \log_{2}{x} = 1 - \log_{2}{3}$$. Then $$xy$$ equals
Solution
We have, $$\log_{5}{(x + y)} + \log_{5}{(x - y)} = 3$$
=> $$x^2-y^2=125$$......(1)
$$\log_{2}{y} - \log_{2}{x} = 1 - \log_{2}{3}$$
=>$$\ \frac{\ y}{x}$$ = $$\ \frac{\ 2}{3}$$
=> 2x=3y => x=$$\ \frac{\ 3y}{2}$$
On substituting the value of x in 1, we get
$$\ \frac{\ 5x^2}{4}$$=125
=>y=10, x=15
Hence xy=150
Video Solution
Create a FREE account and get:
- All Quant CAT complete Formulas and shortcuts PDF
- 35+ CAT previous papers with video solutions PDF
- 5000+ Topic-wise Previous year CAT Solved Questions for Free
CAT Quant Questions | CAT Quantitative Ability
CAT Remainders QuestionsCAT Mensuration QuestionsCAT Time And Work QuestionsCAT Probability, Combinatorics QuestionsCAT Percentages Questions
CAT DILR Questions | LRDI Questions For CAT
CAT Quant Based LR QuestionsCAT Table with Missing values QuestionsCAT Scheduling QuestionsCAT Data Interpretation Basics QuestionsCAT DI Miscellaneous Questions
