Question 18
If the sum of squares of two numbers is 97, then which one of the following cannot be their product?
Solution
Let 'a' and 'b' are those two numbers.
$$\Rightarrow$$ $$a^2+b^2 = 97$$
$$\Rightarrow$$ $$a^2+b^2-2ab = 97-2ab$$
$$\Rightarrow$$ $$(a-b)^2 = 97-2ab$$
We know that $$(a-b)^2$$ $$\geq$$ 0
$$\Rightarrow$$ 97-2ab $$\geq$$ 0
$$\Rightarrow$$ ab $$\leq$$ 48.5
Hence, ab $$\neq$$ 64. Therefore, option D is the correct answer.
Video Solution
CAT Quant Questions | CAT Quantitative Ability
CAT Mensuration QuestionsCAT Algebra QuestionsCAT Probability, Combinatorics QuestionsCAT Geometry QuestionsCAT PGDBA Calculus Questions
CAT DILR Questions | LRDI Questions For CAT
CAT Scheduling QuestionsCAT DI Miscellaneous QuestionsCAT Special Charts QuestionsCAT Games and Tournamnents QuestionsCAT Table with Missing values Questions
