Question : The product of two positive integers is 2048, and one of them is twice the other. The smaller number is:
Option 1: 32
Option 2: 64
Option 3: 16
Option 4: 1024
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Correct Answer: 32
Solution :
Given:
1st number is twice of the 2nd number.
Let the two numbers be $x$ and $2x$ respectively.
According to the question,
$x\times 2x = 2048$
⇒ $2x^{2} = 2048$
⇒ $x^{2} = \frac{2048}{2} = 1024$
⇒ $x = \sqrt{1024} = 32$
So, the smaller number is 32.
Hence, the correct answer is 32.
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