If 2x + 2y = 222, what is the value of x + y?
Solution
Correct Answer: Option D
Here,,
2x + 2y=222
⇒ 2x(1 + 2y - x)=222
2x must be a power of 2 that divides 222
(1 + 2y - x) must be a power of 2
Only way (1 + 2y - x) is a power of 2 is if, y - x = 0
So, y - x = 0
⇒ y = x
∴ 2x + 2x = 222
⇒ 2.2x = 222
⇒ 21 + x=222
⇒ 1 + x = 22
∴ x = 21
∴ x + y = 21 + 21 = 42
2x + 2y=222
⇒ 2x(1 + 2y - x)=222
2x must be a power of 2 that divides 222
(1 + 2y - x) must be a power of 2
Only way (1 + 2y - x) is a power of 2 is if, y - x = 0
So, y - x = 0
⇒ y = x
∴ 2x + 2x = 222
⇒ 2.2x = 222
⇒ 21 + x=222
⇒ 1 + x = 22
∴ x = 21
∴ x + y = 21 + 21 = 42
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