Question : The sum of the two numbers is 37 and the difference between their squares is 185, then the difference between the two numbers is:
Option 1: 10
Option 2: 4
Option 3: 5
Option 4: 3
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Correct Answer: 5
Solution : Let the two numbers be X and Y. Given: X + Y = 37 and X 2 – Y 2 = 185 According to the question X 2 – Y 2 = 185 ⇒ (X + Y)(X – Y) = 185 ⇒ 37(X – Y) = 185 $\therefore$ X – Y = 5 Hence, the correct answer is 5.
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