Subject: General Aptitude · Chapter: Problems on Numbers · Exam: 2014 · Marks: · Difficulty:
The sum of the squares of two positive integers is 100 and the difference of their squares is 28. The 251 sum of the numbers is
(a)12
(b)13
(c)14
(d)15
Answer
Answer (as printed): C
Explanation
Let the positive integers be a and b where a > b. According to the question, 259 a2 + b2 = 100 ….(i) a2 – b2 = 28 ....(ii) By adding (i) and (ii), we get ∴ a 2 + b 2 + a 2 − b 2 = 100 + 28 ⇒ 2a2 = 128 2 128 ⇒a = = 64 2 ∴ a = 64 = 8 From equation (i). 8 2 + b 2 = 100 2 ⇒ b = 100 − 64 = 36 ⇒ b = 36 = 6 ∴ a + b = 8 + 6 = 14
Explanation as extracted from the printed page; notation may be imperfect.