ABC26GN1709 · Problems on Numbers

Subject: General Aptitude · Chapter: Problems on Numbers · Exam: 2003 · Marks: · Difficulty:

The difference between two positive integers is 3. If the sum of their squares is 369, then the sum of the numbers is

(a)25

(b)27

(c)33

(d)81

Answer

Answer (as printed): B

Explanation

Let the numbers be x and (x + 3). Then, x2 + (x + 3)2 = 369 ⇔ x2 + x2 + 9 + 6x = 369 ⇔ 2x2 + 6x – 360 = 0 ⇔ x2 + 3x – 180 = 0 ⇔ (x + 15) (x – 12) = 0 ⇔ x = 12. So, the numbers are 12 and 15. \ Required sum = (12 + 15) = 27.

Explanation as extracted from the printed page; notation may be imperfect.

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