Subject: General Aptitude · Chapter: Problems on Numbers · Exam: 2002 · Marks: · Difficulty:
The product of two numbers is 45 and the sum of their squares is 106. The numbers are
(a)3 and 5
(b)5 and 9
(c)5 and 19
(d)45 and 1
Answer
Answer (as printed): B
Explanation
Let the numbers be x and y. Then, xy = 45 and x2 + y2 = 106. ( x + y) = ( x 2 + y 2 ) + 2 xy = 106 + 90 = 196 ⇒ x + y = 14 ( x − y) = ( x 2 + y 2 ) − 2 xy = 106 − 90 = 16 ⇒ x − y = 4 Solving (i) and (ii), we get : x = 9 and y = 5.
Explanation as extracted from the printed page; notation may be imperfect.