Miscellaneous Question 66
- The difference between two numbers is 18 and their H.C.F. and LC.M. are 6 and 168 respectively. What is the sum of squares of these two numbers?
(1) 2280
(2) 2260
(3) 2420
(4) 2340
(5) 2380
(IBPS Specialist Officer CWE (Prelim Exam) 31.01.2019)
Show Answer
Correct Answer: 66. (4)
Solution: 66. (4) Let the numbers be $x$ and $x$ $+18$
$\therefore$ Product of numbers
$=\mathrm{HCF} \times \mathrm{LCM}$
$\Rightarrow x(x+18)=6 \times 168$
$=6 \times 4 \times 42$
$\Rightarrow x(x+18)=24 \times 42$
$=24(24+18)$
$\therefore x=24$
$\therefore$ Second number
$=24+18=42$
$\therefore$ Required sum
$=(24)^{2}+(42)^{2}$
$=576+1764=2340$
OR
Numbers $=a$ and $b$ where $a>b$
$\therefore a-b=18$ and $a b=6 \times 168$
$\therefore a^{2}+b^{2}=(a-b)^{2}+2 a b$
$=(18)^{2}+2 \times 6 \times 168$
$=324+2016=2340$
BETA
