Quantitative Aptitude Ques 1262
Question: The difference between two numbers is 18 and their HCF and LCM are 6 and 168, respectively. What is the sum of squares of the two numbers? [RBI (Assistant) 2015]
Options:
A) 2280
B) 2260
C) 2420
D) 2340
E) 2380
Show Answer
Answer:
Correct Answer: D
Solution:
- Let one number be $ x. $ Then, another number is $ x+18. $ Now, product of two numbers $ =HCF\times LCM $
$ \Rightarrow $ $ x\times (x+18)=6\times 168 $
$ \Rightarrow $ $ x^{2}+18x=1008 $
$ \Rightarrow $ $ x^{2}+18x-1008=0 $
$ \Rightarrow $ $ x^{2}-24x+42x-1008=0 $
$ \Rightarrow $ $ x(x-24)+42x(x-24)=0 $
$ \Rightarrow $ $ (x+42)(x-24)=0 $
$ \Rightarrow $ $ x=24, $ $ x\ne -42 $
$ \therefore $ Another number is 42. Required sum of squares $ ={{(24)}^{2}}+{{(42)}^{2}} $ $ =576+1764=2340 $
BETA
