Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-33

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]

A) 2280

B) 2260

C) 2420

D) 2340

E) 2380

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 \[={{(24)}^{2}}+{{(42)}^{2}}\]

\[=576+1764=2340\]