Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-49

The sum of two odd numbers is 38 and their product is 325. What is three times the larger number? [IBPS (SO) 2014]

A) 42

B) 39

C) 75

D) 72

E) 78

Correct Answer: C

Solution :

Let the first odd number be x.

Then, second odd number is y.

Then, \[x+y=38\] ...(i)

and \[x\times y=325\]

\[{{(x-y)}^{2}}={{(x+y)}^{2}}-4xy\]

\[={{(38)}^{2}}-4\times 325\]

\[=1444-1300\]

\[x-y=\sqrt{144}\]

or \[x-y=12\] (ii)

On solving Eqs. (i) and (ii), we get

\[2x=50\]\[\Rightarrow \]\[x=25\]and \[y=13\]

\[\therefore \]Required number \[=3\times 25=75\]

Alternate Method

We can directly do it through eliminating options as

If \[x=14\]

and \[y=24\]

Then, \[24\times 14\ne 325\]

If \[x=13\]

and \[y=25\]

Then, \[13\times 25=325\]

\[\therefore \]Larger number \[=25\]

\[\therefore \]Correct option is 75,

Its product is 325 but larger number is 25 here.