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. |
You need to login to perform this action.
You will be redirected in
3 sec