Question

Find the odd one among: 49, 121, 169, 225, 289, 361
(a) 225
(b) 121
(c) 49
(d) 361

Answer 1

Hint:First of all, write all the terms in the form of their square roots that is \[49\text{ as }{{\left( 7 \right)}^{2}},121\text{ as }{{\left( 11 \right)}^{2}},169\text{ as }{{\left( 13 \right)}^{2}}\] , etc. Now, observe the difference between the square roots and wherever it is different would be the odd term.

Complete step-by-step answer:
Here, we have to find the odd one among: 49, 121, 169, 225, 289, 361. Let us observe the given sequence carefully
49, 121, 169, 225, 289, 361
In the above sequence, we can write different terms as follows:
\[49=7\times 7={{\left( 7 \right)}^{2}}\]
\[121=11\times 11={{\left( 11 \right)}^{2}}\]
\[169=13\times 13={{\left( 13 \right)}^{2}}\]
\[225=15\times 15={{\left( 15 \right)}^{2}}\]
\[289=17\times 17={{\left( 17 \right)}^{2}}\]
\[361=19\times 19={{\left( 19 \right)}^{2}}\]
So, we get our sequence as,
\[{{7}^{2}},{{11}^{2}},{{13}^{2}},{{15}^{2}},{{17}^{2}},{{19}^{2}}\]
In the above sequence, we can see that between any terms inside the sequence and its previous terms, the difference is 2, that is,
19 – 17 = 2
17 – 15 = 2
15 – 13 = 2
13 – 11 = 2
11 – 7 = 4
Here, we can see that all the differences are equal to 2 except (11 – 7) which is equal to 4. So, our odd term is \[{{7}^{2}}=49\]. In place of \[{{7}^{2}}\], if it would have been \[{{\left( 9 \right)}^{2}}\], then it would be a proper sequence because then 11 – 9 = 2 which is the same as the other differences.
Hence, the option (c) is the right answer.

Note: In this question, many students get confused between 7 and 11 while choosing the odd one out among them. So, in this case, students should try to replace each of the terms with other correct values whichever replacement would complete the sequence properly would be the odd one out. For example, in the above question, the replacement of \[{{\left( 7 \right)}^{2}}\text{ with }{{\left( 9 \right)}^{2}}\] would complete the sequence. So, \[{{\left( 7 \right)}^{2}}=49\] would be the odd one out. Likewise, we should do in all odd one out questions.