| The difference of the squares of two consecutive odd integers is divisible by which of the following integers? |
A) 3
B) 6
C) 7
D) 8
Correct Answer: D
Solution :
| Let the two consecutive odd integers be \[(2n+3)\]and \[(2n+1).\] |
| Then, \[{{(2n+3)}^{2}}-{{(2n+1)}^{2}}\] |
| \[=(4{{n}^{2}}+9+12n)-(4{{n}^{2}}+1+4n)\] |
| \[=8+8n=8\,(1+n)\] |
| Clearly, the number is divisible by 8. |
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