Which number should replace the question mark?
0, 3, 4, 7, 8, ?

13

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11

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14

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15

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Solution

The correct option is B $11$

The original series that we have to consider is 1, 3, 5, 7, 9, .....
Subtract '1' from the alternate terms of the above series starting from the 1st term, we get
1-1, 3, 5-1, 7, 9-1, 11, 13-1,.....
The series is 0, 3, 4, 7, 8, 11,....
So, the next term after 8 is 11.

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Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

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Which number should replace the question mark?0, 3, 4, 7, 8, ?

The correct option is B 11The original series that we have to consider is 1, 3, 5, 7, 9, .....Subtract '1' from the alternate terms of the above series starting from the 1st term, we get1-1, 3, 5-1, 7, 9-1, 11, 13-1,.....The series is 0, 3, 4, 7, 8, 11,....So, the next term after 8 is 11.

Which number should replace the question mark?
0, 3, 4, 7, 8, ?

The correct option is B $11$

The original series that we have to consider is 1, 3, 5, 7, 9, .....
Subtract '1' from the alternate terms of the above series starting from the 1st term, we get
1-1, 3, 5-1, 7, 9-1, 11, 13-1,.....
The series is 0, 3, 4, 7, 8, 11,....
So, the next term after 8 is 11.