UPSC Exam > UPSC Questions > What is X in the sequence 4, 196, 16, 144, 36...
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What is X in the sequence 4, 196, 16, 144, 36, 100, 64, X?
- a)48
- b)64
- c)125
- d)256
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
What is X in the sequence 4, 196, 16, 144, 36, 100, 64, X?a)48b)64c)12...
Solution:
The sequence seems to be a mix of squares of even numbers and squares of odd numbers. Let's analyze it step by step.
Step 1: 4 is the square of 2, which is an even number.
Step 2: 196 is the square of 14, which is an even number.
Step 3: 16 is the square of 4, which is an even number.
Step 4: 144 is the square of 12, which is an even number.
Step 5: 36 is the square of 6, which is an even number.
Step 6: 100 is the square of 10, which is an even number.
Step 7: 64 is the square of 8, which is an even number.
Step 8: Therefore, the next number in the sequence should be the square of an even number.
Step 9: The only even number left in the sequence is 4, and its square is 16. However, 16 has already occurred in the sequence.
Step 10: The next even square after 16 is 36, which has already occurred in the sequence.
Step 11: The next even square after 36 is 64, which is the answer.
Therefore, the missing number in the sequence is 64. Hence, the correct answer is option 'B'.
The sequence seems to be a mix of squares of even numbers and squares of odd numbers. Let's analyze it step by step.
Step 1: 4 is the square of 2, which is an even number.
Step 2: 196 is the square of 14, which is an even number.
Step 3: 16 is the square of 4, which is an even number.
Step 4: 144 is the square of 12, which is an even number.
Step 5: 36 is the square of 6, which is an even number.
Step 6: 100 is the square of 10, which is an even number.
Step 7: 64 is the square of 8, which is an even number.
Step 8: Therefore, the next number in the sequence should be the square of an even number.
Step 9: The only even number left in the sequence is 4, and its square is 16. However, 16 has already occurred in the sequence.
Step 10: The next even square after 16 is 36, which has already occurred in the sequence.
Step 11: The next even square after 36 is 64, which is the answer.
Therefore, the missing number in the sequence is 64. Hence, the correct answer is option 'B'.
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What is X in the sequence 4, 196, 16, 144, 36, 100, 64, X?a)48b)64c)12...
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What is X in the sequence 4, 196, 16, 144, 36, 100, 64, X?a)48b)64c)125d)256Correct answer is option 'B'. Can you explain this answer?
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