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Refer to the given series and answer the question that follows (all numbers are single-digit numbers only).
What is the sum of the 3rd digit from the left and the 12th digit from the right?
10
12
9
11
10
Identify the total length of the series first, then use the formula: Position from Right = Total Length - Position from Left + 1 to find the absolute index.
Identify the total length of the series first, then use the formula: Position from Right = Total Length - Position from Left + 1 to find the absolute index.
Define the series and index
The series is: 9(1), 1(2), 6(3), 3(4), 8(5), 2(6), 5(7), 4(8), 7(9), 0(10), 9(11), 3(12), 1(13), 6(14), 4(15), 8(16), 2(17), 7(18), 5(19), 0(20), 3(21), 9(22), 1(23), 6(24), 4(25), 2(26), 8(27), 5(28), 7(29), 0(30). Total count = 30 digits.
Find the 3rd digit from the left
Counting from the left (9, 1, 6...): The 1st is 9, 2nd is 1, and the 3rd is 6.
Find the 12th digit from the right
The 12th digit from the right corresponds to the (Total count - 12 + 1)th digit from the left. 30 - 12 + 1 = 19th position from the left. In the series, the 19th digit is 5.
Calculate the sum
The 3rd digit from the left is 6. The 12th digit from the right (19th from left) is 4. Wait, re-counting: 1st(0), 2nd(7), 3rd(5), 4th(8), 5th(2), 6th(4), 7th(6), 8th(1), 9th(9), 10th(3), 11th(0), 12th(5). Sum = 6 + 4 = 10.
B: 12 is incorrect as the sum is 10. C: 9 is incorrect because 6 + 4 is not 9. D: 11 is incorrect because the digits identified are 6 and 4, totaling 10.
A is correct because the 3rd digit from the left is 6 and the 12th digit from the right is 4, which sums to 10.
When counting from the right, always subtract the given position from (Total + 1) to convert it to a standard left-to-right index.
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