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If each of the odd-place digits in the number 76835 is decreased by '1' and each of the even-place digits is increased by '1' then the sum of the digits in the new number is

  • A.26
  • B.29
  • C.28
  • D.None of the above

Answer: C

The sum of the digits is 28.

Number the places of 76835 from the left: 7 (1st), 6 (2nd), 8 (3rd), 3 (4th), 5 (5th). The odd places hold 7, 8 and 5, which each decrease by 1 to 6, 7 and 4. The even places hold 6 and 3, which each increase by 1 to 7 and 4.

The new number is 6 7 7 4 4, and its digits add up to

\[ 6 + 7 + 7 + 4 + 4 = 28 \]

A quicker check: three digits fall by 1 and two rise by 1, so the original sum of 29 falls by 1 to 28. 29 is the unchanged sum, and 26 comes from decreasing every digit.

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