Question 1133189: In a Maple Street the odd numbers are on one side of the street and the even-numbered houses on the other. On one side of Maple Street there are six houses and one vacant allotment. The sum of the numbers on that side is 38. If a house is built on the vacant allotment its number will be
A. 6
B. 11
C. 13
D. 14
Answer by greenestamps(13198)   (Show Source):
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The sum of the 6 smallest even numbers is 2+4+6+8+10+12 = 42. Since the sum of the 6 house numbers already on the street is 38, the houses in the problem are not even numbers.
The sum of the 6 smallest odd numbers is 1+3+5+7+9+11 = 36. For the sum of the house numbers already on the street to be 38, the house numbers have to be 1, 3, 5, 7, 9, and 13.
So the house number of the newly built house is odd -- either answer B (11) or answer C (13). But 13 is the number of one of the houses already on the street.
So the house number of the newly built house will be 11 -- answer B.
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