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16 Sep 2014, 00:54
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A
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Difficulty:
15%
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Question Stats:
86% (01:39) correct
14%
(01:59)
wrong
based on 69
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How many positive four-digit integers consist only of the digits 1 or 0 and have the property that the sum of the first two digits is equal to the sum of the last two digits?
A. 3
B. 4
C. 8
D. 10
E. 12
A. 3
B. 4
C. 8
D. 10
E. 12
16 Sep 2014, 00:55
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Official Solution:
How many positive four-digit integers consist only of the digits 1 or 0 and have the property that the sum of the first two digits is equal to the sum of the last two digits?
A. 3
B. 4
C. 8
D. 10
E. 12
The sum of the first two digits (or the last two) cannot be 0, as 0000 doesn't qualify as a four-digit integer.
When the sum of the first two digits is 1, considering that the first digit cannot be 0, we have two possible combinations: 1001 and 1010.
If the sum of the initial two digits is 2, the only valid combination is 1111.
Thus, there are three numbers that meet the criteria: 1001, 1010, and 1111.
Answer: A
How many positive four-digit integers consist only of the digits 1 or 0 and have the property that the sum of the first two digits is equal to the sum of the last two digits?
A. 3
B. 4
C. 8
D. 10
E. 12
The sum of the first two digits (or the last two) cannot be 0, as 0000 doesn't qualify as a four-digit integer.
When the sum of the first two digits is 1, considering that the first digit cannot be 0, we have two possible combinations: 1001 and 1010.
If the sum of the initial two digits is 2, the only valid combination is 1111.
Thus, there are three numbers that meet the criteria: 1001, 1010, and 1111.
Answer: A
18 Oct 2023, 10:10
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
