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The “hash” of a three-digit integer with three distinct digi
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23 Jan 2020, 10:54
23 Jan 2020, 10:54
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The “hash” of a three-digit integer with three distinct digits is defined as the result of interchanging its units and hundreds digits. The absolute value of the difference between a three-digit integer and its hash must be divisible by which of the following integers?
A. 9
B. 7
C. 5
D. 4
E. 2
Kudos for the right answer and explanation
A. 9
B. 7
C. 5
D. 4
E. 2
Kudos for the right answer and explanation
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Re: The “hash” of a three-digit integer with three distinct digi
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23 Jan 2020, 12:01
23 Jan 2020, 12:01
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Question:
The “hash” of a three-digit integer with three distinct digits is defined as the result of interchanging its units and hundreds digits. The absolute value of the difference between a three-digit integer and its hash must be divisible by which of the following integers?
A. 9
B. 7
C. 5
D. 4
E. 2
Solution:
Let the 3-digit number be N = abc where a is the hundreds digit, b is the tens digit and c is the units digit
Thus, we can write the number as: N = 100a + 10b + c
Thus, "hash" N i.e. #N = 100c + 10b + a (since we have to interchange the units and hundreds digits keeping the tens digit unchanged)
Thus, absolute value of the difference: |N - #N| = |99a - 99c| = 99 * |a - c|
Thus, the difference is divisible by 9 and 11.
Answer A
The “hash” of a three-digit integer with three distinct digits is defined as the result of interchanging its units and hundreds digits. The absolute value of the difference between a three-digit integer and its hash must be divisible by which of the following integers?
A. 9
B. 7
C. 5
D. 4
E. 2
Solution:
Let the 3-digit number be N = abc where a is the hundreds digit, b is the tens digit and c is the units digit
Thus, we can write the number as: N = 100a + 10b + c
Thus, "hash" N i.e. #N = 100c + 10b + a (since we have to interchange the units and hundreds digits keeping the tens digit unchanged)
Thus, absolute value of the difference: |N - #N| = |99a - 99c| = 99 * |a - c|
Thus, the difference is divisible by 9 and 11.
Answer A
Re: The “hash” of a three-digit integer with three distinct digi
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02 Mar 2022, 21:26
02 Mar 2022, 21:26
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