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26 Nov 2021, 01:41
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
50% (01:55) correct
50%
(01:32)
wrong
based on 20
sessions
History
Date
Time
Result
Not Attempted Yet
If a three-digit positive integer has its digits reversed, the resulting three-digit positive integer is less than the original integer by 297. How many such pairs are possible?
A. \(3\)
B. \(6\)
C. \(7\)
D. \(60\)
E. \(70\)
A. \(3\)
B. \(6\)
C. \(7\)
D. \(60\)
E. \(70\)
26 Nov 2021, 01:41
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Official Solution:
If a three-digit positive integer has its digits reversed, the resulting three-digit positive integer is less than the original integer by 297. How many such pairs are possible?
A. \(3\)
B. \(6\)
C. \(7\)
D. \(60\)
E. \(70\)
Say the original three-digit number is \(abc\) and the reversed number is \(cba\).
Given: \(abc-cba=297\);
\((100a + 10b + c ) - (100c + 10b + a) = 297\);
\(a-c=3\).
\((a, c)\) can be (9, 6), (8, 5), (7, 4), (6, 3), (5, 2), and (4, 1) (6 pairs). Notice that (3, 0) pair is not possible: \(c\) cannot be 0 because in this case \(cba\) would be a two-digit number, not a three-digit number as given in the stem.
Finally, don't forget about \(b\). It can take 10 values: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
So, there are a total of \(6*10=60\) numbers are possible.
Answer: D
If a three-digit positive integer has its digits reversed, the resulting three-digit positive integer is less than the original integer by 297. How many such pairs are possible?
A. \(3\)
B. \(6\)
C. \(7\)
D. \(60\)
E. \(70\)
Say the original three-digit number is \(abc\) and the reversed number is \(cba\).
Given: \(abc-cba=297\);
\((100a + 10b + c ) - (100c + 10b + a) = 297\);
\(a-c=3\).
\((a, c)\) can be (9, 6), (8, 5), (7, 4), (6, 3), (5, 2), and (4, 1) (6 pairs). Notice that (3, 0) pair is not possible: \(c\) cannot be 0 because in this case \(cba\) would be a two-digit number, not a three-digit number as given in the stem.
Finally, don't forget about \(b\). It can take 10 values: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
So, there are a total of \(6*10=60\) numbers are possible.
Answer: D
