1955 AMC 12 Problem 37
Attempt Problem 37 of the 1955 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1955 AMC 12 solutions, or check the answer key.
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37.
A three-digit number has, from left to right, the digits and with When the number with the digits reversed is subtracted from the original number, the units’ digit in the difference is The next two digits, from right to left, are:
and
and
impossible to tell
and
and
Answer: B
Small Hint:
Subtract algebraically:
Big Hint:
Find the digit for which ends in
Solution:
The difference is Since is an integer from through and the units digit is we need This gives so the difference is Moving from right to left after the units digit the next digits are and
Thus, the correct answer is B.
Problem 37 in Other Years
1950 AMC 12 · 1951 AMC 12 · 1952 AMC 12 · 1953 AMC 12 · 1954 AMC 12 · 1956 AMC 12 · 1957 AMC 12 · 1958 AMC 12 · 1959 AMC 12 · 1960 AMC 12 · 1961 AMC 12 · 1962 AMC 12 · 1963 AMC 12 · 1964 AMC 12 · 1965 AMC 12 · 1966 AMC 12 · 1967 AMC 12