Difference between revisions of "2011 AMC 10B Problems/Problem 5"
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− | == Problem | + | == Problem== |
In multiplying two positive integers <math>a</math> and <math>b</math>, Ron reversed the digits of the two-digit number <math>a</math>. His erroneous product was <math>161</math>. What is the correct value of the product of <math>a</math> and <math>b</math>? | In multiplying two positive integers <math>a</math> and <math>b</math>, Ron reversed the digits of the two-digit number <math>a</math>. His erroneous product was <math>161</math>. What is the correct value of the product of <math>a</math> and <math>b</math>? | ||
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== Solution == | == Solution == | ||
− | + | We have <math>161 = 7 \cdot 23.</math> Since <math>a</math> has two digits, the factors must be <math>23</math> and <math>7,</math> so <math>a = 32</math> and <math>b = 7.</math> Then, <math>ab = 7 \times 32 = \boxed{\mathrm{(E) \ } 224}.</math> | |
+ | |||
+ | ==Video Solution== | ||
+ | https://youtu.be/b3Vorx_bnpU | ||
+ | |||
+ | ~savannahsolver | ||
+ | |||
+ | == See Also== | ||
+ | |||
+ | {{AMC10 box|year=2011|ab=B|num-b=4|num-a=6}} | ||
+ | {{MAA Notice}} |
Latest revision as of 12:29, 7 November 2020
Contents
Problem
In multiplying two positive integers and , Ron reversed the digits of the two-digit number . His erroneous product was . What is the correct value of the product of and ?
Solution
We have Since has two digits, the factors must be and so and Then,
Video Solution
~savannahsolver
See Also
2011 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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