Difference between revisions of "1967 AHSME Problems/Problem 1"

Revision as of 21:36, 5 June 2012

The three-digit number $2a3$ is added to the number $326$ to give the three-digit number $5b9$ . If $5b9$ is divisible by 9, then $a+b$ equals

$\text{(A)}\ 2\qquad\text{(B)}\ 4\qquad\text{(C)}\ 6\qquad\text{(D)}\ 8\qquad\text{(E)}\ 9$

If $5b9$ is divisible by $9$ , this must mean that $5 + b + 9$ is a multiple of $9$ . So, $5 + b + 9 = 9, 18, 27, 36...$ .

Because $5 + 9 = 14$ and $b$ is in between 0 and 9,

$$ (Error compiling LaTeX. Unknown error_msg)5 + b + 9 = 18 $and$ b = 4$$ (Error compiling LaTeX. Unknown error_msg)

$2a3 + 326 = 549$ , so $2a3 = 549 - 326$ $a = 2$

$a + b = 6$ which is answer choice $\boxed{C}$ .

1967 AHSC (Problems • Answer Key • Resources)
Preceded by First Question	Followed by Problem 2
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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50
All AHSME Problems and Solutions

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	Because <math>5 + 9 = 14</math> and <math>b</math> is in between 0 and 9,		Because <math>5 + 9 = 14</math> and <math>b</math> is in between 0 and 9,
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	<math></math>5 + b + 9 = 18<math> and </math>b = 4<math></math>		<math></math>5 + b + 9 = 18<math> and </math>b = 4<math></math>