Difference between revisions of "1996 AJHSME Problems/Problem 1"

Revision as of 20:04, 1 August 2011

How many positive factors of 36 are also multiples of 4?

$\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 6$

The factors of $36$ are $1, 2, 3, 4, 6, 9, 12, 18,$ and $36$ .

The multiples of $4$ up to $36$ are $4, 8, 12, 16, 20, 24, 28, 32$ and $36$ .

Only $4, 12$ and $36$ appear on both lists, so the answer is $3$ , which is option $\boxed{B}$ .

1996 AJHSME (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
All AJHSME/AMC 8 Problems and Solutions

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-b
+==Problem 1==
+How many positive factors of 36 are also multiples of 4?
+<math>\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 6</math>
+==Solution==
+The factors of <math>36</math> are <math>1, 2, 3, 4, 6, 9, 12, 18, </math> and <math>36</math>.
+The multiples of <math>4</math> up to <math>36</math> are <math>4, 8, 12, 16, 20, 24, 28, 32</math> and <math>36</math>.
+Only <math>4, 12</math> and <math>36</math> appear on both lists, so the answer is <math>3</math>, which is option <math>\boxed{B}</math>.
 == See also ==