Difference between revisions of "1999 CEMC Gauss (Grade 7) Problems/Problem 14"

Latest revision as of 14:02, 15 September 2025

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-==Problem==
+#Redirect [[1999 CEMC Gauss (Grade 8) Problems/Problem 11]]
-Which of the following is an odd integer, contains the digit <math>5</math>, is divisible by <math>3</math>, and lies between <math>12^2</math> and <math>13^2</math>?
-<math>\text{(A)}\ 105 \qquad \text{(B)}\ 147 \qquad \text{(C)}\ 156 \qquad \text{(D)}\ 165 \qquad \text{(E)}\ 175 </math>
-==Solution==
-<math>156</math> is [[even]], so it cannot be the answer.
-<math>147</math> does not contain the digit <math>5</math>, so it can be eliminated. This means the answer must be A, D, or E.
-We have <math>12^2 = 144</math> and <math>13^2 = 169</math>. The only remaining answer that is between those two numbers is <math>\boxed {\textbf {(D)} 165}</math>.