Daily Practice

A12 B12.5 C13 D13.5 E14</math>

Ahspace{.05in}frac{9}{23}<frac{7}{21}<frac{5}{19}quadtextbf{(B)}hspace{.05in}frac{5}{19}<frac{7}{21}<frac{9}{23}quadtextbf{(C)}hspace{.05in}frac{9}{23}<frac{5}{19}<frac{7}{21} </imath> C<imath> textbf{(D)}hspace{.05in}frac{5}{19}<frac{9}{23}<frac{7}{21}quadtextbf{(E)}hspace{.05in}frac{7}{21}<frac{5}{19}<frac{9}{23} </imath>

A10 B12 C15 D17 E19

A10 B15 C25 D50 E82</math>

A15 B16 C17 D18 E20</math> == Solution 1== If we start off with the first digit, we know that it can't be <math>9</math> since <math>9</math> is not a factor of <math>120</math>. We go down to the digit <math>8</math>, which does work since it is a factor of <math>120</math>. Now, we have to know what digits will take up the remaining four spots. To find this result, just divide <math>frac{120}{8}=15</math>. The next place can be <math>5</math>, as it is the largest factor, aside from <math>15</math>. Consequently, our next three values will be <math>3,1</math> and <math>1</math> if we use the same logic. Therefore, our five-digit number is <math>85311</math>, so the sum is <math>8+5+3+1+1=18implies boxed{textbf{(D) }18}</math>. == Solution 2 (Factorial) == <math>120</math> is <math>5!</math>, so we have <math>(5)(4)(3)(2)(1) = 120</math>. (Alternatively, you could identify the prime factors <math>(5)(3)(2)(2)(2) = 120</math>.) Now look for the largest digit you can create by combining these factors. <math>8=4 cdot 2</math> Use this largest digit for the ten-thousands place: <math>8</math>_ , _ _ _ Next you use the <math>5</math> and the <math>3</math> for the next places: <math>85,3</math> _ _ (You can't use <math>3 cdot 2=6</math> because the <math>2</math> was used to make <math>8</math>.) Fill the remaining places with 1: <math>85,311</math> <math> = (5)(8)(3)(1)(1) =120</math> <math>8+5+3+1+1=boxed{textbf{(D) }18}</math>. ==Video Solution (CREATIVE ANALYSIS!!!)== https://youtu.be/zxEO6amczPU ~Education, the Study of Everything ==Video Solutions== https://youtu.be/IAKhC_A0kok https://youtu.be/7an5wU9Q5hk?t=13 https://youtu.be/Q5YrDW62VDU ~savannahsolver