For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 940, what is the maximum possible sum of the length of x and the length of y?	Select:
A) 24
B) 22
C) 16
D) 18
E) 20
we know that : x &gt; 1, y &gt; 1, and x + 3y &lt; 940,   and it is given that length means no of factors.   for any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal.   hence, lets start with smallest no 2.   2^1 =2   2^2 =4   2^3=8   2^4=16   2^5=32   2^6=64   2^7=128   2^8=256   2^9=512   2^10 =1024 (opps//it exceeds 1000, so, x can't be 2^10)   so, max value that X can take is 2^9 , for which haslength of integeris 9.   now, since x =512 ,x+3y&lt;940   so, 3y&lt;428   ==&gt; y&lt;428/3   so, y can take any value which is less than 428/3. and to get the maximum no of factors of smallest integer, we can say y=2^7   for 2^7 has length of integer is 7.   SO, combined together : 9+7= 
<gadget id="calculator">9+7</gadget>
<output>16</output>
16.   16
<result>C</result>
For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 940, what is the maximum possible sum of the length of x and the length of y?