motion2020 wrote:
KarunMendiratta wrote:
motion2020 wrote:
Find the value of x+y, given \(29!/5^x\) and \(37!/3^y\) are divided evenly and result in the smallest possible whole numbers?
A) 25
B) 24
C) 23
D) 22
E) 21
I have no OA, as this is my made-up entry. Please, kindly contribute your solutions for this question.
motion2020I am glad we are getting new questions. Kindly add the answer to the question now!
To find the maximum value of x, see how many 5s we can have in 29!
one in 5, 10, 15, and 20
two in 25
So, a total of 6 5s
or we can also find it by using;
\(\frac{29}{5^1}+\frac{29}{5^2}+\frac{29}{5^3}+....\)
Consider only whose fractions with Numerator > Denominator
So, \(\frac{29}{5^1}+\frac{29}{5^2}\)
5 integers + 1 integer value = 6 integer values
Similarly, y would be 17
\(\frac{37}{3^1}+\frac{37}{3^2}+\frac{37}{3^3}\)
12 integers + 4 integers + 1 integer value = 17 integer values
x + y = 23
Hence, option C