+0

0
287
2

$$\text{Suppose a is an integer such that 0 \le a \le 14, and 235935623_{74}-a is a multiple of 15. What is a? }$$

Jul 31, 2019

#1
+1

If we convert 235935623 from base 74 to base 10 = 1,835,684,416,755,975. This number is ALREADY  a multiple of 15, which means that a = 0.

Jul 31, 2019
#2
+112010
+1

I just lost a very time consuming answer. But yes that number mod 15 is 0 so  a must be zero.

Here is the short version.

This is a very weirdly presented question.  That number is base 74 (very strange) but 15 is base 10

Use the fact that     74 mod 15 = -1

So when mod 15 of that number is taken we get

2-3+5-9+3-5+6-2+3 = 0

In other words that number is already a multiple of 15 (base10)  so a = 0

Aug 1, 2019