The number \(n=10^x+10^y+10^z\) is a sum of powers of 10 . Each term contributes a digit (1,2, or 3) at a particular position, with zeros everywhere else. The "total number of zeros" counts every zero digit anywhere to the left of the decimal point.



Testing Each Option

Option A: x+y zeros
Let \(x=1, y=1, z=3\). Then:


\(10^1+10^1+10^3=10+10+1000=1020\)



The number 1020 has two zeros (in the units place and hundreds place), and x+y=1+1= 2.

Option B: y-z zeros
Let x=2, y=2, z=1. Then: gmatclub


\(10^2+10^2+10^1=100+100+10=210\)



The number 210 has one zero, and y-z=2-1=1 .

Option C: z zeros

Let x=2, y=2, z=2. Then: gmatclub


\(10^2+10^2+10^2=300\)



The number 300 has two zeros, and z=2 .

Answer

All three options - \(\mathbf{A}(x+y), \mathbf{B}(y-z)\), and \(\mathbf{C}(z)\) - can each represent the number of zeros in $n$ for appropriate choices of x, y, and z. The key insight is that you only need to test simple small-exponent examples to verify each case, since the question asks what could be true, not what is always true.