## anonymous one year ago If 10^x equals 0.1 percent of 10^y, where x and y are integers, which of the following must be true? A. y=x+2 B. y=x+3 C. x=y+3 D. y=1,000x E. x=1,000y

1. kropot72

The given relationship between x and y can be expressed as $\large 10^{x}=\frac{10^{y}}{1000}\ .........(1)$ Does that make sense as a first step towards a solution?

2. anonymous

hmmmm.... why?

3. anonymous

wait nvm i get it

4. anonymous

5. anonymous

wait why is the 1 at the end? what is that?

6. kropot72

To find 0.1% of a quantity, we divide the quantity by 1000. The (1) at the end is simply a reference number for this equation. We need to use equation (1) to form another equation.

7. anonymous

okay

8. kropot72

Next step is to take logs of both sides of equation (1). Please do that and post your result.

9. anonymous

Hey we don't use logs for this question

10. kropot72

Who says we don't use logs?

11. anonymous

The GRE book I'm using ... There isn't any logs at all

12. kropot72

Does the book suggest a method of solving that doesn't use logs?

13. anonymous

well the solutio|dw:1436987482723:dw|n is this but i don't understand it....

14. kropot72

I understand the method which gives a correct result. It expresses 1/1000 as $\large \frac{1}{1000}=\frac{1}{10^{3}}=10^{-3}$ Do you understand this step?

15. kropot72

So equation (1) now becomes $\large 10^{x}=10^{y} \times 10^{-3}\ ......(2)$

16. kropot72

Now we use the rule of indices $\large a^{b} \times a^{c}=a^{b+c}$ to turn equation (2) into $\large 10^{x}=10^{y-3}\ .............(3)$ which get the result that x = y - 3 ............(4)

17. kropot72

Equation (4) can be rearranged to make one of the given answer choices.

18. kropot72