Bunuel wrote:

If z is a positive integer and \(y = 6.038 * 10^{z}\), what is the value of z?

(1) \(6500 < y < 65,000\)

(2) \(10^{4}< y < 10^{5}\)

Target question: What is the value of z? Given: z is a positive integer and y = (6.038)(10^z) Since z is a positive integer, let's see how different values of z affect the value of y

Case a: z = 1: y = (6.038)(10^1) = (6.038)(10) = 60.38

Case b: z = 2: y = (6.038)(10^2) = (6.038)(100) = 603.8

Case c: z = 3: y = (6.038)(10^3) = (6.038)(1,000) = 6,038

Case d: z = 4: y = (6.038)(10^4) = (6.038)(10,000) = 60,380

Case e: z = 5: y = (6.038)(10^5) = (6.038)(100,000) = 603,800

Case e: z = 6: y = (6.038)(10^6) = (6.038)(1,000,000) = 6,038,000

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So,

y can equal 60.38 or 603.8 or 6,038 or 60,380 or 603,800 or 6,038,000 or . . . etc Statement 1: 6500 < y < 65,000 Only one possible value of y lies between 6500 and 65,000

That value is 60,380 (case d)

So, y MUST equal 60,380, which mean

z MUST equal 4Since we can answer the

target question with certainty, statement 1 is SUFFICIENT

Statement 2: 10^4 < y < 10^510^4 = 10,000 and 10^5 = 100,000

Only one possible value of y lies between 10,000 and 100,000

That value is 60,380 (case d)

So, y MUST equal 60,380, which mean

z MUST equal 4Since we can answer the

target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,

Brent

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