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
.
.
.
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