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24 Apr 2022, 16:00
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
61% (01:40) correct
39%
(02:29)
wrong
based on 75
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If y is positive, is \(y^x > 1000\)?
(1) \(y^x = 3000 + y^{(x –1)}\)
(2) \(x > 1000\)
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(1) \(y^x = 3000 + y^{(x –1)}\)
(2) \(x > 1000\)
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
24 Apr 2022, 16:18
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Given y is (+), means y^x means be >0 and the question is more than 1000?
Is y^x > 1000?
stmt (1) says y^x = 3000 + y^(x-1)
is this 3000+ y^(x-1) > 1000?
is y^(x-1) > -2000 if base (y) is positive, the value can never be negative. This is sufficient
stmt (2) allows us to get x and y, both are (+)
You can have a y^(positive infinity) and still have that value less than 1000 and similarly you can have it greater than 1000. Not sufficient.
Choice A
Is y^x > 1000?
stmt (1) says y^x = 3000 + y^(x-1)
is this 3000+ y^(x-1) > 1000?
is y^(x-1) > -2000 if base (y) is positive, the value can never be negative. This is sufficient
stmt (2) allows us to get x and y, both are (+)
You can have a y^(positive infinity) and still have that value less than 1000 and similarly you can have it greater than 1000. Not sufficient.
Choice A
25 Apr 2022, 10:29
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Bunuel
Given: y is positive
Target question: Is \(y^x > 1000\)?
Statement 1: \(y^x = 3000 + y^{(x –1)}\)
Key property: If \(y\) is positive, then \(y^x > 0\) for all values of \(x\)
This means statement 1 is actually telling us that: \(y^x = 3000 + \) some positive value, which means \(y^x > 3000\)
If \(y^x > 3000\), then we can be certain that \(y^x > 1000\)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: \(x > 1000\)
There are several values of x and y that satisfy statement 2. Here are two:
Case a: \(y = 1\) and \(x = 2000\). Since \(1^{2000} = 1\), the answer to the target question is NO, \(y^x\) is not greater than \(1000\)
Case b: \(y = 10\) and \(x = 2000\). In this case, we can clearly see that \(10^{2000}\) is definitely greater than \(1000\)
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
