If y is positive, is y^x > 1000?
(1) y^x = 3000 + y^x-1
(2) x > 1000
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If y is positive, is y^x > 1000?
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NOTE: I added some brackets in statement 1 to show the intent of the question.
Given: y is positive
Statement 1: y^x = 3000 + y^(x-1)
If y is positive (as given), then y raised to ANY power will be POSITIVE.
In other words, y^(x-1) is POSITIVE, which means 3000 + y^(x-1) MUST BE GREATER THAN 3000
This means y^x > 3000, which means 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: x = 1001 and y = 1, in which case y^x = 1^1001 = 1, which is NOT greater than 1000
Case b: x = 1001 and y = 2, in which case y^x = 2^1001, and 2^1001 IS DEFINITELY greater than 1000
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
Target question: Is y^x > 1000?kassim wrote:If y is positive, is y^x > 1000?
(1) y^x = 3000 + y^(x-1)
(2) x > 1000
Given: y is positive
Statement 1: y^x = 3000 + y^(x-1)
If y is positive (as given), then y raised to ANY power will be POSITIVE.
In other words, y^(x-1) is POSITIVE, which means 3000 + y^(x-1) MUST BE GREATER THAN 3000
This means y^x > 3000, which means 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: x = 1001 and y = 1, in which case y^x = 1^1001 = 1, which is NOT greater than 1000
Case b: x = 1001 and y = 2, in which case y^x = 2^1001, and 2^1001 IS DEFINITELY greater than 1000
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
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Matt@VeritasPrep
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S1::
yˣ = 3000 + yˣ�¹
yˣ - yˣ�¹ = 3000
Since yˣ > yˣ�¹ for all y > 1, we must have yˣ > 3000. (Otherwise yˣ�¹ would be negative.)
S2::
x > 1000 simply changes the original question is "Is y¹��� > 1000?" Yes, if y > 1-ish; no, if 1-ish ≥ y.
yˣ = 3000 + yˣ�¹
yˣ - yˣ�¹ = 3000
Since yˣ > yˣ�¹ for all y > 1, we must have yˣ > 3000. (Otherwise yˣ�¹ would be negative.)
S2::
x > 1000 simply changes the original question is "Is y¹��� > 1000?" Yes, if y > 1-ish; no, if 1-ish ≥ y.
