is x^2 <=2x
statement 1.x>0
statment 2.x<3
answer please?
Answer please
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Hi Vangala Gyaneshwar Reddy,
This DS question is perfect for TESTing VALUES:
We're asked if X^2 is <= 2X. This is a YES/NO question.
Fact 1: X > 0
If X = 1, then the answer to the question is YES.
If X = 3, then the answer to the question is NO.
Fact 1 is INSUFFICIENT
Fact 2: X < 3
If X = 1, then the answer to the question is YES.
If X = -1, then the answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined we know....
0 < X < 3
If X = 1, then the answer to the question is YES.
If X = 2.5, then the answer to the question is NO.
Combined, INSUFFICIENT.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
This DS question is perfect for TESTing VALUES:
We're asked if X^2 is <= 2X. This is a YES/NO question.
Fact 1: X > 0
If X = 1, then the answer to the question is YES.
If X = 3, then the answer to the question is NO.
Fact 1 is INSUFFICIENT
Fact 2: X < 3
If X = 1, then the answer to the question is YES.
If X = -1, then the answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined we know....
0 < X < 3
If X = 1, then the answer to the question is YES.
If X = 2.5, then the answer to the question is NO.
Combined, INSUFFICIENT.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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Question : Is x^2 <=2x ?VANGALA GYANESHWAR REDDY wrote:Is x^2 <=2x?
statement 1.x>0
statment 2.x<3
answer please?
Is x^2 - 2x <= 0?
Rephrased Question : Is x(x - 2) <= 0?
Statement 1) x>0
If x>3 then x and (x-2) both will be positive therefore product of them will be positive.
It answers the Question as NO
For 0<x<2, the answer to the question is YES
INSUFFICIENT
Statement 2) x<3
For 2<x<3, the answer to the question is NO
For 0<x<2, the answer to the question is YES
INSUFFICIENT
Combining the statement we end up checking the range that we have checked already in Statement 2 therefore INSUFFICIENT
Answer: Option E
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Here is how I would solve this one in less than 25 secs. See Image.
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PM me so we can get started.
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Here's an approach.
Let's start with the prompt first. 2x ≥ x² implies 2x - x² ≥ 0, or x(2 - x) ≥ 0.
If x(2-x) ≥ 0, one of three things will be true:
1: x = 0
2: 2 - x = 0, in which case 2 = x
3: Both x and (2 - x) are positive, in which case 2 > x > 0
So we know that if 2 ≥ x ≥ 0, we'll have 2x ≥ x².
On the other hand, if x > 2 or 0 > x, we'll have x² > 2x.
S1 tells us that x > 0, but this isn't enough: if x = 2.5, x² > 2x, but if x = 2, 2x ≥ x².
S2 tells us that 3 > x, but this isn't enough: we could still have x = 2.5 or x = 2.
S1 + S2 tells us that 3 > x > 0, but we still don't have enough: we could still have x = 2.5 or x = 2.
Let's start with the prompt first. 2x ≥ x² implies 2x - x² ≥ 0, or x(2 - x) ≥ 0.
If x(2-x) ≥ 0, one of three things will be true:
1: x = 0
2: 2 - x = 0, in which case 2 = x
3: Both x and (2 - x) are positive, in which case 2 > x > 0
So we know that if 2 ≥ x ≥ 0, we'll have 2x ≥ x².
On the other hand, if x > 2 or 0 > x, we'll have x² > 2x.
S1 tells us that x > 0, but this isn't enough: if x = 2.5, x² > 2x, but if x = 2, 2x ≥ x².
S2 tells us that 3 > x, but this isn't enough: we could still have x = 2.5 or x = 2.
S1 + S2 tells us that 3 > x > 0, but we still don't have enough: we could still have x = 2.5 or x = 2.