If x > 3, then which of the following must be true?
(1) x > 3
(2) x^2 > 9
(3) x1 > 2
A. (1) only
B. (2) only
C. (1) and (2) only
D. (2) and (3) only
E. (1),(2) and (3)
My only doubt here is with statement 3.
x1 > 3 => x > 3 or x < 1
x > 3 is fine as x > 3 for all those x but if x < 1 then all the values dont saisfy x > 3 for e.g x = 2 then x = 2 < 3 so why should D be the OA.
Pls explain
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 prachi18oct
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If x > 3, then it must be true that EITHER x > 3 OR x < 3prachi18oct wrote:If x > 3, then which of the following must be true?
(1) x > 3
(2) x^2 > 9
(3) x1 > 2
A. (1) only
B. (2) only
C. (1) and (2) only
D. (2) and (3) only
E. (1),(2) and (3)
My only doubt here is with statement 3.
x1 > 3 => x > 3 or x < 1
x > 3 is fine as x > 3 for all those x but if x < 1 then all the values dont saisfy x > 3 for e.g x = 2 then x = 2 < 3 so why should D be the OA.
(1) x > 3
This need not be true, since it's also possible that x < 3.
For example, x COULD equal 5
(2) xÂ² > 9
This means that EITHER x > 3 OR x < 3
Perfect  this matches our original conclusion that EITHER x > 3 OR x < 3
(3) x1 > 2
Let's solve this further.
We get two cases:
case a) x  1 > 2, which means x > 3 PERFECT
or
case b) x  1 < 2, which means x < 1
Must it be true that x < 1?
YES.
We already learned that EITHER x > 3 OR x < 3
If x < 3, then we can be certain that x < 1
For example, if I tell you that the temperature is less than 3 degrees Celsius, can we be certain that the temperature is less than 1 degrees? Yes.
So, statement 3 must also be true.
Answer: D
If anyone is interested, we have a free video on solving inequalities involving absolute value: https://www.gmatprepnow.com/module/gmat ... ing?id=985
Cheers,
Brent
Last edited by Brent@GMATPrepNow on Fri Jul 31, 2015 8:47 am, edited 1 time in total.
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You went wrong because you went in the wrong direction. We already know that x > 3. So that's not what you are proving.prachi18oct wrote:If x > 3, then which of the following must be true?
(1) x > 3
(2) x^2 > 9
(3) x1 > 2
A. (1) only
B. (2) only
C. (1) and (2) only
D. (2) and (3) only
E. (1),(2) and (3)
My only doubt here is with statement 3.
x1 > 2 => x > 3 or x < 1
x > 3 is fine as x > 3 for all those x but if x < 1 then all the values dont saisfy x > 3 for e.g x = 2 then x = 2 < 3 so why should D be the OA.
You are proving that x1 > 2.
If x > 3, then x > 3 or x < 3. So x  1 > 2 or x  1 < 4. Any number > 2 or < 4 has an absolute value > 2.
So (3) holds true at for all x such that x > 3, and D is correct.
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 GMATGuruNY
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a = the distance between a and 0.
ab = the distance between a and b.
This means that the distance between x and 0 is greater than 3.
Any value in the two red ranges below satisfies this constraint:
<(3).......(3)>
I: x>3
The red range on the left illustrates that x does not have to be greater than 3.
Eliminate A, C, and E.
III: x1 > 2.
This statement implies that the distance between x and 1 must be greater than 2.
Every value in the red ranges above is more than 2 places away from 1.
Thus, statement III must be true.
Eliminate B.
The correct answer is D.
ab = the distance between a and b.
Constraint: x > 3If X>3, which of the following must be true?
A) X>3
B) X^2>9
c) X1>2
I only
II only
I and II only
II and III only
I, II, and III
This means that the distance between x and 0 is greater than 3.
Any value in the two red ranges below satisfies this constraint:
<(3).......(3)>
I: x>3
The red range on the left illustrates that x does not have to be greater than 3.
Eliminate A, C, and E.
III: x1 > 2.
This statement implies that the distance between x and 1 must be greater than 2.
Every value in the red ranges above is more than 2 places away from 1.
Thus, statement III must be true.
Eliminate B.
The correct answer is D.
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(3) x1 > 2
Let's solve this further.
We get two cases:
case a) x  1 > 2, which means x > 3 PERFECT
or
case b) x  1 < 2, which means x < 1
Must it be true that x < 1?
YES.
Hi ,
If I solve this , then I get.
x1>2
x>3 and x>1
so what will be my next step?
Please help me in solving this.
Thanks in advance.
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Hi SJ,
You have to remember the first piece of information that you've been given: X > 3. Using THAT information, you know that X < 3 or X > 3.
So when you determine that X1 > 2 means that X > 3 or X < 1 you have a basis for comparison. Does that initial piece of information 'match up' with what Roman Numeral 3 defines? YES it does. Every potential value of X in the prompt fits the possibilities that are defined by that Roman Numeral.
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You have to remember the first piece of information that you've been given: X > 3. Using THAT information, you know that X < 3 or X > 3.
So when you determine that X1 > 2 means that X > 3 or X < 1 you have a basis for comparison. Does that initial piece of information 'match up' with what Roman Numeral 3 defines? YES it does. Every potential value of X in the prompt fits the possibilities that are defined by that Roman Numeral.
GMAT assassins aren't born, they're made,
Rich

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x1 > 3 => x > 3 or x < 1
Can someone explain the above inequality? How is it x > 3 or X < 3
Can someone explain the above inequality? How is it x > 3 or X < 3
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According to the prompt:santhosh_katkurwar wrote:x1 > 3 => x > 3 or x < 1
Can someone explain the above inequality? How is it x > 3 or X < 3
x > 3.
This inequality implies that x < 3 or x > 3.
Values of x such x < 3 or x > 3 include the following:
...6, 5, 4....4, 5, 6....
Statement II: x1 > 2
Case 1: Signs unchanged
x1 > 2
x > 3.
Case 2: Signs changed in the absolute value
x+1 > 2
1 > x
x < 1.
Thus:
x < 1 or x > 3.
Every value in the blue list above is either less than 1 or greater than 3.
Thus, Statement II must be true.
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a  b = the distance from a to bsanthosh_katkurwar wrote:x1 > 3 => x > 3 or x < 1
Can someone explain the above inequality? How is it x > 3 or X < 3
With that, we can say
x  1 > 3
really means
the distance from x to 1 is greater than 3
That means that x is greater than 4 (since 4 is exactly 3 units from 1) or that 2 > x (since 2 is exactly 3 units from 1).
x > 3 is similar: the distance from x to 0 is greater than 3. That means x > 3 or 3 > x.