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# Is X an odd integer? (1) x^2 - 2x-3=0

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Intern
Joined: 21 Aug 2010
Posts: 5
Is X an odd integer? (1) x^2 - 2x-3=0  [#permalink]

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26 Aug 2010, 15:08
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Difficulty:

95% (hard)

Question Stats:

26% (01:21) correct 74% (01:24) wrong based on 259 sessions

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Hi All!! I have just started preparing for the Gmat. I'm attending a course that lasts three month.

Hereafter you can find my doubts:

Is X an odd integer?

(1) x^2 - 2x-3=0
(2) x^2 + 2x = 0

I took the roots

(1) 3 and -1
(2) 0 and -2

D would be the answer Sufficient/ Sufficient( According to the book).I don't get the point.

Is X<0?

(1) x^2 - 4x + 3=0
(2) x^2 + 2x -3 =0

Roots for (1)= 3 and 1. In this case, the answer should be sufficient. As both X are > 0. Is this correct?
Roots for (2) = -3 and 1 . In this case, the answer should be insufficient, as I got two ansers, one positive and one negative. Is this correct?

Is X>0?

(1) X^2 -X- -6=0
(2) X2 -4x -12= 0

Roots for (1)= 3 and -2. In this case, it would be insufficient because I have to answers and one is positive and the other one negative. Is this correct?
Roots for (2)= 6 and -2. Idem to (1)

Another question for Algebraic Manipulation:

If @X@ denotes the greatest integer that is less than or equal to X, then @-1@/@1@=

A) -2
B) -1
C) 0
D) 1
E) 2

Are they refering to absolute value?
You're help will be higlhly appreciated

Best regards

Brian
Math Expert
Joined: 02 Sep 2009
Posts: 60778
Re: HELP - Data Sufficiency Equation and Inequalities  [#permalink]

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26 Aug 2010, 16:00
4
1
briandoldan wrote:
Hi All!! I have just started preparing for the Gmat. I'm attending a course that lasts three month.

Hereafter you can find my doubts:

Is X an odd integer?

(1) x^2 - 2x-3=0
(2) x^2 + 2x = 0

I took the roots

(1) 3 and -1
(2) 0 and -2

D would be the answer Sufficient/ Sufficient( According to the book).I don't get the point.

Is X<0?

(1) x^2 - 4x + 3=0
(2) x^2 + 2x -3 =0

Roots for (1)= 3 and 1. In this case, the answer should be sufficient. As both X are > 0. Is this correct?
Roots for (2) = -3 and 1 . In this case, the answer should be insufficient, as I got two ansers, one positive and one negative. Is this correct?

Is X>0?

(1) X^2 -X- -6=0
(2) X2 -4x -12= 0

Roots for (1)= 3 and -2. In this case, it would be insufficient because I have to answers and one is positive and the other one negative. Is this correct?
Roots for (2)= 6 and -2. Idem to (1)

Another question for Algebraic Manipulation:

If @X@ denotes the greatest integer that is less than or equal to X, then @-1@/@1@=

A) -2
B) -1
C) 0
D) 1
E) 2

Are they refering to absolute value?
You're help will be higlhly appreciated

Best regards

Brian

Hi, and welcome to GMAT Club. In the future can you please post one question per topic and also post PS questions in PS subforum and DS questions in DS subforum.

As for the problems:

1. Is x an odd integer?

(1) $$x^2-2x-3=0$$ --> $$x=3$$ or $$x=-1$$ --> as both values are odd numbers, then the answer to the question "is $$x$$ an odd integer" would be YES. Sufficient.
(2) $$x^2+2x=0$$ --> $$x=0$$ or $$x=-2$$ --> as both values are even numbers, then the answer to the question "is $$x$$ an odd integer" would be NO. Sufficient.

But even though formal answer to the question is D (EACH statement ALONE is sufficient), this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. So we can not have answer YES from statement (1) and answer NO from statement (2).

2. Is x<0?

(1) $$x^2-4x+3=0$$ --> $$x=3$$ or $$x=1$$ --> as both values are positive, then the answer to the question "is $$x<0$$" would be NO. Sufficient.
(2) $$x^2+2x-3=0$$ --> $$x=-3$$ or $$x=1$$ --> one value is negative and another value is positive, hence this statement is NOT sufficient to answer the question "is $$x<0$$". Not sufficient.

Answer: A (Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient).

3. Is x>0?

(1) $$x^2-x-6=0$$ --> $$x=3$$ or $$x=-2$$ --> one value is negative and another value is positive, hence this statement is NOT sufficient to answer the question "is $$x>0$$". Not sufficient.
(2) $$x^2-4x-12=0$$ --> $$x=6$$ or $$x=-2$$ --> one value is negative and another value is positive, hence this statement is NOT sufficient to answer the question "is $$x>0$$". Not sufficient.

(1)+(2) Intersection of the values from (1) and (2) is $$x=-2$$, which is negative, hence the answer to the question "is $$x>0$$" is NO. Sufficient.

Answer: C ( BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient).

4. If @X@ denotes the greatest integer that is less than or equal to X, then @-1@/@1@=

A. -2
B. -1
C. 0
D. 1
E. 2

@x@ is some function defined as "the greatest integer that is less than or equal to x", so for example @1.2@=1, as 1 is the greatest integer less than or equal to 1.2. Or another example: @-1.4@=-2, as -2 is the greatest integer less than or equal to -1.4. (Basically @x@ function just rounds down the value of the number x to the integer).

So, @-1@=-1, as -1 is the greatest integer less than or equal to -1 and @1@=1, as 1 is the greatest integer less than or equal to 1. Therefore $$\frac{@-1@}{@1@}=\frac{-1}{1}=-1$$.

Hope it helps.
_________________
##### General Discussion
Intern
Joined: 05 Aug 2010
Posts: 3
Re: HELP - Data Sufficiency Equation and Inequalities  [#permalink]

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26 Aug 2010, 15:48
Brian,
Here's what i did to get the answer:
Is X an odd integer?

(1) x^2 - 2x-3=0
(2) x^2 + 2x = 0

1) if x= even, then x^2 = even, 2x = even, and 3 = odd. So even - even - odd = odd. Since you know the answer must be zero (which is even), this can't be a possibility. Thus x MUST be odd. It works out as well. If x = odd x^2 = odd, 2x = even, 3 = odd. So odd - even -odd = even.

2) take the same approach. If x = even, x^2 = even, and 2x = even. even + even = even. If x = odd then x^2 = odd, and 2x = even. Thus odd + even = odd. Since 0 is an even number, you know that x CAN'T be odd and thus it has to be even. Therefore, X isn't an odd number which is sufficient.

Intern
Joined: 05 Aug 2010
Posts: 3
Re: HELP - Data Sufficiency Equation and Inequalities  [#permalink]

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26 Aug 2010, 15:53
I got the same answer for the following two questions so i would say that yes you are correct (or we are both wrong?). I'm not sure about that last problem though with the @@ symbols, I'm not sure though. Hopefully someone can post an answer though!
Intern
Joined: 05 Aug 2010
Posts: 3
Re: HELP - Data Sufficiency Equation and Inequalities  [#permalink]

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27 Aug 2010, 06:15
Thanks for that Bunuel. Makes since now
Re: HELP - Data Sufficiency Equation and Inequalities   [#permalink] 27 Aug 2010, 06:15
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# Is X an odd integer? (1) x^2 - 2x-3=0

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