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 \(\frac{@-1@}{@1@}=\frac{-1}{1}=-1\).

Answer: B.

Hope it helps.

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