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 Post subject: GMAT Algebra (Data Sufficiency)
PostPosted: Fri Feb 24, 2012 7:12 pm 
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Is (x – 4)(x – 3)(x + 2)(x + 1) > 0 ?
(1) 3 > x
(2) x > -1

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(C) The expression (x – 4)(x – 3)(x + 2)(x + 1) is composed of four factors. It will equal 0 if at least one of the factors is 0. It will be positive if all the four factors are positive, if all the four factors are negative, or if two of them are negative and the other two are positive. Otherwise the epxression will be negative.

Statement (1), 3 > x, implies that the factors (x – 4) and (x – 3) are negative. The signs of the other two factors, (x + 2) and (x + 1), are not defined. E.g. they both can be positive if x = 1. Or one of them can equal 0 if x = -1 or x = -2. Or (x + 2) can be positive and (x + 1) can be negative if x = -1.5, etc. Therefore the original expression can be positive, negative or 0 and we can NOT give a definite answer to the original question. Statement (1) by itself is NOT sufficient.

Statement (2), x > -1, implies that the factors (x + 2) and (x + 1) are positive. The signs of the other two factors, (x – 4) and (x – 3) , are not defined. E.g. they both can be positive if x = 5. Or one of them can equal 0 if x = 3 or x = 4. Or (x – 3) can be positive and (x – 4) can be negative if x = 3.5, etc. Therefore the original expression can be positive, negative or 0 and we can NOT give a definite answer to the original question. Statement (2) by itself is NOT sufficient.

If we use the both statements together, statement (1) implies that factors (x – 4) and (x – 3) are negative. Statement (2) implies that factors (x + 2) and (x + 1) are positive. Therefore the original expression must be positive (2 negative factors × 2 positive factors). The both statements taken together are sufficient to answer the question. The correct answer is C.

Alternative method:
You may solve the original inequality first and then compare the solution with the inequality (1), inequality (2) and a system of inequalities (1) and (2) using the number line.
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Between -1 & 3 the expression acquires negative as well as positive values.


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 Post subject: Re: t.1, qt. 13: inequalities. data sufficiency
PostPosted: Fri Feb 24, 2012 7:23 pm 
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 Post subject: Re: t.1, qt. 13: inequalities. data sufficiency
PostPosted: Fri Mar 23, 2012 3:52 pm 
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1st won't work - check for x = 3.5 and 7 - they will give opposite signs.
2nd won't work - check for x = 1 and 5 - they will give opposite sings.

Combining the both won't work - check for x = 1 and -1.5 - they again give opposite signs.

Hence the answer is E.


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 Post subject: Re: t.1, qt. 13: inequalities. data sufficiency
PostPosted: Fri Mar 23, 2012 4:24 pm 
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 Post subject: Re: t.1, qt. 13: inequalities. data sufficiency
PostPosted: Sat Mar 24, 2012 2:15 am 
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OKk..how about this..
1st won't work - check for x=1 and -1.5 - they will give opp.signs and satisfies x<3
2nd won't work - check for x=3.5 and 5 - they will give opp.sings and satisfies x > -1

combining both won't work- check for x=1 and -1.5 - they again give opp.signs and satisfies -1<x<3

hence ans is E


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 Post subject: Re: t.1, qt. 13: inequalities. data sufficiency
PostPosted: Sat Mar 24, 2012 2:32 pm 
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 Post subject: Re: t.1, qt. 13: inequalities. data sufficiency
PostPosted: Mon May 07, 2012 4:36 am 
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For x = -3/2 the answer is -ive while for x = 0 it will be +ive. Thus even if we use both A and B, the value for the expression is not certain.
For range -1 to -2 the expression is -ive
For range -2 to -3 the expression is +ive

Thus answer should be E


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 Post subject: Re: t.1, qt. 13: inequalities. data sufficiency
PostPosted: Mon May 07, 2012 6:46 am 
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 Post subject: Re: t.1, qt. 13: inequalities. data sufficiency
PostPosted: Sat Jul 14, 2012 4:07 pm 
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Can you explain the alternative method in a little more detail.


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 Post subject: Re: t.1, qt. 13: inequalities. data sufficiency
PostPosted: Sat Jul 14, 2012 4:31 pm 
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