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Post subject: GMAT Algebra (Data Sufficiency) Posted: Fri Feb 24, 2012 7:12 pm 

Joined: Sun May 30, 2010 3:15 am Posts: 424

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. 
Between 1 & 3 the expression acquires negative as well as positive values.


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Gennadiy

Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Fri Feb 24, 2012 7:23 pm 

Joined: Sun May 30, 2010 2:23 am Posts: 498


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questioner

Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Fri Mar 23, 2012 3:52 pm 

Joined: Sun May 30, 2010 3:15 am Posts: 424

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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Gennadiy

Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Fri Mar 23, 2012 4:24 pm 

Joined: Sun May 30, 2010 2:23 am Posts: 498


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baphna

Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Sat Mar 24, 2012 2:15 am 

Joined: Sat Mar 24, 2012 2:10 am Posts: 1

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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Gennadiy

Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Sat Mar 24, 2012 2:32 pm 

Joined: Sun May 30, 2010 2:23 am Posts: 498


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questioner

Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Mon May 07, 2012 4:36 am 

Joined: Sun May 30, 2010 3:15 am Posts: 424

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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Gennadiy

Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Mon May 07, 2012 6:46 am 

Joined: Sun May 30, 2010 2:23 am Posts: 498


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questioner

Post subject: Re: t.1, qt. 13: inequalities. data sufficiency Posted: Sat Jul 14, 2012 4:07 pm 

Joined: Sun May 30, 2010 3:15 am Posts: 424

Can you explain the alternative method in a little more detail.


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Gennadiy

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

Joined: Sun May 30, 2010 2:23 am Posts: 498


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