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 Author: questioner [ Sat Apr 07, 2012 6:47 am ] Post subject: GMAT Algebra For any a and b that satisfy |a – b| = b – a and a > 0, then|a + 3| + |-b| + |b – a| + |ab| =A. -ab + 3B. ab + 3C. -ab + 2b + 3D. ab + 2b – 2a – 3E. ab + 2b + 3(E) We know that |a – b| = b – a, so b – a > 0, or b > a. We also know that a > 0, so b > 0.Knowing that both a and b are positive we can easily simplify:|a + 3| + |-b| + |b – a| + |ab| =a + 3 + b + b – a + ab =ab + 2b + 3The right answer is choice (E).----------How would the equation be exactly transformed given that either a or b or both are negative?Thank you in advance for your help.

 Author: Gennadiy [ Sat Apr 07, 2012 7:07 am ] Post subject: Re: GMAT Algebra Quote:How would the equation be exactly transformed given that either a or b or both are negative?I'd like to stress that this is a hypothetical situation, because in the question we show that b > a > 0.So let's try the proposed conditions. |a + 3| + |-b| + |b – a| + |ab| = ?1) b < 0In this case we can simplify |-b| = -b, because -b > 0. But we can NOT simplify any other absolute value, because we know nothing about a.2) a < 0In this case we can NOT simplify any absolute value, because|a + 3| can be a + 3 (if a is from -3 to 0)OR|a + 3| can be -a – 3 (if a is less than -3)Any other absolute value contains b and we know nothing about it.3) a < 0 and b < 0In this case we can simplify:|-b| = -b, because -b > 0;|ab| = ab, because ab > 0.We can NOT simplify:|a + 3| for the same reasons as in 2)|b – a| can be b – a (if b > a)|b – a| can be -b + a (if b < a).You may try to plug some numbers in the absolute values we could NOT simplify:3) a < 0 and b < 0a = -1 < 0 , b = -4 < 0|a + 3| = |-1 + 3| = -1 + 3 = 2in this case we used |a + 3| = a + 3, because (a = -1 is between -3 and 0)|b – a| = |-4 – (-1)| = -(-4) + (-1) = 3in this case we used |b – a| = -b + a, because (b = -4 < -1 = a)a = -4 < 0 , b = -1 < 0|a + 3| = |-4 + 3| = -(-4) – 3 = 1in this case we used |a + 3| = -a – 3, because (a = -1 is less than -3)|b – a| = |-1 – (-4)| = -1 – (-4) = 3in this case we used |b – a| = b – a, because (b = -1 > -4 = a)

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