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GMAT Club invites you to test your GRE knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GRE Strategy guide. What are you waiting for? Get out your scrap paper and start solving! Click here to view contest & prize details

This week's question: \(| a | > | d |\) \(| a |*b^3*c^2*| d |*e^5*f ^6*g < 0\)

A

B

\(g(| a |*b*e)\)

\(g(b*e*| d |)\)

Compare Quantity A and Quantity B using the information given above, and select one of the following answer choices: A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.

Please post your answer, along with the explanation, below. Get cracking!

Edit: This challenge is now closed

Solution

First, let’s look at the common information. If |a| > |d|, then a is further from 0 than d is, but we don’t know their signs. Since |a|b3c2|d|e5f6g and we know that |a|, c2, |d|, and f6 must be positive (any nonzero number becomes positive when put in an absolute value sign or given an even exponent), then whatever is “left over” must be causing the entire expression to be negative. Therefore, b3e5g < 0. Since an odd exponent merely preserves the sign of the original number (that is, a negative number to a power of 1, 3, 5, etc. will still be negative, and a positive number to a power of 1, 3, 5, etc. will still be positive), we can ignore the exponents for the purposes of evaluating the signs of our variables: beg < 0 For three numbers multiplied together to yield a negative, there are two possibilities: neg x neg x neg = neg pos x pos x neg = neg Of course, we have no way to know which of b, e, and g are negative, but we know that either all of them are negative, or exactly one of them is negative. Now that we have fully processed the common information, we are ready to proceed to Columns A and B. In any problem of this type, it is important to draw logical conclusions from the common information before approaching the Columns. First, note that order doesn’t matter when multiplying, so the parentheses are meaningless, and the Columns can be re-ordered to look more similar to one another:

Column A

Column B

|a| beg

|d| beg

Although b, e, and g appear on both sides, we cannot simply ignore them—importantly, the term beg is negative. We cannot “divide out” a term from both sides unless it is known to be positive. Let’s rephrase what we now know about the Columns:

Column A

Column B

(big absolute value)(negative)

(small absolute value)(negative)

Multiplying the negative term beg by a big absolute value will make it bigger on the negative side. Multiplying this same negative term beg by a smaller absolute value will result in a negative, but a negative closer to zero than Column A's value. Still confused? Let's illustrate with real numbers. For instance, imagine that beg is equal to –2. The terms a and d could be something like 5 and 3, or –7 and 4, or –100 and –50, etc. (as long as the absolute value of a is bigger than the absolute value of d). So, if a and d were originally –6 and 3, for instance, then their absolute values would be 6 and 3, and when we multiplied them by –2, we’d get that Column A = –12 and Column B = –6. Since –6 is closer to zero, it is larger and the answer is B. This will work for any numbers you select that follow the rules of the problem (that is, beg is negative and |a| > |d|). The answer is B.

The winner of this Week's Challenge is... (drum roll).... Ardarandir. Congratulations! Please send me a pm with your shipping address, and choice of Manhattan GRE Guide

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_________________

Since in : | a |*b^3*c^2*| d |*e^5*f ^6*g < 0 |a|, |d|, c^2, f^6 can not be negative. One (or all three) of b, e, g must be negative and since | a | > | d |,

given: | a | > | d | -->eqn 1 as the above has modulus on both side we know |a| and |b| are positive.

| a |*b^3*c^2*| d |*e^5*f ^6*g < 0 -->eqn 2 from eqn 2 , it is seen that all the even powers will be positive i.e c^2 and f^6, hence, b^3*e^5*g<0 from the above we can deduce b*e*g <0 (or a -ve value)

the question asked to compare the two terms: first term :g(| a |*b*e) -->g*b*e <0 and |a| >0 2nd term : g(b*e*| d |) --->g*b*e <0 and |b| >0

hence , from eqn 1, we know |a| >|b|. therefore -|a|<-|b|

Quantity B is greater. according to the second statement b,e,g have odd power....... so either all of them or any one of them is negative... so therefore b*g*e < 0....... since |a|>|d|......... therefore magnitude of A is greater than Magnitude of B......... And due to minus sign B will be greater...