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# |a| > |d|

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|a| > |d| [#permalink]  27 Nov 2018, 15:47
Expert's post
00:00

Question Stats:

31% (01:09) correct 68% (00:26) wrong based on 19 sessions
$$|a| > |d|$$

$$|a| * b^3 * c^2 * |d| * e^5 * f^6 * g < 0$$

 Quantity A Quantity B $$g( |a| * b * e)$$ $$g(b * e * |d|$$)

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.
[Reveal] Spoiler: OA

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Re: |a| > |d| [#permalink]  28 Nov 2018, 10:45
I think the answer should be A

Qty A = g(|a|*b*e)
Qty B = g(b*e*|d|)

Since neither of g , b or e is 0 , we can divide both quantities by g*b*e
We are left with
Qty A = |a|
Qty B = |d|

Since |a| > |d|

A > B
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Re: |a| > |d| [#permalink]  28 Nov 2018, 12:08
Expert's post
I think you didn't evaluate carefully the question Sir.

$$|a| > |d|$$ means that a is > 0 and further from zero on the number line than |d| which is still positive and close to zero.

We also do know that $$|a|, c^2, |d|,$$ and $$f^6$$ must be positive > 0

On the other hand, $$b^3, e^5$$, and $$g$$ must be a negative number <0 , of which all 3 numbers are negative OR two are positive and one is negative to obtain $$beg < 0$$

Looking at the two quantities, we do have

A) $$|a| * beg$$

B) $$|d| * beg$$

and we do know for sure that beg <0 or negative regardless the sign of the numbers.

A negative number * a bigger positive number ($$|a|$$) we will have a number further from zero on the negative side of the number line.

A negative number * a smaller positive number ( $$|d|$$ ) we will have a number closer to zero on the negative side of the number line.

Therefore, $$|d| > |a|$$ and the answer is B
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Re: |a| > |d| [#permalink]  28 Nov 2018, 12:39
2
KUDOS

|a | > |d|
A: g(|a| * b * e)
B. g(b * e * |d|)

|a|*b^3 * c^2 * |d| * e^5 * f^6 * g <0
We analyze the above expression,
|a|, c^2, |d|, f^6 are definitely positive,
Odd numbers(1 or 3) of other factors(b^3, e^5, g) are negative. Then either one of (b, e, g) are negative or the three of them

A: g(|a| * b * e)
As explained in above, either the three of (b, e, g) are negative or one of them
1: three of them are negative then we will have :
g(|a| * b * e) = g(positive * negative * negative) = g(positive) = negative (because g is considered as negative)
2.one of them is negative ( for example e):
g(|a| * b * e) = g(positive * positive * negative) = g(negative) = negative (because g is considered as positive here)
[the same situation happens when g or b is negative)

B. g(b * e * |d|)
As explained in above, either the three of (b, e, g) are negative or one of them
1: three of them are negative then we will have :
g(|d| * b * e) = g(positive * negative * negative) = g(positive) = negative (because g is considered as negative)
2.one of them is negative ( for example e):
g(|d| * b * e) = g(positive * positive * negative) = g(negative) = negative (because g is considered as positive here)
[the same situation happens when g or b is negative)

So we see both of them are negative, the one which is less is bigger, as |a| > |d| then B is bigger than A.
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Re: |a| > |d| [#permalink]  29 Nov 2018, 08:58
Expert's post
Carcass wrote:
$$|a| > |d|$$

$$|a| * b^3 * c^2 * |d| * e^5 * f^6 * g < 0$$

 Quantity A Quantity B $$g( |a| * b * e)$$ $$g(b * e * |d|$$)

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.

Ok..
Too many variables.. What do we do? - we try to remove as many variables as possible..

$$|a| * b^3 * c^2 * |d| * e^5 * f^6 * g < 0$$
Of course we cannot find the values of variables but it can tell us what all lead to a NEGATIVE value..
so discard the positive terms as they do not affect the equation..
$$|a| * b^3 * c^2 * |d| * e^5 * f^6 * g < 0...........b^3*e^5*g<0$$
Now whatever be the values of b, g and e, $$b*g*e<0$$

With this information let us see if we can compare A and B.
$$g( |a| * b * e)$$)($$g(b * e * |d|$$)
Now both have three terms same, so we compare |a| and |d| and we know |a|>|d|, so the numeric value ||a|*b*g*e|>||d|*b*g*e|
BUT since b*g*e<0 both A and B are NEGATIVE..

We know larger the negative value, the smaller it is.
so |A|>|B| hence A<B..

B
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: |a| > |d|   [#permalink] 29 Nov 2018, 08:58
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