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TAGS: Moderator  Joined: 18 Apr 2015
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x is an integer such that –x|x| ≥ 4. [#permalink]
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Expert's post 00:00

Question Stats: 61% (00:49) correct 38% (00:53) wrong based on 42 sessions
x is an integer such that $$- x|x| ≥ 4$$.

 Quantity A Quantity B x 2

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.

Kudos for R.A.E
[Reveal] Spoiler: OA

_________________ Manager  Joined: 06 Jun 2018
Posts: 94
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Re: x is an integer such that –x|x| ≥ 4. [#permalink]
1
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Carcass wrote:
x is an integer such that $$- x|x| ≥ 4$$.

 Quantity A Quantity B x 2

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.

Kudos for R.A.E

Given

$$- x|x| ≥ 4$$

Note:

|x| is always positive.

we have a negative sign with x but ultimate value is positive. So x have to be negative. Negative times negative is positive.

The best answer is B. 2 is greater than x, a negative integer.
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 107 , given: 4

Re: x is an integer such that –x|x| ≥ 4. [#permalink]
Expert's post
Carcass wrote:
x is an integer such that $$- x|x| ≥ 4$$.

 Quantity A Quantity B x 2

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.

Kudos for R.A.E

Now $$- x|x| ≥ 4$$ which means $$- x|x| > 0$$ which is possible when both -x and |x| have same sign. |x|>0 so -x>0...
Multiply the sides if equation by '-', so -(-x)<-(0)...x<0

Since x<0, x has to be less than 2..
Thus B>A

B
_________________

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

Manager Joined: 23 Oct 2018
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Re: x is an integer such that –x|x| ≥ 4. [#permalink]
it was interesting.
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Re: x is an integer such that –x|x| ≥ 4. [#permalink]
Divide both sides by -x gives you |x| (< or =) 4/-x noting that you will be flipping the direction of the greater than sign since you are dividing by a negative. While you can then go and solve as you would any absolute value, having isolated the absolute value onto one side at this point, you can also see that the only way for the absolute value to be equal to a positive number (absolute values cannot be negative) is if the x value itself is negative. Since any negative number (x > 0) is going to be less than 2, we know that the answer will be B. Re: x is an integer such that –x|x| ≥ 4.   [#permalink] 23 Oct 2018, 20:00
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