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# x is an integer such that –x|x| ≥ 4.

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x is an integer such that –x|x| ≥ 4. [#permalink]  08 Aug 2018, 16:37
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Question Stats:

65% (00:45) correct 34% (00:58) wrong based on 145 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

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Manager
Joined: 06 Jun 2018
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Re: x is an integer such that –x|x| ≥ 4. [#permalink]  09 Aug 2018, 15:15
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.
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Re: x is an integer such that –x|x| ≥ 4. [#permalink]  23 Oct 2018, 03:02
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
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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

Manager
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Re: x is an integer such that –x|x| ≥ 4. [#permalink]  23 Oct 2018, 08:41
it was interesting.
Intern
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Re: x is an integer such that –x|x| ≥ 4. [#permalink]  23 Oct 2018, 20:00
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.
Director
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Re: x is an integer such that –x|x| ≥ 4. [#permalink]  05 Jul 2019, 04:25
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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

Need a better explanation.
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Re: x is an integer such that –x|x| ≥ 4. [#permalink]  15 Jul 2020, 10:46
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A more human-like approach:

1. You first try to solve it conventionally, but quickly find out that it's not the right method.

2. You then analyze it logically like how chetan2u explained.
-x|x| must be positive; the element |x| is always positive; so the element -x must become positive. Thus, x must be negative so the answer is B.
Re: x is an integer such that –x|x| ≥ 4.   [#permalink] 15 Jul 2020, 10:46
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