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Manager Joined: 22 Jul 2018
Posts: 79
Followers: 0

Kudos [?]: 13 , given: 42

x=4√(x3+6x2) [#permalink] 00:00

Question Stats: 33% (00:42) correct 66% (01:13) wrong based on 33 sessions
$$x=4$$$$\sqrt{(x^3+6x^2)}$$

 Quantity A Quantity B The sum of all possible roots of x 1

Quantity A is greater
Quantity B is greater
The two quantities are equal
The relationship cannot be determined from the information given
[Reveal] Spoiler: OA
Manager Joined: 22 Jul 2018
Posts: 79
Followers: 0

Kudos [?]: 13 , given: 42

Re: x=4√(x3+6x2) [#permalink]
Please explain the solution
Founder  Joined: 18 Apr 2015
Posts: 7737
Followers: 143

Kudos [?]: 1593 , given: 7027

Re: x=4√(x3+6x2) [#permalink]
Expert's post
Please see how to format a question in the right manner .
https://greprepclub.com/forum/qq-how-to ... -2357.html

Thank you so much
_________________
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 123 , given: 4

Re: x=4√(x3+6x2) [#permalink]
Expert's post
Sawant91 wrote:
$$x=4$$$$\sqrt{(x^3+6x^2)}$$

 Quantity A Quantity B The sum of all possible roots of x 1

Quantity A is greater
Quantity B is greater
The two quantities are equal
The relationship cannot be determined from the information given

the answer depends on what 4 means is it 4th root, or 4* something
_________________

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

Intern Joined: 21 Nov 2018
Posts: 21
Followers: 0

Kudos [?]: 3 , given: 1

Re: x=4√(x3+6x2) [#permalink]
If we consider that the expression given is the 4th root , then the answer should be C . Can someone please explain how is the answer A ?
Intern Joined: 07 Dec 2018
Posts: 3
Followers: 0

Kudos [?]: 0 , given: 2

Re: x=4√(x3+6x2) [#permalink]
kunalkmr62 wrote:
If we consider that the expression given is the 4th root , then the answer should be C . Can someone please explain how is the answer A ?

Agree, For the 4th root, x can be solved for 3&-2, hence sum of the roots is 1, so C should be the option.
Manager Joined: 22 Jul 2018
Posts: 79
Followers: 0

Kudos [?]: 13 , given: 42

Re: x=4√(x3+6x2) [#permalink]
It is said sum of all possible root:
I am getting possible values 1,3
As 3 is greater than 1 hence answer is A
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 123 , given: 4

Re: x=4√(x3+6x2) [#permalink]
Expert's post
Sawant91 wrote:
$$x=4$$$$\sqrt{(x^3+6x^2)}$$

 Quantity A Quantity B The sum of all possible roots of x 1

Quantity A is greater
Quantity B is greater
The two quantities are equal
The relationship cannot be determined from the information given

The question could mean two things..
(I) If it is what it is given- $$x=4$$$$\sqrt{(x^3+6x^2)}$$
Square both sides - $$x^2=16(x^3+6x^2).......16x^3-95x^2=0....x^2(16x-95)=0$$.. Sum of roots = $$0+\frac{95}{16}$$ so A>B
(II) If there is a typo and it meant \$th root and not 4*..
so take the 4th power - $$x^4=x^3+6x^2......x^4-x^3-6x^2=0.....x^2(x-3)(x+2)=0$$ Hence, the sum is 0+3-2=1
here A=B..
so C
_________________

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

Intern Joined: 12 Nov 2018
Posts: 25
Followers: 0

Kudos [?]: 8 , given: 17

Re: x=4√(x3+6x2) [#permalink]
''x2=16(x3+6x2).......16x3−95x2=0....x2(16x−95)=0''
how is the above possible , i.e. ( -95x)?
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 123 , given: 4

Re: x=4√(x3+6x2) [#permalink]
Expert's post
JelalHossain wrote:
''x2=16(x3+6x2).......16x3−95x2=0....x2(16x−95)=0''
how is the above possible , i.e. ( -95x)?

$$\(x^2=16(x^3+6x^2).......16x^3-95x^2=0....x^2(16x-95)=0$$\)

Take out x^2 from $$16x^3-95x^2=0......x^2*16x-x^2*95=x^2(16x-95)=0$$
_________________

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: x=4√(x3+6x2)   [#permalink] 11 Feb 2019, 07:34
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