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# Which is larger, the sum of the roots of equation A or the

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Manager
Joined: 24 Nov 2010
Posts: 157
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Which is larger, the sum of the roots of equation A or the  [#permalink]

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30 Jul 2011, 15:05
00:00

Difficulty:

55% (hard)

Question Stats:

53% (01:36) correct 47% (02:01) wrong based on 82 sessions

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A: x^2 + 6x - 40 = 0
B: x^2 + kx + j = 0

Which is larger, the sum of the roots of equation A or the sum of the roots of equation B?

(1) j = k

(2) k is negative
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Joined: 20 Dec 2010
Posts: 1533

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30 Jul 2011, 18:15
1
dreambeliever wrote:
A: $$x^2$$ + 6x - 40 = 0
B: $$x^2$$ + kx + j = 0
Which is larger, the sum of the roots of equation A or the sum of the roots of equation B?

1. j = k
2. k is negative

Sum of roots of an equation:
$$ax^2+bx+c=0$$
Is
$$\frac{-b}{a}$$

So,

A. $$x^2 + 6x - 40 = 0$$
Sum of roots$$=\frac{-6}{1}=-6$$

B. $$x^2 + kx + j = 0$$
Sum of roots$$=\frac{-k}{1}=-k$$

We need to find
Larger of (-6, -k)

1. $$j=k$$
k can be 100 or -100.
Not Sufficient.

2. k<0
Thus, -k>0
Any positive number will always be greater than -6.
Thus, -k > -6
OR
Sum of roots of B > Sum of roots of A
Sufficient.

Ans: "B"
Manager
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31 Jul 2011, 22:17
fluke wrote:
dreambeliever wrote:
A: $$x^2$$ + 6x - 40 = 0
B: $$x^2$$ + kx + j = 0
Which is larger, the sum of the roots of equation A or the sum of the roots of equation B?

1. j = k
2. k is negative

Sum of roots of an equation:
$$ax^2+bx+c=0$$
Is
$$\frac{-b}{a}$$

So,

A. $$x^2 + 6x - 40 = 0$$
Sum of roots$$=\frac{-6}{1}=-6$$

B. $$x^2 + kx + j = 0$$
Sum of roots$$=\frac{-k}{1}=-k$$

We need to find
Larger of (-6, -k)

1. $$j=k$$
k can be 100 or -100.
Not Sufficient.

2. k<0
Thus, -k>0
Any positive number will always be greater than -6.
Thus, -k > -6
OR
Sum of roots of B > Sum of roots of A
Sufficient.

Ans: "B"

Funnily enough I could not move on this till clock ticked one minutes then I moved to shortcuts (lazy me ) and picked B (obviously I was not sure though!) but when I saw only this part- sum of root = -b/a (Fluke's explanation) I was like ok I have done it right
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Joined: 01 Feb 2011
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01 Aug 2011, 07:03
Sum of roots = -b/a

A Sum of roots = -6
B sum of roots = -k

so the comparison is between -6 and -k , to see which one is greater

1. Not sufficient
j=k

k=2 => -k>-6 = > B>A
k=8 => -k<-6 =>B<A

2. Sufficient

As k is negative -k is always going to be positive
=> -k is always greater than -6
=> sum of roots of B is always greater than sum of roots of A.

Manager
Joined: 19 Oct 2010
Posts: 151
Location: India
GMAT 1: 560 Q36 V31
GPA: 3

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13 Aug 2011, 08:28
fluke wrote:
dreambeliever wrote:
2. k<0
Thus, -k>0
Any positive number will always be greater than -6.
Thus, -k > -6
OR
Sum of roots of B > Sum of roots of A
Sufficient.

Ans: "B"

Fluke,

Can you please explain the part show in the question better? I didn't understand how you obtained a positive number
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petrifiedbutstanding
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Joined: 16 May 2011
Posts: 145
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
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13 Aug 2011, 12:29
1
to petrifiedbutstanding i'll try:
if k is negative
thenthe equation looks like: X^2 -kx + j = 0

so the sum of roots is: (minus)- (b)/(a) or in our case -(minus) (-k)/1
which makes it: --(minus minus) k/1 or +k which is a positve number.

if k is a positive number it will allways be bigeer than -6
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Joined: 05 Feb 2014
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Re: A: x^2 + 6x - 40 = 0 B: x^2 + kx + j = 0 Which is larger,  [#permalink]

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14 May 2014, 16:34
I don't understand how j and k could be anything other than 4. Can anybody give me roots of this equation other than 2 that both add to and multiply to the same number?
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Joined: 02 Sep 2009
Posts: 60644
Re: A: x^2 + 6x - 40 = 0 B: x^2 + kx + j = 0 Which is larger,  [#permalink]

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15 May 2014, 01:11
williambrubaker wrote:
I don't understand how j and k could be anything other than 4. Can anybody give me roots of this equation other than 2 that both add to and multiply to the same number?

Why should the roots the roots add to and multiply to the same number?

Also, note that we are not told that j and k are integers...
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Re: A: x^2 + 6x - 40 = 0 B: x^2 + kx + j = 0 Which is larger,   [#permalink] 15 May 2014, 01:11
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