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# GMAT Diagnostic Test Question 41

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GMAT Diagnostic Test Question 41 [#permalink]

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29 Sep 2013, 21:57
Expert's post
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GMAT Diagnostic Test Question 41

Field: algebra
Difficulty: 650

The equation $$x^2 + ax - b = 0$$ has equal roots, and one of the roots of the equation $$x^2 + ax + 15 = 0$$is 3. What is the value of b?

A. $$-\frac{1}{64}$$
B. $$-\frac{1}{16}$$
C. -15
D. -16
E. -64
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Last edited by Bunuel on 08 Oct 2013, 00:29, edited 1 time in total.
Edited the question.
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Re: GMAT Diagnostic Test Question 41 [#permalink]

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08 Oct 2013, 00:19
1
KUDOS
bb wrote:

GMAT Diagnostic Test Question 41

Field: algebra
Difficulty: 650

The equation $$x^2 + ax + 15 = 0$$ has equal roots, and one of the roots of the equation $$x^2 + ax + 15 = 0$$is 3. What is the value of b?

A. $$\frac{-1}{64}$$
B. $$\frac{-1}{16}$$
C. -15
D. -16
E. -64

Somethings is missing here. Question is "What is the value of b?" but 'b' is not present in the given data.
Founder
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
Posts: 14639
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
Followers: 3831

Kudos [?]: 24052 [0], given: 4603

Re: GMAT Diagnostic Test Question 41 [#permalink]

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29 Sep 2013, 21:58
Since one of the roots of the equation $$x^2 + ax + 15 = 0$$ is 3, then substituting we'll get: $$3^3+3a+15=0$$. Solving for $$a$$ gives $$a=-8$$.

Substitute $$a=-8$$ in the first equation: $$x^2-8x-b=0$$.

Now, we know that it has equal roots thus its discriminant must equal to zero: $$d=(-8)^2+4b=0$$. Solving for $$b$$ gives $$b=-16$$.

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Re: GMAT Diagnostic Test Question 41 [#permalink]

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08 Oct 2013, 00:29
Phoenix22 wrote:
bb wrote:

GMAT Diagnostic Test Question 41

Field: algebra
Difficulty: 650

The equation $$x^2 + ax + 15 = 0$$ has equal roots, and one of the roots of the equation $$x^2 + ax + 15 = 0$$is 3. What is the value of b?

A. $$\frac{-1}{64}$$
B. $$\frac{-1}{16}$$
C. -15
D. -16
E. -64

Somethings is missing here. Question is "What is the value of b?" but 'b' is not present in the given data.

Edited the question. Thank you.
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Re: GMAT Diagnostic Test Question 41 [#permalink]

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25 Oct 2013, 07:58
The PDF has option D switched with Option B on this Page.
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Re: GMAT Diagnostic Test Question 41 [#permalink]

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16 Dec 2013, 04:51
bb wrote:

GMAT Diagnostic Test Question 41

Field: algebra
Difficulty: 650

The equation $$x^2 + ax - b = 0$$ has equal roots, and one of the roots of the equation $$x^2 + ax + 15 = 0$$is 3. What is the value of b?

A. $$-\frac{1}{64}$$
B. $$-\frac{1}{16}$$
C. -15
D. -16
E. -64

thanks for useful simple algebra example but could you explain what does mean has equal roots, please?

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Intern
Joined: 11 Oct 2013
Posts: 18
Location: United Kingdom
GMAT 1: 490 Q32 V25
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WE: Other (Other)
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Kudos [?]: 22 [0], given: 34

Re: GMAT Diagnostic Test Question 41 [#permalink]

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16 Dec 2013, 04:57
3111987 wrote:
bb wrote:

GMAT Diagnostic Test Question 41

Field: algebra
Difficulty: 650

The equation $$x^2 + ax - b = 0$$ has equal roots, and one of the roots of the equation $$x^2 + ax + 15 = 0$$is 3. What is the value of b?

A. $$-\frac{1}{64}$$
B. $$-\frac{1}{16}$$
C. -15
D. -16
E. -64

thanks for useful simple algebra example but could you explain what does mean has equal roots, please?

or this just means equation has only one solution( one root)?
many thanks
_________________

Good things come to those who wait… greater things come to those who get off their ass and do anything to make it happen...

Math Expert
Joined: 02 Sep 2009
Posts: 37560
Followers: 7391

Kudos [?]: 99278 [0], given: 11010

Re: GMAT Diagnostic Test Question 41 [#permalink]

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16 Dec 2013, 05:01
3111987 wrote:
3111987 wrote:
bb wrote:

GMAT Diagnostic Test Question 41

Field: algebra
Difficulty: 650

The equation $$x^2 + ax - b = 0$$ has equal roots, and one of the roots of the equation $$x^2 + ax + 15 = 0$$is 3. What is the value of b?

A. $$-\frac{1}{64}$$
B. $$-\frac{1}{16}$$
C. -15
D. -16
E. -64

thanks for useful simple algebra example but could you explain what does mean has equal roots, please?

or this just means equation has only one solution( one root)?
many thanks

Yes, it means that the equation has one root.
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Re: GMAT Diagnostic Test Question 41 [#permalink]

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06 Jan 2014, 02:19
1
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BOOKMARKED
bb wrote:
Since one of the roots of the equation $$x^2 + ax + 15 = 0$$ is 3, then substituting we'll get: $$3^3+3a+15=0$$. Solving for $$a$$ gives $$a=-8$$.

Substitute $$a=-8$$ in the first equation: $$x^2-8x-b=0$$.

Now, we know that it has equal roots thus its discriminant must equal to zero: $$d=(-8)^2+4b=0$$. Solving for $$b$$ gives $$b=-16$$.

could you please explain the highlighted text. I don't understand what "discriminant" means.
Math Expert
Joined: 02 Sep 2009
Posts: 37560
Followers: 7391

Kudos [?]: 99278 [0], given: 11010

Re: GMAT Diagnostic Test Question 41 [#permalink]

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06 Jan 2014, 03:28
Expert's post
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BOOKMARKED
khushboobhatia wrote:
bb wrote:
Since one of the roots of the equation $$x^2 + ax + 15 = 0$$ is 3, then substituting we'll get: $$3^3+3a+15=0$$. Solving for $$a$$ gives $$a=-8$$.

Substitute $$a=-8$$ in the first equation: $$x^2-8x-b=0$$.

Now, we know that it has equal roots thus its discriminant must equal to zero: $$d=(-8)^2+4b=0$$. Solving for $$b$$ gives $$b=-16$$.

could you please explain the highlighted text. I don't understand what "discriminant" means.

You should brush up fundamentals.

Hope this helps.
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Re: GMAT Diagnostic Test Question 41 [#permalink]

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27 Mar 2014, 11:32
The PDF still notes that option D is the correct answer while B is noted as correct on this page, which is a result of the choices being flip-flopped.
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Re: GMAT Diagnostic Test Question 41   [#permalink] 27 Mar 2014, 11:32
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# GMAT Diagnostic Test Question 41

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