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GMAT Diagnostic Test Question 41

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GMAT Diagnostic Test Question 41 [#permalink]

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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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New post 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 \(b=-16\).

Answer: D
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Re: GMAT Diagnostic Test Question 41 [#permalink]

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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.

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Re: GMAT Diagnostic Test Question 41 [#permalink]

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New post 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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New post 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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New post 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?
:wink:
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Re: GMAT Diagnostic Test Question 41 [#permalink]

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New post 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?
:wink:


or this just means equation has only one solution( one root)?
many thanks :wink:
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Re: GMAT Diagnostic Test Question 41 [#permalink]

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New post 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?
:wink:


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


Yes, it means that the equation has one root.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: GMAT Diagnostic Test Question 41 [#permalink]

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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 \(b=-16\).

Answer: D


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

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Re: GMAT Diagnostic Test Question 41 [#permalink]

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New post 06 Jan 2014, 03:28
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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 \(b=-16\).

Answer: D


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


You should brush up fundamentals.

Factoring Quadratics: http://www.purplemath.com/modules/factquad.htm

Solving Quadratic Equations: http://www.purplemath.com/modules/solvquad.htm

Hope this helps.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: GMAT Diagnostic Test Question 41 [#permalink]

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New post 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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