Last visit was: 19 Nov 2025, 03:41 It is currently 19 Nov 2025, 03:41
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
805+ Level|   Algebra|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,379
Own Kudos:
778,193
 [10]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,379
Kudos: 778,193
 [10]
In the equation x^2 + bx + 7= 0, where x is a variable, and b is a con 09 Dec 2019, 01:13
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

31% (01:53) correct 69% (01:57) wrong based on 154 sessions

History

Date
Time
Result
Not Attempted Yet
In the equation \(x^2 + bx + 7= 0\), where x is a variable, and b is a constant. What is the value of b?

(1) x can take only positive integer values
(2) b is a negative integer


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
A
User avatar
TestPrepUnlimited
User avatar
Joined: 17 Sep 2014
Last visit: 30 Jun 2022
Posts: 1,224
Own Kudos:
1,111
 [2]
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Expert
Expert reply
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Posts: 1,224
Kudos: 1,111
 [2]
In the equation x^2 + bx + 7= 0, where x is a variable, and b is a con Updated on: 04 Aug 2020, 19:41
Originally posted by TestPrepUnlimited on 09 Dec 2019, 09:46.
Last edited by TestPrepUnlimited on 04 Aug 2020, 19:41, edited 1 time in total.
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
In the equation \(x^2 + bx + 7= 0\), where x is a variable, and b is a constant. What is the value of b?

(1) x can take only positive integer values
(2) b is a negative integer


Are You Up For the Challenge: 700 Level Questions
Show more

Analyzing the Question:
If we have an equation in the form \(x^2 + ax + b= 0\), a is the negative sum of the two roots and b is the product of the two roots. So for \(x^2 + bx + 7= 0\) if we declare the two roots and m and n we have \(m*n = 7\) and \(m + n = -b\).

Statement 1:
m and n are positive and must be integers as x can only take integer values. Due to knowing \(m*n = 7\), we can only have m = 1, n = 7 or m = 7, n = 1. Thus either way we have \(b = -(m+n) = -8\)

Statement 2:
b can be any negative integer. Although the equation might not have solutions for a particular range of b, that is not an issue as we're asking for b. Insufficient.

Ans: A
User avatar
nikhil553
User avatar
Joined: 23 Nov 2017
Last visit: 07 Apr 2023
Posts: 22
Own Kudos:
30
 [1]
Given Kudos: 59
Location: India
Posts: 22
Kudos: 30
 [1]
In the equation x^2 + bx + 7= 0, where x is a variable, and b is a con 09 Dec 2019, 13:31
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
TestPrepUnlimited
Bunuel
In the equation \(x^2 + bx + 7= 0\), where x is a variable, and b is a constant. What is the value of b?

(1) x can take only positive integer values
(2) b is a negative integer


Are You Up For the Challenge: 700 Level Questions

Analyzing the Question:
If we have an equation in the form \(x^2 + ax + b= 0\), a is the negative sum of the two roots and b is the product of the two roots. So for \(x^2 + bx + 7= 0\) if we declare the two roots and m and n we have \(m*n = 7\) and \(m + n = -b\).

Statement 1:
m and n are positive, therefore -b must be positive and b must be negative. Insufficient.

Statement 2:
Insufficient.

Combined:
We have duplicate information, we can automatically choose E. Besides m = 1 and n = 7 we can also have m = 0.5, n = 14, or m = n = sqrt(7) etc so there are multiple values of b we can take.
Show more
Statement A says postive integer value; can we use m = 0.5, n = 14 is it correct ? i think the answer is C
User avatar
gvij2017
User avatar
Joined: 09 Aug 2017
Last visit: 18 Jun 2024
Posts: 674
Own Kudos:
486
 [2]
Given Kudos: 778
Posts: 674
Kudos: 486
 [2]
In the equation x^2 + bx + 7= 0, where x is a variable, and b is a con 09 Dec 2019, 17:19
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
x1*x2= 7,
x1+x2= -b

Statement 1
x can be only positive integer.
x can be 7, 1

7+1= 8= -b so b must be -8.
A is sufficient.

St. 2
b is negative.
Not sufficient.

A is answer.
User avatar
ShankSouljaBoi
User avatar
Joined: 21 Jun 2017
Last visit: 17 Apr 2024
Posts: 622
Own Kudos:
603
Given Kudos: 4,090
Location: India
Concentration: Finance, Economics
Schools: Rotman '23 (D) IIMA PGPX'22 (D) Desautels '23 (D) Schulich Sept '23 (D) WBS (D) IIML IPMX'25 (A)
GMAT 1: 660 Q49 V31
GMAT 2: 620 Q47 V30
GMAT 3: 650 Q48 V31
GPA: 3.1
WE:Corporate Finance (Non-Profit and Government)
Products:
My Reviews
Schools: Rotman '23 (D) IIMA PGPX'22 (D) Desautels '23 (D) Schulich Sept '23 (D) WBS (D) IIML IPMX'25 (A)
GMAT 3: 650 Q48 V31
Posts: 622
Kudos: 603
In the equation x^2 + bx + 7= 0, where x is a variable, and b is a con 12 Jan 2020, 09:02
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statement 2 is insufficient because

roots can be 7 and 1 , which means b = -8 and roots can be 3.5 and 2 meaning that b = -5.5.

Hence, insufficient.
A
User avatar
catinabox
User avatar
Joined: 27 Nov 2019
Last visit: 18 Nov 2025
Posts: 567
Own Kudos:
588
Given Kudos: 223
Location: United States (IL)
Schools: Kellogg '24 (M)
GMAT 1: 770 Q50 V44
GPA: 4
Products:
GMAT Club Tests
Schools: Kellogg '24 (M)
GMAT 1: 770 Q50 V44
Posts: 567
Kudos: 588
In the equation x^2 + bx + 7= 0, where x is a variable, and b is a con 04 Aug 2020, 09:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gvij2017
x1*x2= 7,
x1+x2= -b

Statement 1
x can be only positive integer.
x can be 7, 1

7+1= 8= -b so b must be -8.
A is sufficient.

St. 2
b is negative.
Not sufficient.

A is answer.
Show more
Why can x only be 7 or 1? It isn't mentioned that x can take only integral values.
avatar
AdiBir
avatar
Joined: 08 Feb 2020
Last visit: 06 Jul 2021
Posts: 33
Own Kudos:
33
Given Kudos: 146
GMAT 1: 780 Q50 V47
GMAT 1: 780 Q50 V47
Posts: 33
Kudos: 33
In the equation x^2 + bx + 7= 0, where x is a variable, and b is a con 04 Aug 2020, 13:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ShankSouljaBoi
Statement 2 is insufficient because

roots can be 7 and 1 , which means b = -8 and roots can be 3.5 and 2 meaning that b = -5.5.

Hence, insufficient.
A
Show more
b is given as a negative integer. but in your example it’s not an integer.

Posted from my mobile device
avatar
AdiBir
avatar
Joined: 08 Feb 2020
Last visit: 06 Jul 2021
Posts: 33
Own Kudos:
33
Given Kudos: 146
GMAT 1: 780 Q50 V47
GMAT 1: 780 Q50 V47
Posts: 33
Kudos: 33
In the equation x^2 + bx + 7= 0, where x is a variable, and b is a con 04 Aug 2020, 13:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
TestPrepUnlimited
TestPrepUnlimited
Bunuel
In the equation \(x^2 + bx + 7= 0\), where x is a variable, and b is a constant. What is the value of b?

(1) x can take only positive integer values
(2) b is a negative integer


Are You Up For the Challenge: 700 Level Questions

Analyzing the Question:
If we have an equation in the form \(x^2 + ax + b= 0\), a is the negative sum of the two roots and b is the product of the two roots. So for \(x^2 + bx + 7= 0\) if we declare the two roots and m and n we have \(m*n = 7\) and \(m + n = -b\).

Statement 1:
m and n are positive, therefore -b must be positive and b must be negative. Insufficient.

Statement 2:
Insufficient.

Combined:
We have duplicate information, we can automatically choose E. Besides m = 1 and n = 7 we can also have m = 0.5, n = 14, or m = n = sqrt(7) etc so there are multiple values of b we can take.
Show more
Can you please elaborate how statement B is insufficient. Maybe a counterexample.
Thanks in advance :)
User avatar
TestPrepUnlimited
User avatar
Joined: 17 Sep 2014
Last visit: 30 Jun 2022
Posts: 1,224
Own Kudos:
1,111
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Expert
Expert reply
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Posts: 1,224
Kudos: 1,111
In the equation x^2 + bx + 7= 0, where x is a variable, and b is a con 04 Aug 2020, 19:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi AdiBir ,

Thanks for the question! I edited my original post, we're asking for b and the given equation doesn't tell us anything about b. Then with only statement 2, b is allowed to be any negative integer and since we can't confirm a single value it would be insufficient.
User avatar
StacyArko
User avatar
Joined: 24 Jan 2020
Last visit: 18 Nov 2025
Posts: 21
Own Kudos:
7
Given Kudos: 153
Location: Ghana
GMAT 1: 600 Q39 V34
GMAT 1: 600 Q39 V34
Posts: 21
Kudos: 7
In the equation x^2 + bx + 7= 0, where x is a variable, and b is a con 21 Mar 2022, 10:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ShankSouljaBoi
Statement 2 is insufficient because

roots can be 7 and 1 , which means b = -8 and roots can be 3.5 and 2 meaning that b = -5.5.

Hence, insufficient.
A
Show more


But b is a negative integer. And an integer plus a fraction can't be an integer.

However, there can be more than two set of fractional divisors of 7, which give a negative number when added.

Posted from my mobile device
Moderators:
Bunuel
Math Expert
105379 posts
kingbucky
496 posts