Last visit was: 26 Apr 2026, 00:27 It is currently 26 Apr 2026, 00:27
Home
Messages
Tests
Schools
Events
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
655-705 (Hard)|   Algebra|   Inequalities|   Roots|      
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,886
 [15]
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,886
 [15]
Does at least one root of the equation x^2 - 2x - 35 = 0 lie between 23 May 2017, 07:30
2
Kudos
Add Kudos
13
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

66% (02:11) correct 34% (02:09) wrong based on 479 sessions

History

Date
Time
Result
Not Attempted Yet
Does at least one root of the equation \(x^2 - 2x - 35 = 0\) lie between integers a and b ?

    (1) \(ab < 0\)

    (2) \(a + b > 10\)



Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

ShowHide Answer
Official Answer
C
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,886
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,886
Does at least one root of the equation x^2 - 2x - 35 = 0 lie between Updated on: 31 May 2017, 05:21
Originally posted by EgmatQuantExpert on 23 May 2017, 07:31.
Last edited by EgmatQuantExpert on 31 May 2017, 05:21, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The official solution has been posted. Looking forward to a healthy discussion..:)
User avatar
quantumliner
User avatar
Joined: 24 Apr 2016
Last visit: 26 Sep 2018
Posts: 240
Own Kudos:
804
Given Kudos: 48
Posts: 240
Kudos: 804
Does at least one root of the equation x^2 - 2x - 35 = 0 lie between 23 May 2017, 10:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x^2 - 2x - 35 = 0
(x-7)(x+5) = 0
x = 7 or -5

Statement 1:ab<0
This statement tells us that one of a or b is negative and the other is positive.
So if a = -1 and b is 8, then one of the roots is in between a and b
But if a is -1 and b is 2, then none of the roots is in between a and b.
This statement is not sufficient.

Statement 2: a+b>10
So if a = 3 and b is 8, then one of the roots is in between a and b
But if a is 11 and b is 22, then none of the roots is in between a and b.
This statement is not sufficient.

Combining the two statements, we know one of a or b is positive and the other is negative.

So if a is negative, the maximum value a can take is -1,
so applying that to a+b>10, gives b >11, so 7 is in between a and b.

As b is positive, the minimum value b can take is 1.
so applying that to -a+b>10, gives a < -9, so 7 is in between a and b.

Combining both statements is sufficient.

Answer is C
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,886
 [2]
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,886
 [2]
Does at least one root of the equation x^2 - 2x - 35 = 0 lie between 31 May 2017, 05:21
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post

Official Solution



Steps 1 & 2: Understand Question and Draw Inferences

Given: \(x^2−2x−35=0\)

    • a, b are integers

To find: Does at-least one root of the equation \(x^2−2x−35=0\) lie between a and b?

Let’s find the roots of equation

    \(x^2−2x−35=0\)

    ⇒\(x^2−7x+5x−35=0\)

    ⇒\(x=7\) or \(−5\)

Step 3: Analyze Statement 1 independently

(1) \(ab < 0\)

    • a and b are of opposite signs. Does not tell us for sure if 7 or -5 lie between a and b.
Insufficient to answer

Step 4: Analyze Statement 2 independently

(2) \(a + b > 10\)

    • Does not tell us anything about the values of a and b.

    • For example, if \(a = 6\) and \(b = 5, 7\) does not lie between a and b, however if \(a = 8\) and \(b = 5, 7\) lies between a and b.

Insufficient to answer

Step 5: Analyze Both Statements Together (if needed)

(1) From statement-1, a, b are of opposite signs

(2) From statement-2, \(a + b > 10\)

    • Assuming \(a > 0\) and \(b < 0\). Now, we know that \(a + b > 10\)

    • So, the maximum possible value of \(b = -1\). So, we can write \(a – 1 > 10\), i.e. \(a > 11\). So, the minimum possible value of \(a = 12\).Thus, 7 will lie between a and b

    • For the minimum possible value of b(let’s say some large negative integer), a will be a large positive integer.In such a case, both 7 and -5 will lie between a and b.

    • So, at least one of the roots (i.e. 7) lies between a and b. Sufficient to answer the question

Answer: C


Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,986
Own Kudos:
1,118
Posts: 38,986
Kudos: 1,118
Does at least one root of the equation x^2 - 2x - 35 = 0 lie between 15 Jul 2025, 16:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109831 posts
kingbucky
498 posts
Gmat860sanskar
212 posts