NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 23:50 It is currently 27 Apr 2024, 23:50
Decision Tracker
My Rewards
New posts
New comers' posts

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

If x is a positive integer, what is the value of x?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92959
Own Kudos [?]: 619542 [1]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
If x is a positive integer, what is the value of x? [#permalink] New post   20 May 2020, 00:54
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

58% (01:34) correct 42% (01:53) wrong based on 55 sessions
Hide Show timer Statistics

Competition Mode Question



If x is a positive integer, what is the value of x?

(1) (6 - 2x)(6 - x) < 0
(2) (x - 5)(x + 7) < 0
ShowHide Answer
Official Answer
C
User avatar
L
GMATWhizTeam
GMATWhiz Representative
Joined: 07 May 2019
Posts: 3409
Own Kudos [?]: 1802 [1]
Given Kudos: 68
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Send PM
Re: If x is a positive integer, what is the value of x? [#permalink] New post   20 May 2020, 03:02
1
Kudos
Expert Reply

Solution


Step 1: Analyse Question Stem


    • x is a positive integer.
    • We need to find the value of x.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE


Statement 1: (6 -2x)(6-x) < 0
    • The two critical points of the given inequality is x = 3 and x = 6.



    • From the above, we have \((6 -2x)(6-x) < 0 ⟹ 3< x < 6\)
    • Therefore, x = 4 or 5
    • We are not getting a unique value of x here.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2: (x -5)(x+7) < 0
    • The two critical points of the given inequality is x = 5 and x = -7.



    • From the above, we have \((x-5)(x+7) < 0 ⟹ -7 < x < 5\)
    • Therefore, x can be 1, 2, 3, or 4.
    • We are not getting a unique value of x here.
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining.


From statement 1: x can be 4 or 5
From statement 2: x can be 1, 2, 3, or 4.
On combining both, we got, x = 4
Thus, the correct answer is Option C.
User avatar
L
freedom128
Director
Director
Joined: 30 Sep 2017
Posts: 956
Own Kudos [?]: 1256 [1]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Send PM
Reviews Badge
Re: If x is a positive integer, what is the value of x? [#permalink] New post   20 May 2020, 04:27
1
Kudos
x is a positive integer, what is the value of x?

(1) (6 - 2x)(6 - x) < 0
3 < x < 6
x = 4 or 5. We don't know which one.
NOT SUFFICIENT

(2) (x - 5)(x + 7) < 0
-7 < x < 5
x = -6, -5,..., 3, 4. We don't know which one.

COMBINED
Now we know that x=4.
SUFFICIENT

FINAL ANSWER IS (C)

Posted from my mobile device
User avatar
D
exc4libur
SVP
SVP
Joined: 24 Nov 2016
Posts: 1720
Own Kudos [?]: 1344 [1]
Given Kudos: 607
Location: United States
Send PM
Re: If x is a positive integer, what is the value of x? [#permalink] New post   20 May 2020, 05:02
1
Kudos
Quote:
If x is a positive integer, what is the value of x?

(1) (6 - 2x)(6 - x) < 0
(2) (x - 5)(x + 7) < 0


x≥1 (posinteger)

(1) insufic
(6 - 2x)(6 - x) < 0, 2x^2-18x+36<0,
x^2-9x+18<0, (x-3)(x-6)<0,
3<x<6: x=4,5

(2) insufic
(x - 5)(x + 7) < 0,
-7<x<5, 0<x<5, x=1,2,3,4

(1/2) sufic
combined x=4

ans (C)
User avatar
B
aka007
Intern
Intern
Joined: 15 Nov 2019
Posts: 13
Own Kudos [?]: 9 [1]
Given Kudos: 75
Send PM
Re: If x is a positive integer, what is the value of x? [#permalink] New post   20 May 2020, 06:58
1
Kudos
The answer is C

From Statement 1
(x-6)(x-3)<0, therefore x is negative between 3-6 exclusive i.e. only two int values 4&5

From statement 2
(x-5)(x+7)<0, therefore x is negative between -7 to 5 exclusive, multiple +ve int values

combining both statements we get x=4
User avatar
L
MayankSingh
Senior Manager
Senior Manager
Joined: 08 Jan 2018
Posts: 297
Own Kudos [?]: 257 [1]
Given Kudos: 249
Location: India
Concentration: Operations, General Management
Schools: McDonough '25 (A) Marshall '25 (D) Tepper '25 (WA$) Kenan-Flagler '25 (A) ISB '25 (WL) IIMC '25 (A) Owen '26 (A$$$$)
GMAT 1: 640 Q48 V27
GMAT 2: 730 Q51 V38
GPA: 3.9
WE:Project Management (Manufacturing)
Send PM
GMAT ToolKit User Reviews Badge
Re: If x is a positive integer, what is the value of x? [#permalink] New post   20 May 2020, 08:14
1
Kudos
IMO C

If x is a positive integer, what is the value of x?

(1) (6 - 2x)(6 - x) < 0

......+Ve ...... 3 ... -Ve ....... 6 ..... +Ve
So , 3< x < 6
Not sufficient

(2) (x - 5)(x + 7) < 0

.... +Ve....... -7 ..... -Ve ..... 5
So -7 < x < 5
Not Sufficient

Together: x= 4
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8021
Own Kudos [?]: 4100 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: If x is a positive integer, what is the value of x? [#permalink] New post   20 May 2020, 08:26
#1
(6 - 2x)(6 - x) < 0
solve for x we get
x^2-9x+18<0
x= 4,5
insufficient
#2
(x - 5)(x + 7) < 0
value of x = 1,2,3,4
sufficient
from 1 &2
x has to be +4
sufficient
OPTION C

If x is a positive integer, what is the value of x?

(1) (6 - 2x)(6 - x) < 0
(2) (x - 5)(x + 7) < 0
User avatar
P
monikakumar
Manager
Manager
Joined: 23 Jan 2020
Posts: 239
Own Kudos [?]: 143 [1]
Given Kudos: 467
Send PM
GMAT ToolKit User Reviews Badge
Re: If x is a positive integer, what is the value of x? [#permalink] New post   20 May 2020, 22:18
1
Kudos
If x is a positive integer, what is the value of x?

(1) (6 - 2x)(6 - x) < 0
(2) (x - 5)(x + 7) < 0

1) 3<x<6
x=4,5

2) -7<X<5
x=0,1,2,3,4,-6,...

1+2)
x=4
Ans C
GMAT Club Bot
gmatclubot
Re: If x is a positive integer, what is the value of x? [#permalink]
20 May 2020, 22:18
Moderator:
Bunuel
Math Expert
92959 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions