NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 18:56 It is currently 24 Apr 2024, 18:56
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 an integer and 0 < x < 67, 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: 92900
Own Kudos [?]: 618822 [4]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
If x is an integer and 0 < x < 67, what is the value of x? [#permalink] New post   15 Nov 2019, 00:41
1
Kudos
3
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

67% (02:20) correct 33% (02:22) wrong based on 142 sessions
Hide Show timer Statistics

Competition Mode Question



If x is an integer and 0 < x < 67, what is the value of x?

(1) x is divisible by at least two prime numbers greater than 2.
(2) \(\sqrt{x+1} -1\) is prime.


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
E
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8018
Own Kudos [?]: 4096 [2]
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 an integer and 0 < x < 67, what is the value of x? [#permalink] New post   15 Nov 2019, 01:23
1
Kudos
1
Bookmarks
#1
x is divisible by at least two prime numbers greater than 2.
we can have 15,35,55,39 insufficeint
#2
√x+1−1 is prime
x=8,63,35,15
insufficient
from 1 & 2
x=63,35,15
insufficient
IMO E

If x is an integer and 0 < x < 67, what is the value of x?

(1) x is divisible by at least two prime numbers greater than 2.
(2) x+1‾‾‾‾‾√−1x+1−1 is prime.
User avatar
L
CareerGeek
VP
VP
Joined: 20 Jul 2017
Posts: 1300
Own Kudos [?]: 3450 [1]
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
Send PM
Re: If x is an integer and 0 < x < 67, what is the value of x? [#permalink] New post   15 Nov 2019, 01:23
1
Kudos
(1) x is divisible by at least two prime numbers greater than 2.
--> Possible values of x = {15, 21, 33, 35, 39, 51, 55, 57, 63, 65} --> Insufficient

(2) \(\sqrt{x+1}\) - 1 is prime.
--> Possible values of x = {8, 15, 35, 63} --> Insufficient

Combining (1) & (2),
--> Possible values of x = {15, 35, 63} --> No Definite value --> Insufficient

IMO Option E
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 an integer and 0 < x < 67, what is the value of x? [#permalink] New post   15 Nov 2019, 04:13
1
Kudos
Quote:
If x is an integer and 0 < x < 67, what is the value of x?

(1) x is divisible by at least two prime numbers greater than 2.
(2) \(\sqrt{x+1}−1\) is prime.


(1) x is divisible by at least two prime numbers greater than 2. insufic

\(x=(15,35,63)=(5*3,5*7,7*3^2)…\)

(2) \(\sqrt{x+1}−1\) is prime. insufic

\(\sqrt{x+1}−1=p…x+1=(p+1)^2=perf.square\)
\(0<(p+1)^2-1<67…1<(p+1)^2<68…1<p+1≤8…0<p≤7\)
\(p=(2,3,5,7)…(p+1)^2=(9,15,36,64)\)
\(x+1=(9,15,36,64)…x=(8,14,35,63)\)

(1&2) insufic

\(x=(35,63)=(5*7,7*3^2)\)

Ans (E)
User avatar
L
unraveled
CEO
CEO
Joined: 07 Mar 2019
Posts: 2553
Own Kudos [?]: 1813 [1]
Given Kudos: 763
Location: India
WE:Sales (Energy and Utilities)
Send PM
Re: If x is an integer and 0 < x < 67, what is the value of x? [#permalink] New post   15 Nov 2019, 07:52
1
Kudos
If x is an integer and 0 < x < 67, what is the value of x?

(1) x is divisible by at least two prime numbers greater than 2.
x div. by 3 and 5. x = 15 or 45 ..
OR
x div. by 5 and 7. x = 35

INSUFFICIENT.

(2) \(\sqrt{x+1}−1\) is prime.
\(\sqrt{x+1}−1 = p\)
\(\sqrt{x+1} = p + 1\)
x + 1 = \(p^2 + 1 + 2p\)
x = p * (p + 2)
So, x = 2 * (2 + 2) = 8 OR x = 3 * (3 + 2) = 15 OR x = 5 * (5 + 2) = 35

INSUFFICIENT.

Together 1 and 2
Two possibilities still exists, x = 15 or x = 35. Hence

INSUFFICIENT.

IMO Answer E.
User avatar
L
madgmat2019
Director
Director
Joined: 01 Mar 2019
Posts: 592
Own Kudos [?]: 506 [0]
Given Kudos: 207
Location: India
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 580 Q48 V21
GPA: 4
Send PM
Reviews Badge
Re: If x is an integer and 0 < x < 67, what is the value of x? [#permalink] New post   15 Nov 2019, 11:00
(1) x is divisible by at least two prime numbers greater than 2.
There are many numbers b/w 0 and 67.... INSUFFICIENT

(2) √x+1−1 is prime.

√63+1 -1 = 7
√35+1 -1 = 5
√8+1 -1 =3

So insufficient


Combining both only 35 is having two prime factors greater than 2

OA:C
avatar
G
suchithra
Manager
Manager
Joined: 31 Oct 2015
Posts: 92
Own Kudos [?]: 109 [1]
Given Kudos: 179
Send PM
GMAT ToolKit User
Re: If x is an integer and 0 < x < 67, what is the value of x? [#permalink] New post   15 Nov 2019, 12:21
1
Kudos
(1) x is divisible by at least two prime numbers greater than 2.

The prime numbers could be 3,5,7,11,13 etc . Therefore numbers could be 15, 21,35,65 Insufficient.

(2) \sqrt{x+1}-1 is prime.

Let the above expression equal to Y.

Y+1 = \sqrt{X+1}

(y+1)^2 = x+1

Since Y is any prime number 1,2,3,5,7, 11.. there could a multitude of values for x like 3, 8,15,35,63

Insufficient

Both statements together, we see X could be 15, 35,65 . Therefore insufficient

Answer is E
User avatar
D
minustark
Senior Manager
Senior Manager
Joined: 14 Jul 2019
Status:Student
Posts: 478
Own Kudos [?]: 369 [1]
Given Kudos: 52
Location: United States
Concentration: Accounting, Finance
Schools: Zicklin Baruch "22
GMAT 1: 650 Q45 V35
GPA: 3.9
WE:Education (Accounting)
Send PM
Reviews Badge
Re: If x is an integer and 0 < x < 67, what is the value of x? [#permalink] New post   15 Nov 2019, 15:03
1
Kudos
If x is an integer and 0 < x < 67, what is the value of x?

(1) x is divisible by at least two prime numbers greater than 2.
(2)\(\sqrt{x+1}\)−1 is prime.

(1) x can be 15, 30, 45, 60 (divisible by 3 and 5 ), or 35 (divisible by 5 and 7) or 33,66 (divisible by 3 and 11), 55 (divisible by 5 and 11), 21, 42 (divisible by 3 and 7). So, Not sufficient.

(2) x can be 15 (3 is the resulting integer) or 35 (5 is the resulting integer). Not sufficient

Combining both, x can be either 15 or 35. Not sufficient.
E is the answer.
User avatar
D
eakabuah
Retired Moderator
Joined: 18 May 2019
Posts: 785
Own Kudos [?]: 1040 [1]
Given Kudos: 101
Send PM
GMAT ToolKit User
Re: If x is an integer and 0 < x < 67, what is the value of x? [#permalink] New post   15 Nov 2019, 21:10
1
Kudos
We are given that x is divisible by at least two prime numbers greater than 2 and that 0<x<67.

Statement 1: x is divisible by at least two prime numbers greater than 2.
Possible values of x: 15, 21, 30, 33, 35, etc.
Statement 1 does not lead to a unique value of x, hence it is not sufficient.

Statement 2: √(x+1)-1 is prime
Possible values of x: 8, 15, 35, 63.
Statement 2 does not lead to a unique value of x, hence it is not sufficient.

1+2
The numbers that satisfy conditions 1 and 2 are: 15, 35, and 63.
Statements 1 and 2 when combined do not lead to a unique value of x. This means both statements even when combined are not sufficient.

The answer is, therefore, option E.
avatar
B
GmatAssasin24
Intern
Intern
Joined: 01 Jul 2016
Posts: 15
Own Kudos [?]: 1 [0]
Given Kudos: 17
Location: India
Schools: Foster '24 Katz Simon '24
Send PM
Re: If x is an integer and 0 < x < 67, what is the value of x? [#permalink] New post   16 Nov 2019, 05:17
St 1 : clearly not sufficient.

St 2: Not sufficient.

Both : sufficient.

Considering that X is divisible by at least 2 primes >2, then we can test for values ..3,5,7 etc.

35 = 7×5 satisfies the condition.

√35+1-1 = 5. Prime no.

That's why (c)

Posted from my mobile device
avatar
B
ankitprad
Intern
Intern
Joined: 18 Jul 2019
Posts: 36
Own Kudos [?]: 35 [1]
Given Kudos: 128
Send PM
Re: If x is an integer and 0 < x < 67, what is the value of x? [#permalink] New post   16 Nov 2019, 07:20
1
Kudos
IMO E
Statement 1 : x can be 15 / 21 / 35, both divisible by 3 & 5, 3 & 7 and 7 & 5 respectively. Not sufficient.
Statement 2 : sqrt 35+1 = 6 -1 = 5, which is a prime number or x = 15. sqrt 15+ 1 = 4 -1 = 3 . Not sufficient.
Combine both statements, we have x = 15 or 35.
avatar
Lana656
Intern
Intern
Joined: 10 May 2016
Posts: 3
Own Kudos [?]: 1 [0]
Given Kudos: 1
Send PM
Re: If x is an integer and 0 < x < 67, what is the value of x? [#permalink] New post   16 Nov 2019, 12:12
Possible values for x are: x=3*5=15, x= 5*7=35, x=11*13=143, x=17*19=323, x=29*31=899, x=41*43=1763, x=59*61=3599.
User avatar
D
lacktutor
Director
Director
Joined: 25 Jul 2018
Posts: 668
Own Kudos [?]: 1117 [1]
Given Kudos: 69
Send PM
Re: If x is an integer and 0 < x < 67, what is the value of x? [#permalink] New post   16 Nov 2019, 13:26
1
Kudos
If x is an integer and 0 < x < 67, what is the value of x?

(Statement1):
—> x could be 15(3*5 ), or 35( 5*7), or 63 (7*9)
Insufficient

(Statement2):
If x=8, then \((8+1)^{1/2} —1= 3–1=2\)(prime)

If x=15, then \((15+1)^{1/2}—1= 4–1=3\) (prime)

Insufficient

Taken together 1&2,
x could be 15(3*5)
—> \((15+1)^{1/2} —1= 4–1=3\) (prime)

x could be 35 (5*7)
—> \((35+1)^{1/2}—1= 6–1=5\) (prime)

Also, x could be 63

Insufficient

The answer is E.

Posted from my mobile device
GMAT Club Bot
gmatclubot
Re: If x is an integer and 0 < x < 67, what is the value of x? [#permalink]
16 Nov 2019, 13:26
Moderator:
Bunuel
Math Expert
92900 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