GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Oct 2019, 16:43 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

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.  Is integer x prime?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Senior Manager  Joined: 22 Dec 2009
Posts: 253
Is integer x prime?  [#permalink]

Show Tags

1 00:00

Difficulty:   15% (low)

Question Stats: 85% (01:20) correct 15% (01:50) wrong based on 111 sessions

HideShow timer Statistics

Is integer x prime?

(1) $$x^2-3$$ is an even number

(2) $$x+2$$ is an odd number

_________________
Cheers!
JT...........
If u like my post..... payback in Kudos!! |Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~

Originally posted by jeeteshsingh on 07 Mar 2010, 10:23.
Last edited by Bunuel on 07 Jan 2014, 07:13, edited 3 times in total.
Edited the question and added the OA.
Manager  Joined: 30 Aug 2009
Posts: 226
Location: India
Concentration: General Management
Re: Is integer x prime?  [#permalink]

Show Tags

jeeteshsingh wrote:
kp1811 wrote:
jeeteshsingh wrote:
Is Integer x prime?
1. $$x^2-3$$ is an even number
2. $$x+2$$ is an odd number

E...

Made the question more clear for you...!

will try to make it more clearer.....

stmnt1) x^2 - 3 is even

let x = 3 (prime) then 3^2 - 3 = 6 even
let x =9 (non prime) then 9^2 - 3 = 78 even
hence insuff

stmnt2) x+2 is odd
let x = 3 (prime) then 3 + 2 = 5 odd
let x =9 (non prime) then 9 + 2 = 11 odd
hence insuff

even together they don't suffice. Hence E
Senior Manager  Joined: 22 Dec 2009
Posts: 253
Re: Is integer x prime?  [#permalink]

Show Tags

kp1811 wrote:
jeeteshsingh wrote:

will try to make it more clearer.....

stmnt1) x^2 - 3 is even

let x = 3 (prime) then 3^2 - 3 = 6 even
let x =9 (non prime) then 9^2 - 3 = 78 even
hence insuff

stmnt2) x+2 is odd
let x = 3 (prime) then 3 + 2 = 5 odd
let x =9 (non prime) then 9 + 2 = 11 odd
hence insuff

even together they don't suffice. Hence E

Some how I dont get this approach as you use the ques to prove the statement below. This question is from PR 1012 and I see the same solution there which isnt convincing for me.

My approach is as follows:

Given x is an integer.
Ques is x prime?

S1: x^2 - 3 = even
x^2 - 3 = 2m where m is an integer
x = sqrt(2m + 3) where m is >= 0 as you cannot have - ve sqrt.

This gives x = $$\sqrt{3},\sqrt{5},\sqrt{7},3,\sqrt{11},\sqrt{13},\sqrt{15},\sqrt{17},\sqrt{19},\sqrt{21},\sqrt{23},5,\sqrt{27},\sqrt{29},.....$$
Since it is given that x is an integer we get only 3, 5, 7..... which are all prime. Hence SUFF.

S2: x + 2 is odd
x + 2 = 2k + 1 where k is an integer
x = 2k - 1
Therefore x = ....-7,-5,-3,-1,1,3,5,7,9,11... which means all odd numbers and hence not necessarily be prime. Therefore NOT SUFF.

Hence answer is A....!

Can someone highlight what is wrong in my approach!
_________________
Cheers!
JT...........
If u like my post..... payback in Kudos!! |Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~
Manager  Joined: 30 Aug 2009
Posts: 226
Location: India
Concentration: General Management
Re: Is integer x prime?  [#permalink]

Show Tags

2
jeeteshsingh wrote:
kp1811 wrote:
jeeteshsingh wrote:

will try to make it more clearer.....

stmnt1) x^2 - 3 is even

let x = 3 (prime) then 3^2 - 3 = 6 even
let x =9 (non prime) then 9^2 - 3 = 78 even
hence insuff

stmnt2) x+2 is odd
let x = 3 (prime) then 3 + 2 = 5 odd
let x =9 (non prime) then 9 + 2 = 11 odd
hence insuff

even together they don't suffice. Hence E

Some how I dont get this approach as you use the ques to prove the statement below. This question is from PR 1012 and I see the same solution there which isnt convincing for me.

My approach is as follows:

Given x is an integer.
Ques is x prime?

S1: x^2 - 3 = even
x^2 - 3 = 2m where m is an integer
x = sqrt(2m + 3) where m is >= 0 as you cannot have - ve sqrt.

This gives x = $$\sqrt{3},\sqrt{5},\sqrt{7},3,\sqrt{11},\sqrt{13},\sqrt{15},\sqrt{17},\sqrt{19},\sqrt{21},\sqrt{23},5,\sqrt{27},\sqrt{29},.....$$
Since it is given that x is an integer we get only 3, 5, 7..... which are all prime. Hence SUFF.

S2: x + 2 is odd
x + 2 = 2k + 1 where k is an integer
x = 2k - 1
Therefore x = ....-7,-5,-3,-1,1,3,5,7,9,11... which means all odd numbers and hence not necessarily be prime. Therefore NOT SUFF.

Hence answer is A....!

Can someone highlight what is wrong in my approach!

in highlighted part after 3,5, 7 .... 9 will come [ for m = 39] which is non prime
Senior Manager  Joined: 22 Dec 2009
Posts: 253
Re: Is integer x prime?  [#permalink]

Show Tags

kp1811 wrote:
jeeteshsingh wrote:

Some how I dont get this approach as you use the ques to prove the statement below. This question is from PR 1012 and I see the same solution there which isnt convincing for me.

My approach is as follows:

Given x is an integer.
Ques is x prime?

S1: x^2 - 3 = even
x^2 - 3 = 2m where m is an integer
x = sqrt(2m + 3) where m is >= 0 as you cannot have - ve sqrt.

This gives x = $$\sqrt{3},\sqrt{5},\sqrt{7},3,\sqrt{11},\sqrt{13},\sqrt{15},\sqrt{17},\sqrt{19},\sqrt{21},\sqrt{23},5,\sqrt{27},\sqrt{29},.....$$
Since it is given that x is an integer we get only 3, 5, 7..... which are all prime. Hence SUFF.

S2: x + 2 is odd
x + 2 = 2k + 1 where k is an integer
x = 2k - 1
Therefore x = ....-7,-5,-3,-1,1,3,5,7,9,11... which means all odd numbers and hence not necessarily be prime. Therefore NOT SUFF.

Hence answer is A....!

Can someone highlight what is wrong in my approach!

in highlighted part after 3,5, 7 .... 9 will come [ for m = 39] which is non prime

Thanks mate! Got it Now! Kudos +1
_________________
Cheers!
JT...........
If u like my post..... payback in Kudos!! |Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~
SVP  Joined: 06 Sep 2013
Posts: 1570
Concentration: Finance
Re: Is Integer x prime? 1. x^2-3 is an even number 2. x+2 is an  [#permalink]

Show Tags

jeeteshsingh wrote:
Is Integer x prime?
1. $$x^2-3$$ is an even number
2. $$x+2$$ is an odd number

Yeah answer is clearly A cause in B, 1 is obviously not a prime number

Now question, when they say that something is an odd number

Do they mean odd integer? Cause I'm pretty sure the definitions of number and integer are different

Now, can a decimal be odd? Say like 1.5 is odd and 1.2 is even I guess so right?

Just wanted to clarify on those

Cheers!
J Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: Is Integer x prime? 1. x^2-3 is an even number 2. x+2 is an  [#permalink]

Show Tags

jlgdr wrote:
jeeteshsingh wrote:
Is Integer x prime?
1. $$x^2-3$$ is an even number
2. $$x+2$$ is an odd number

Yeah answer is clearly A cause in B, 1 is obviously not a prime number

Now question, when they say that something is an odd number

Do they mean odd integer? Cause I'm pretty sure the definitions of number and integer are different

Now, can a decimal be odd? Say like 1.5 is odd and 1.2 is even I guess so right?

Just wanted to clarify on those

Cheers!
J Only integers can be odd or even. So, odd number and odd integer are the same thing.
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: Is Integer x prime? 1. x^2-3 is an even number 2. x+2 is an  [#permalink]

Show Tags

1
jlgdr wrote:
jeeteshsingh wrote:
Is Integer x prime?
1. $$x^2-3$$ is an even number
2. $$x+2$$ is an odd number

Yeah answer is clearly A cause in B, 1 is obviously not a prime number

Now question, when they say that something is an odd number

Do they mean odd integer? Cause I'm pretty sure the definitions of number and integer are different

Now, can a decimal be odd? Say like 1.5 is odd and 1.2 is even I guess so right?

Just wanted to clarify on those

Cheers!
J The correct answer is not A, it's E. Consider x=1 and x=3.

Hope it helps.
_________________
Intern  Joined: 10 Oct 2013
Posts: 33
Concentration: Marketing, Entrepreneurship
GMAT 1: 730 Q50 V38 Re: Is integer x prime?  [#permalink]

Show Tags

jeeteshsingh wrote:
kp1811 wrote:
jeeteshsingh wrote:

will try to make it more clearer.....

stmnt1) x^2 - 3 is even

let x = 3 (prime) then 3^2 - 3 = 6 even
let x =9 (non prime) then 9^2 - 3 = 78 even
hence insuff

stmnt2) x+2 is odd
let x = 3 (prime) then 3 + 2 = 5 odd
let x =9 (non prime) then 9 + 2 = 11 odd
hence insuff

even together they don't suffice. Hence E

Some how I dont get this approach as you use the ques to prove the statement below. This question is from PR 1012 and I see the same solution there which isnt convincing for me.

My approach is as follows:

Given x is an integer.
Ques is x prime?

S1: x^2 - 3 = even
x^2 - 3 = 2m where m is an integer
x = sqrt(2m + 3) where m is >= 0 as you cannot have - ve sqrt.

This gives x = $$\sqrt{3},\sqrt{5},\sqrt{7},3,\sqrt{11},\sqrt{13},\sqrt{15},\sqrt{17},\sqrt{19},\sqrt{21},\sqrt{23},5,\sqrt{27},\sqrt{29},.....$$
Since it is given that x is an integer we get only 3, 5, 7..... which are all prime. Hence SUFF.

S2: x + 2 is odd
x + 2 = 2k + 1 where k is an integer
x = 2k - 1
Therefore x = ....-7,-5,-3,-1,1,3,5,7,9,11... which means all odd numbers and hence not necessarily be prime. Therefore NOT SUFF.

Hence answer is A....!

Can someone highlight what is wrong in my approach!

Hello,
Just a small thing
You say "x = sqrt(2m + 3) where m is >= 0 as you cannot have - ve sqrt."
but your m can be -1, still square root would be +ve i.e 1;
now you have to add x=1 to your list :1,3,5,7 etc.
As 1 is not prime.
A becomes insufficient.

Cheers!!! Manager  Joined: 20 Dec 2013
Posts: 116
Re: Is integer x prime?  [#permalink]

Show Tags

jeeteshsingh wrote:
Is integer x prime?

(1) $$x^2-3$$ is an even number

(2) $$x+2$$ is an odd number

X is an integer.

Statement I is insufficient:

x = 5 (Prime) x = 9 (Not Prime)

Statement II is insufficient:

5 + 2 is odd 9 + 2 is odd

No need to combine since we are using the same set of numbers to disprove each statement individually

Hence answer is E
_________________
76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org
Manager  Joined: 25 Oct 2013
Posts: 142
Re: Is integer x prime?  [#permalink]

Show Tags

Stmt 1: $$x^2-3$$ is even simply means x is odd integer. Now x being odd is not sufficient for it to be prime. INSUFF
Stm2: x+2 is odd means x is odd integer. Therefore stmt 1 & 2 are same. INSUFF

Both statements together give no new information. hence E.
_________________
Click on Kudos if you liked the post!

Practice makes Perfect.
Non-Human User Joined: 09 Sep 2013
Posts: 13262
Re: Is integer x prime?  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: Is integer x prime?   [#permalink] 24 Jan 2018, 04:34
Display posts from previous: Sort by

Is integer x prime?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  