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

 It is currently 23 Sep 2018, 04:06

### 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

# If 3x + 5 < x + 11, is x prime?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 14 Mar 2010
Posts: 68
If 3x + 5 < x + 11, is x prime?  [#permalink]

### Show Tags

Updated on: 20 Jan 2013, 05:30
1
10
00:00

Difficulty:

95% (hard)

Question Stats:

30% (01:05) correct 70% (00:43) wrong based on 348 sessions

### HideShow timer Statistics

If 3x + 5 < x + 11, is x prime?

(1) The sum of x and y is even
(2) The product of x and y is odd.

_________________

MGMAT CAT MATH http://gmatclub.com/forum/mgmat-cat-math-144609.html
MGMAT SC SUMMARY: http://gmatclub.com/forum/mgmat-sc-summary-144610.html

Originally posted by monir6000 on 19 Jan 2013, 21:32.
Last edited by Bunuel on 20 Jan 2013, 05:30, edited 1 time in total.
Moved to DS forum.
Math Expert
Joined: 02 Sep 2009
Posts: 49314
Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

### Show Tags

20 Jan 2013, 05:46
6
If 3x + 5 < x + 11, is x prime?

$$3x + 5 < x + 11$$ --> $$x<3$$. So, we have that x is less than 3. There is only one prime number less than 3, namely 2. So, the question basically asks whether $$x=2$$. Notice here that we are not told that x and y are integers.

(1) The sum of x and y is even. It's certainly possible that x is a prime number, for example if $$x=y=2$$, but it's also possible that x is NOT a prime number, for example if $$x=y=1$$. Not sufficient.

(2) The product of x and y is odd. The same here: it's possible that x is a prime number, for example if $$x=2$$ and $$y=0.5$$, but it's also possible that x is NOT a prime number, for example if $$x=y=1$$. Not sufficient.

(1)+(2) Suppose $$x=2=prime$$, then from (1) it follows that $$y=even$$, but in this case $$xy=even$$, not odd as stated in (2). Thus our assumption that $$x=2=prime$$ was wrong. Therefore, x cannot be a prime number. Sufficient.

Hope it's clear.

P.S. Please post PS questions in PS forum and DS questions in DS forum. Thank you.
_________________
##### General Discussion
Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 146
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

### Show Tags

19 Jan 2013, 22:58
1
First of all, the question should be in DS section... and second, question stem seem to be missing Y... is it 3x + 5 < y + 11 or 3y + 5 < x + 11 ?

And if question stem is correct, then here is the solution:
3x + 5 < x + 11
2x <6
x < 3 (so possible values .....0,1,2)

St1. x+y= Even ... this will happen only if both are even or if both are odd.... so not-sufficient

St2. XY=Odd ... both has to be odd....So x can have only one value i.e. 1 as 0 and 2 are Even

So B is sufficient to answer the question.
_________________

Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Senior Manager
Joined: 27 Jun 2012
Posts: 387
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

### Show Tags

20 Jan 2013, 01:33
2
daviesj wrote:
First of all, the question should be in DS section... and second, question stem seem to be missing Y... is it 3x + 5 < y + 11 or 3y + 5 < x + 11 ?

And if question stem is correct, then here is the solution:
3x + 5 < x + 11
2x <6
x < 3 (so possible values .....0,1,2)

St1. x+y= Even ... this will happen only if both are even or if both are odd.... so not-sufficient

St2. XY=Odd ... both has to be odd....So x can have only one value i.e. 1 as 0 and 2 are Even

So B is sufficient to answer the question.

Only B is NOT sufficient. We dont know whether y is integer.
x=2, y=1.5 -> xy=3 odd
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here
Finance your Student loan through SoFi and get $100 referral bonus : Click here Senior Manager Joined: 27 Jun 2012 Posts: 387 Concentration: Strategy, Finance Schools: Haas EWMBA '17 Re: If 3x + 5 < x + 11, is x prime? [#permalink] ### Show Tags 20 Jan 2013, 02:34 Question: If 3x + 5 < x + 11, is x prime? Simplify equation to x<3. Hence question becomes is x=2? (1) the sum of x and y is even INSUFFICIENT: We dont know y (2) The product of x and y is odd. INSUFFICIENT: We dont know whether y is integer e.g. x=2, y=1.5 then xy=3 (ODD) e.g. x=1, y=3 then xy=3 (ODD) x can be 1 or 2, hence its not sufficient. Combining (1) & (2) SUFFICIENT: If x = 2, y must be 1.5 or -1.5 to make xy (ODD), however x + y cannot be EVEN. If x = 2, y must be 0 or even to make x + y (EVEN), however xy cannot be ODD Thus if x=2, both statements cannot be true simultaneously. This information is SUFFICIENT to prove x cannot be 2. Hence choice(C) is the answer. _________________ Thanks, Prashant Ponde Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here Finance your Student loan through SoFi and get$100 referral bonus : Click here

Manager
Joined: 04 Oct 2011
Posts: 197
Location: India
GMAT 1: 440 Q33 V13
GPA: 3
Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

### Show Tags

20 Jan 2013, 06:06
1
PraPon wrote:
Question: If 3x + 5 < x + 11, is x prime?
Simplify equation to x<3. Hence question becomes is x=2?

(1) the sum of x and y is even
INSUFFICIENT: We dont know y

(2) The product of x and y is odd.
INSUFFICIENT: We dont know whether y is integer
e.g. x=2, y=1.5 then xy=3 (ODD)
e.g. x=1, y=3 then xy=3 (ODD)
x can be 1 or 2, hence its not sufficient.

Combining (1) & (2)
SUFFICIENT:
If x = 2, y must be 1.5 or -1.5 to make xy (ODD), however x + y cannot be EVEN.
If x = 2, y must be 0 or even to make x + y (EVEN), however xy cannot be ODD
Thus if x=2, both statements cannot be true simultaneously.
This information is SUFFICIENT to prove x cannot be 2.

Hi PraPon,

Here u are assuming x=2 and moving forward!

But wat if x is negative?
if x= -3 or x= -10

coz question doesnt state x is positive !
_________________

GMAT - Practice, Patience, Persistence
Kudos if u like

Math Expert
Joined: 02 Sep 2009
Posts: 49314
Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

### Show Tags

20 Jan 2013, 06:11
shanmugamgsn wrote:
PraPon wrote:
Question: If 3x + 5 < x + 11, is x prime?
Simplify equation to x<3. Hence question becomes is x=2?

(1) the sum of x and y is even
INSUFFICIENT: We dont know y

(2) The product of x and y is odd.
INSUFFICIENT: We dont know whether y is integer
e.g. x=2, y=1.5 then xy=3 (ODD)
e.g. x=1, y=3 then xy=3 (ODD)
x can be 1 or 2, hence its not sufficient.

Combining (1) & (2)
SUFFICIENT:
If x = 2, y must be 1.5 or -1.5 to make xy (ODD), however x + y cannot be EVEN.
If x = 2, y must be 0 or even to make x + y (EVEN), however xy cannot be ODD
Thus if x=2, both statements cannot be true simultaneously.
This information is SUFFICIENT to prove x cannot be 2.

Hi PraPon,

Here u are assuming x=2 and moving forward!

But wat if x is negative?
if x= -3 or x= -10

coz question doesnt state x is positive !

The point is if we assume that x=2=prime, then both statements cannot be true at the same time, which means that x cannot be 2. Check here: if-3x-5-x-11-is-x-prime-146067.html#p1171395

Hope it;s clear.
_________________
Board of Directors
Joined: 01 Sep 2010
Posts: 3415
Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

### Show Tags

20 Jan 2013, 07:33
Moreover if we rephrasing the question we have to find if x=2 yes or not....but if x=2 (prime or not prime) then we deal only with positive number. Prime are only positive integers
_________________
Intern
Joined: 16 Jan 2014
Posts: 14
Location: India
GMAT Date: 09-19-2014
GPA: 3.8
WE: Design (Aerospace and Defense)
Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

### Show Tags

10 Jul 2014, 04:40
PrashantPonde wrote:
Question: If 3x + 5 < x + 11, is x prime?
Simplify equation to x<3. Hence question becomes is x=2?

(1) the sum of x and y is even
INSUFFICIENT: We dont know y

(2) The product of x and y is odd.
INSUFFICIENT: We dont know whether y is integer
e.g. x=2, y=1.5 then xy=3 (ODD)
e.g. x=1, y=3 then xy=3 (ODD)
x can be 1 or 2, hence its not sufficient.

Combining (1) & (2)
SUFFICIENT:
If x = 2, y must be 1.5 or -1.5 to make xy (ODD), however x + y cannot be EVEN.
If x = 2, y must be 0 or even to make x + y (EVEN), however xy cannot be ODD
Thus if x=2, both statements cannot be true simultaneously.
This information is SUFFICIENT to prove x cannot be 2.

According to my knowledge 1 is Neither Prime nor Composite.
Please correct me if GMAT thinks the other way.
Intern
Joined: 16 Jan 2014
Posts: 14
Location: India
GMAT Date: 09-19-2014
GPA: 3.8
WE: Design (Aerospace and Defense)
Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

### Show Tags

10 Jul 2014, 04:42
shanmugamgsn wrote:
PraPon wrote:
Question: If 3x + 5 < x + 11, is x prime?
Simplify equation to x<3. Hence question becomes is x=2?

(1) the sum of x and y is even
INSUFFICIENT: We dont know y

(2) The product of x and y is odd.
INSUFFICIENT: We dont know whether y is integer
e.g. x=2, y=1.5 then xy=3 (ODD)
e.g. x=1, y=3 then xy=3 (ODD)
x can be 1 or 2, hence its not sufficient.

Combining (1) & (2)
SUFFICIENT:
If x = 2, y must be 1.5 or -1.5 to make xy (ODD), however x + y cannot be EVEN.
If x = 2, y must be 0 or even to make x + y (EVEN), however xy cannot be ODD
Thus if x=2, both statements cannot be true simultaneously.
This information is SUFFICIENT to prove x cannot be 2.

Hi PraPon,

Here u are assuming x=2 and moving forward!

But wat if x is negative?
if x= -3 or x= -10

coz question doesnt state x is positive !

Are prime No. Negative as well.

I thought Primes are from 2,3,5...And 1 being neither prime nor Composite.
Math Expert
Joined: 02 Sep 2009
Posts: 49314
If 3x + 5 < x + 11, is x prime?  [#permalink]

### Show Tags

10 Jul 2014, 04:46
1
karna2129 wrote:
PrashantPonde wrote:
Question: If 3x + 5 < x + 11, is x prime?
Simplify equation to x<3. Hence question becomes is x=2?

(1) the sum of x and y is even
INSUFFICIENT: We dont know y

(2) The product of x and y is odd.
INSUFFICIENT: We dont know whether y is integer
e.g. x=2, y=1.5 then xy=3 (ODD)
e.g. x=1, y=3 then xy=3 (ODD)
x can be 1 or 2, hence its not sufficient.

Combining (1) & (2)
SUFFICIENT:
If x = 2, y must be 1.5 or -1.5 to make xy (ODD), however x + y cannot be EVEN.
If x = 2, y must be 0 or even to make x + y (EVEN), however xy cannot be ODD
Thus if x=2, both statements cannot be true simultaneously.
This information is SUFFICIENT to prove x cannot be 2.

According to my knowledge 1 is Neither Prime nor Composite.
Please correct me if GMAT thinks the other way.

GMAT doe not have some kind of their own math.

1. 1 is not a prime, since it only has one divisor, namely 1.
2. Only positive numbers can be primes.
3. There are infinitely many prime numbers.
4. the only even prime number is 2. Also 2 is the smallest prime.
5. All prime numbers except 2 and 5 end in 1, 3, 7 or 9.

Theory on Number Properties: math-number-theory-88376.html
Number Properties - Tips and hints: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1371030

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59
_________________
Director
Joined: 10 Mar 2013
Posts: 547
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
If 3x + 5 < x + 11, is x prime?  [#permalink]

### Show Tags

10 Dec 2015, 05:05
monir6000 wrote:
If 3x + 5 < x + 11, is x prime?

(1) The sum of x and y is even
(2) The product of x and y is odd.

It's not an original question, see here https://www.manhattanprep.com/gmat/foru ... t2804.html

Please find below the original question from MGMAT

If x and y are positive integers and 3x + 5 < x + 11, is x a prime number?

(1) The sum of x and y is even.
(2) The product of x and y is odd.

And the answer for the original question is B
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Senior Manager
Joined: 02 Apr 2014
Posts: 477
GMAT 1: 700 Q50 V34
Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

### Show Tags

03 Oct 2017, 13:45
I have a different variation of this question from my source.

If x and y are positive integers and 3 x + 5 < x + 11, is x a prime number?
(1) The sum of x and y is even.
(2) The product of x and y is odd.

in this case, answer should be B.

If y is not given as integer explicitly in the question, then answer is C
Re: If 3x + 5 < x + 11, is x prime? &nbs [#permalink] 03 Oct 2017, 13:45
Display posts from previous: Sort by

# If 3x + 5 < x + 11, is x prime?

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.