If 3x + 5 < x + 11, is x prime? : Data Sufficiency (DS)

daviesj

Manager

Joined: 23 Aug 2012

Status:Never ever give up on yourself.Period.

Posts: 115

Own Kudos [?]: 1138 [2]

Given Kudos: 35

Location: India

Concentration: Finance, Human Resources

Schools: MBS '17 (A$) Smurfit FT'16 (A)

GMAT 1: 570 Q47 V21

GMAT 2: 690 Q50 V33

GPA: 3.5

WE:Information Technology (Investment Banking)

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

19 Jan 2013, 22:58

2

Kudos

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.

PrashantPonde

Senior Manager

Joined: 27 Jun 2012

Posts: 325

Own Kudos [?]: 2467 [2]

Given Kudos: 185

Concentration: Strategy, Finance

Schools: Haas EWMBA '17

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

20 Jan 2013, 02:34

1

Kudos

1

Bookmarks

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.

shanmugamgsn

Manager

Joined: 04 Oct 2011

Posts: 144

Own Kudos [?]: 141 [2]

Given Kudos: 44

Location: India

Concentration: Entrepreneurship, International Business

GMAT 1: 440 Q33 V13

GPA: 3

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

20 Jan 2013, 06:06

1

Kudos

1

Bookmarks

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.

Hence choice(C) is the answer.

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 !

P

hellosanthosh2k2

Senior Manager

Joined: 02 Apr 2014

Posts: 371

Own Kudos [?]: 474 [2]

Given Kudos: 1227

Location: India

Schools: XLRI"20

GMAT 1: 700 Q50 V34 Verified score

GPA: 3.5

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

03 Oct 2017, 13:45

2

Kudos

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

L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92887

Own Kudos [?]: 618656 [1]

Given Kudos: 81563

Send PM

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

10 Jul 2014, 04:46

1

Kudos

Expert Reply

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.

Hence choice(C) is the answer.

According to my knowledge 1 is Neither Prime nor Composite.
Please correct me if GMAT thinks the other way.
I am really concerned about this

GMAT doe not have some kind of their own math.

Facts about primes:
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

B

BrainLab

Current Student

Joined: 10 Mar 2013

Posts: 360

Own Kudos [?]: 2696 [1]

Given Kudos: 200

Location: Germany

Concentration: Finance, Entrepreneurship

Schools: WHU MBA"20 (A$)

GMAT 1: 580 Q46 V24

GPA: 3.7

WE:Marketing (Telecommunications)

Send PM

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

10 Dec 2015, 05:05

1

Kudos

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

L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92887

Own Kudos [?]: 618656 [0]

Given Kudos: 81563

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

20 Jan 2013, 06:11

Expert Reply

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.

Hence choice(C) is the answer.

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.

L

carcass

Board of Directors

Joined: 01 Sep 2010

Posts: 4380

Own Kudos [?]: 32864 [0]

Given Kudos: 4453

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

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

karna2129

Intern

Joined: 16 Jan 2014

Posts: 8

Own Kudos [?]: 5 [0]

Given Kudos: 5

Location: India

Concentration: International Business, Leadership

Schools: Stern '17 Kellogg 1YR '17 Tuck '17 HBS '17 Stanford '17

GMAT Date: 09-19-2014

GPA: 3.8

WE:Design (Aerospace and Defense)

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

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.

Hence choice(C) is the answer.

According to my knowledge 1 is Neither Prime nor Composite.
Please correct me if GMAT thinks the other way.
I am really concerned about this

karna2129

Intern

Joined: 16 Jan 2014

Posts: 8

Own Kudos [?]: 5 [0]

Given Kudos: 5

Location: India

Concentration: International Business, Leadership

Schools: Stern '17 Kellogg 1YR '17 Tuck '17 HBS '17 Stanford '17

GMAT Date: 09-19-2014

GPA: 3.8

WE:Design (Aerospace and Defense)

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

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.

Hence choice(C) is the answer.

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.
Please help me on this

fracheva

Intern

Joined: 06 Sep 2018

Posts: 5

Own Kudos [?]: 0 [0]

Given Kudos: 1

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

26 Nov 2018, 08:44

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.

Hence choice(C) is the answer.

I don't really get it. If we assume x = 1 and y = 3 don't we get a different answer? The sum would be even and the product odd.

P

amanvermagmat

Retired Moderator

Joined: 22 Aug 2013

Posts: 1186

Own Kudos [?]: 2499 [0]

Given Kudos: 459

Location: India

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

26 Nov 2018, 11:28

fracheva 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.

Hence choice(C) is the answer.

I don't really get it. If we assume x = 1 and y = 3 don't we get a different answer? The sum would be even and the product odd.

Hello

Yes, thats the point. If we take your example of x=1, y=3, it satisfies both the question statements as you have just written. And what is x here? x=1, which is NOT prime. So this again proves that x is not a prime number.

No matter which values of x/y we take which satisfy both the given statements, we will always get a value of x which is NOT prime. So this is sufficient to answer the question with a NO. Hence C answer

fracheva

Intern

Joined: 06 Sep 2018

Posts: 5

Own Kudos [?]: 0 [0]

Given Kudos: 1

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

27 Nov 2018, 01:18

amanvermagmat wrote:

fracheva 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.

Hence choice(C) is the answer.

I don't really get it. If we assume x = 1 and y = 3 don't we get a different answer? The sum would be even and the product odd.

Hello

Yes, thats the point. If we take your example of x=1, y=3, it satisfies both the question statements as you have just written. And what is x here? x=1, which is NOT prime. So this again proves that x is not a prime number.

No matter which values of x/y we take which satisfy both the given statements, we will always get a value of x which is NOT prime. So this is sufficient to answer the question with a NO. Hence C answer

Oh yeah, you're right indeed. Thanks very much

D

minustark

Senior Manager

Joined: 14 Jul 2019

Status:Student

Posts: 478

Own Kudos [?]: 369 [0]

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

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

05 Mar 2020, 20:27

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.

2x < 6 or, x < 3. whether x is an integer or not, we don't know. Nevertheless, for keeping the procedure simple lets consider only the integer options for x.

1) both of x and y have to be either odd or even. As we don't know y is odd or even, so can't answer the question. Insufficient.

2) x and y are both odd. So, x is 1 which is sufficient.

B is the CA.

B

vps01011989

Current Student

Joined: 10 Mar 2020

Posts: 16

Own Kudos [?]: 11 [0]

Given Kudos: 55

Location: India

Schools: CBS '23 (A) Booth '23 (D) Ross '23 (I) Kellogg '23 (I) Wharton '23 (D)

GMAT 1: 740 Q50 V40 Verified score

GMAT 2: 760 Q50 V44 Verified score

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

03 Apr 2020, 10:42

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.

How is the answer C? What if X is -ve?

B

Rahul5843

Intern

Joined: 30 May 2017

Posts: 38

Own Kudos [?]: 25 [0]

Given Kudos: 42

GMAT 1: 730 Q49 V41

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

22 Apr 2021, 17:25

Bunuel wrote:

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.

Answer: C.

Hope it's clear.

P.S. Please post PS questions in PS forum and DS questions in DS forum. Thank you.

x. y
1. 3
-1. -3

hence E should be the answer
there is no restriction on x to be non-negative in the question

L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92887

Own Kudos [?]: 618656 [0]

Given Kudos: 81563

Send PM

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

23 Apr 2021, 00:38

Expert Reply

Rahul5843 wrote:

Bunuel wrote:

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.

Answer: C.

Hope it's clear.

P.S. Please post PS questions in PS forum and DS questions in DS forum. Thank you.

x. y
1. 3
-1. -3

hence E should be the answer
there is no restriction on x to be non-negative in the question

The question asks whether x is a prime number. According to the solution, when we consider the statements together, we get a definite NO answer to the question - NO, x is NOT a prime number. In your example x is also not a prime. So, C is correct and E is not.

P.S. Please do not post and report at the same time. A post is enough. Thank you.

gmatclubot

Re: If 3x + 5 < x + 11, is x prime? [#permalink]

23 Apr 2021, 00:38

GMAT Data Sufficiency (DS) Questions

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