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

 It is currently 19 Jan 2019, 19:05

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# M01-26

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52294

### Show Tags

15 Sep 2014, 23:16
1
9
00:00

Difficulty:

45% (medium)

Question Stats:

60% (00:38) correct 40% (00:31) wrong based on 274 sessions

### HideShow timer Statistics

If $$x$$ is an integer, then is $$x$$ a prime number?

(1) $$x$$ is a multiple of a prime number.

(2) $$x$$ is a product of two integers.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52294

### Show Tags

15 Sep 2014, 23:16
1
Official Solution:

Statement (1) by itself is not sufficient. Multiples of a prime number are not prime except the prime number itself. For example, 3 is prime and its multiples are 3 itself (prime), 6 (not prime), etc.

Statement (2) by itself is not sufficient. The product of two integers can be prime only if one integer is a prime and the other integer is 1. For example $$3=1*3$$ is prime, but $$6=3*2$$ is not prime.

Statements (1) and (2) combined are not sufficient. If both statements are combined,$$x$$ can still be 3 (prime) or 6 (not prime).

_________________
Intern
Joined: 30 Jan 2015
Posts: 27
GMAT 1: 710 Q41 V46

### Show Tags

25 Feb 2015, 10:23
Bunuel wrote:
Official Solution:

Statement (1) by itself is not sufficient. Multiples of a prime number are not prime except the prime number itself. For example, 3 is prime and its multiples are 3 itself (prime), 6 (not prime), etc.

Statement (2) by itself is not sufficient. The product of two integers can be prime only if one integer is a prime and the other integer is 1. For example $$3=1*3$$ is prime, but $$6=3*2$$ is not prime.

Statements (1) and (2) combined are not sufficient. If both statements are combined,$$x$$ can still be 3 (prime) or 6 (not prime).

Thanks for the explanation Bunuel. I missed this example because I didn't consider that it is true to say that a number is a multiple of itself. For example, 3 is a multiple of 3.
Manager
Joined: 24 Jul 2011
Posts: 179
Location: India
GMAT 1: 570 Q50 V19
GMAT 2: 650 Q49 V28
GMAT 3: 690 Q50 V34
WE: Information Technology (Investment Banking)

### Show Tags

08 Oct 2015, 02:00
In "(2) x is a product of two integers", I was confused with "x is a product of ANY/ONLY two integers". I presupposed that the author meant "ONLY" so question went wrong. Can you please guide how to interpret such questions?
_________________

Middle of nowhere!

Intern
Joined: 27 Jul 2015
Posts: 6

### Show Tags

07 Feb 2016, 04:33
Hi,

in my opinion Statement 1 is sufficient: "(1) x is a multiple of a prime number."
As Bunuel wrote, a multiple of 3 is 6. If x is a multiple of a prime number it is itself definitely not a prime number --> Sufficient.

Where is the error in my thought? I don't get it...

Thanks!!
Math Expert
Joined: 02 Aug 2009
Posts: 7206

### Show Tags

07 Feb 2016, 05:18
AnikaJu wrote:
Hi,

in my opinion Statement 1 is sufficient: "(1) x is a multiple of a prime number."
As Bunuel wrote, a multiple of 3 is 6. If x is a multiple of a prime number it is itself definitely not a prime number --> Sufficient.

Where is the error in my thought? I don't get it...

Thanks!!

Hi,
the point which you are missing is
the number itself is a multiple..
so 3 is a multiple of 3..
3*1=3..
that is the reason statement 1 is not suff
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 26 Jan 2015
Posts: 77

### Show Tags

20 Sep 2016, 10:29
Bunuel wrote:
Official Solution:

Statement (2) by itself is not sufficient. The product of two integers can be prime only if one integer is a prime and the other integer is 1. For example $$3=1*3$$ is prime, but $$6=3*2$$ is not prime.

Dear Bunuel,

When you say, x is a product of 2 integers, and 3 is represented as 3x1, 6 should be represented as 3x2x1? hence stmt 2 is sufficient since only primes can be represented as product of 2 integers?

Thanks,
Alok322
_________________

Kudos is the best way to say Thank you! Please give me a kudos if you like my post

Math Expert
Joined: 02 Sep 2009
Posts: 52294

### Show Tags

21 Sep 2016, 03:07
Alok322 wrote:
Bunuel wrote:
Official Solution:

Statement (2) by itself is not sufficient. The product of two integers can be prime only if one integer is a prime and the other integer is 1. For example $$3=1*3$$ is prime, but $$6=3*2$$ is not prime.

Dear Bunuel,

When you say, x is a product of 2 integers, and 3 is represented as 3x1, 6 should be represented as 3x2x1? hence stmt 2 is sufficient since only primes can be represented as product of 2 integers?

Thanks,
Alok322

x is a product of two integers means that x can be represented as the product of two integers.
_________________
Current Student
Status: CFA Charterholder
Joined: 11 Jun 2014
Posts: 17
Location: Turkey
GMAT 1: 720 Q50 V37
WE: Research (Investment Banking)

### Show Tags

22 Oct 2016, 05:44
I think this is a poor-quality question and I don't agree with the explanation. the question may be misleading since statement 2 can be misunderstood since its vague
Intern
Joined: 08 Aug 2016
Posts: 36

### Show Tags

25 Nov 2016, 07:54
I think this is a poor-quality question. Statement 2 must include ANY or ONLY. It is ambiguous for a DS question. I don't think GMAC will have an ambiguous question
Manager
Joined: 25 Mar 2013
Posts: 240
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5

### Show Tags

08 Dec 2016, 16:18
Is x = Prime?
1, If prime 2 , x could be 2,4,6,8..
If prime 3 , x could be 3,6,9,12..
If prime 5 , x could be 5,10,15,...
So BCE
2, x = 0x1 =0 ( 0 is not prime)
x = 2x-4 = -8 ( -8 is not prime)
x= 2x1 = 2 ( 2 is prime)
So eliminate B
Next, If x = 2,5,7 are prime numbers
so I have chosen C

Pls help me.
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Director
Joined: 02 Sep 2016
Posts: 678

### Show Tags

07 Jan 2017, 21:52
Bunuel wrote:
Alok322 wrote:
Bunuel wrote:
Official Solution:

Statement (2) by itself is not sufficient. The product of two integers can be prime only if one integer is a prime and the other integer is 1. For example $$3=1*3$$ is prime, but $$6=3*2$$ is not prime.

Dear Bunuel,

When you say, x is a product of 2 integers, and 3 is represented as 3x1, 6 should be represented as 3x2x1? hence stmt 2 is sufficient since only primes can be represented as product of 2 integers?

Thanks,
Alok322

x is a product of two integers means that x can be represented as the product of two integers.

Hello Bunuel

Need a clarification here.

I am still confused about the statement 2.
Product of TWO integers: 3*1
Product of THREE integers: 1*3*2= 6 (one is a factor of 3 as well)

Statement 2 should be sufficient according to the above analysis because ONLY PRIME NUMBERS HAVE TWO FACTORS (ONE AND ITSELF).

Thanks.
Intern
Joined: 19 Apr 2017
Posts: 27

### Show Tags

28 Jun 2017, 09:07
in ALL the books I've read they say that one and zero are unique since they are either primes nor composites

why did you consider 1 as prime here? is that a unique thing in GMAT?

also if you count 1 as a prime wouldn't it make the situation as stated in the previous post in this topic?
Math Expert
Joined: 02 Sep 2009
Posts: 52294

### Show Tags

28 Jun 2017, 09:11
kamyar94 wrote:
in ALL the books I've read they say that one and zero are unique since they are either primes nor composites

why did you consider 1 as prime here? is that a unique thing in GMAT?

also if you count 1 as a prime wouldn't it make the situation as stated in the previous post in this topic?

1 is NOT a prime number and nowhere in the solution it is stated otherwise.
_________________
Intern
Joined: 08 Jun 2017
Posts: 4

### Show Tags

03 Jul 2017, 18:15
Good one! I did not think about a number being a multiple of itself
Intern
Joined: 05 Mar 2017
Posts: 6
Location: India
GMAT 1: 620 Q49 V27

### Show Tags

04 Sep 2017, 10:21
There is no where mentioned the sign of integers. Prime numbers are positive. In absence of this information, answer becomes E.

Is it correct to consider this point?
Intern
Joined: 13 Nov 2016
Posts: 8
Location: India

### Show Tags

09 Sep 2017, 09:13
I think this the explanation isn't clear enough, please elaborate. Statement 1 leads to the conclusion that x is not prime. Doesn't this mean it's sufficient?
Math Expert
Joined: 02 Sep 2009
Posts: 52294

### Show Tags

09 Sep 2017, 09:17
shrutip24 wrote:
I think this the explanation isn't clear enough, please elaborate. Statement 1 leads to the conclusion that x is not prime. Doesn't this mean it's sufficient?

x is a multiple of a prime number does not mean that x is not a prime. For example, 5 is a multiple of 5, so x could be a prime.
_________________
Intern
Joined: 02 Jan 2014
Posts: 1

### Show Tags

08 Oct 2017, 20:51
I think this is a high-quality question and I don't agree with the explanation. With the statement 1, we can derive that x is not a prime number as its a multiple of a prime number. Why not option 1 is the correct answer?
Math Expert
Joined: 02 Sep 2009
Posts: 52294

### Show Tags

08 Oct 2017, 20:55
subhash2688 wrote:
I think this is a high-quality question and I don't agree with the explanation. With the statement 1, we can derive that x is not a prime number as its a multiple of a prime number. Why not option 1 is the correct answer?

x is a multiple of a prime number does not mean that x is not a prime. For example, 5 is a multiple of 5, so x could be a prime.
_________________
Re: M01-26 &nbs [#permalink] 08 Oct 2017, 20:55

Go to page    1   2    Next  [ 30 posts ]

Display posts from previous: Sort by

# M01-26

Moderators: chetan2u, Bunuel

 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®.