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

 It is currently 18 Jul 2018, 19:21

### 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

# Q is less than 10. Is Q a prime number?

Author Message
TAGS:

### Hide Tags

Director
Joined: 25 Aug 2007
Posts: 837
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Q is less than 10. Is Q a prime number? [#permalink]

### Show Tags

17 Jun 2010, 04:32
00:00

Difficulty:

65% (hard)

Question Stats:

62% (02:11) correct 38% (01:23) wrong based on 87 sessions

### HideShow timer Statistics

Q is less than 10. Is Q a prime number?

(1) Q^2 - 2 = P; P is prime and P < 10.
(2) Q + 2 is NOT prime, but Q is a positive integer.

_________________

Tricky Quant problems: http://gmatclub.com/forum/50-tricky-questions-92834.html
Important Grammer Fundamentals: http://gmatclub.com/forum/key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

Math Expert
Joined: 02 Sep 2009
Posts: 47084
Re: Q is less than 10. Is Q a prime number? [#permalink]

### Show Tags

17 Jun 2010, 06:26
1
ykaiim wrote:
Q is less than 10. Is Q a prime number?

1) $$Q^2$$ - 2 = P; P is prime and P < 10.
2) Q + 2 is NOT prime, but Q is a positive integer.

Given: $$q<10$$. Question: $$q=prime$$?

(1) $$q^2-2=p=prime<10$$ --> if $$p=7$$, then $$q=3=prime$$ or $$q=-3\neq{prime}$$. Not sufficient.

(2) $$q+2\neq{prime}$$, $$q=positive \ integer$$. If $$q=2$$ then answer is YES but if $$q=4$$, then answer is NO. Not sufficient. From this statement $$q$$ can take the following values: 2, 4, 6, 7, 8 (remember $$q<10$$ and $$q+2\neq{prime}$$).

(1)+(2) The only value from (2) that satisfies $$q^2-2=prime<10$$ is when $$q=2=prime$$. Sufficient.

_________________
Director
Joined: 25 Aug 2007
Posts: 837
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Re: Q is less than 10. Is Q a prime number? [#permalink]

### Show Tags

17 Jun 2010, 07:32
Thanks Bunuel. This confirmed my reasoning.
Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 534
Re: Q is less than 10. Is Q a prime number? [#permalink]

### Show Tags

05 Jan 2017, 10:31
Bunuel wrote:
ykaiim wrote:
Q is less than 10. Is Q a prime number?

1) $$Q^2$$ - 2 = P; P is prime and P < 10.
2) Q + 2 is NOT prime, but Q is a positive integer.

Given: $$q<10$$. Question: $$q=prime$$?

(1) $$q^2-2=p=prime<10$$ --> if $$p=7$$, then $$q=3=prime$$ or $$q=-3\neq{prime}$$. Not sufficient.

(2) $$q+2\neq{prime}$$, $$q=positive \ integer$$. If $$q=2$$ then answer is YES but if $$q=4$$, then answer is NO. Not sufficient. From this statement $$q$$ can take the following values: 2, 4, 6, 7, 8 (remember $$q<10$$ and $$q+2\neq{prime}$$).

(1)+(2) The only value from (2) that satisfies $$q^2-2=prime<10$$ is when $$q=2=prime$$. Sufficient.

"if $$q=4$$, then answer is NO". Is it correct or typing error?
_________________

Hasan Mahmud

Math Expert
Joined: 02 Sep 2009
Posts: 47084
Re: Q is less than 10. Is Q a prime number? [#permalink]

### Show Tags

05 Jan 2017, 10:36
Mahmud6 wrote:
Bunuel wrote:
ykaiim wrote:
Q is less than 10. Is Q a prime number?

1) $$Q^2$$ - 2 = P; P is prime and P < 10.
2) Q + 2 is NOT prime, but Q is a positive integer.

Given: $$q<10$$. Question: $$q=prime$$?

(1) $$q^2-2=p=prime<10$$ --> if $$p=7$$, then $$q=3=prime$$ or $$q=-3\neq{prime}$$. Not sufficient.

(2) $$q+2\neq{prime}$$, $$q=positive \ integer$$. If $$q=2$$ then answer is YES but if $$q=4$$, then answer is NO. Not sufficient. From this statement $$q$$ can take the following values: 2, 4, 6, 7, 8 (remember $$q<10$$ and $$q+2\neq{prime}$$).

(1)+(2) The only value from (2) that satisfies $$q^2-2=prime<10$$ is when $$q=2=prime$$. Sufficient.

"if $$q=4$$, then answer is NO". Is it correct or typing error?

Why do you think it's an error? 4 + 2 = 6, which is not a prime, so the second statement is satisfied and 4 is not a prime, so the answer to the question whether q is a prime is no.
_________________
Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 534
Re: Q is less than 10. Is Q a prime number? [#permalink]

### Show Tags

05 Jan 2017, 10:55
Sorry, Bunuel.
My thought went in different ways, that's why I could not get it. You are right. Thanks.
_________________

Hasan Mahmud

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11987
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Q is less than 10. Is Q a prime number? [#permalink]

### Show Tags

27 Nov 2017, 12:25
1
Hi All,

We're told that Q is less than 10. We're asked if Q is a PRIME number. This is a YES/NO question.

1) Q^2 - 2 = P; P is prime and P < 10.

The information in Fact 1 severely limits the possible values of P (which will limit the possible values of Q. Since P is PRIME and P < 10....
P can be 2, 3, 5 or 7
By extension, Q could be +2, - 2, +√5, -√5, +√7, -√7, +3 or -3
IF...
Q=2 or 3, then the answer to the question is YES.
Q = any of the other values, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) Q + 2 is NOT prime, but Q is a positive integer.

The information in Fact 2 limits the possible values of Q to the following: 2, 4, 6, 7 or 8
IF...
Q = 2 or 7, then the answer to the question is YES.
Q = 4, 6 or 8, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, there's ONLY ONE value that 'fits' both Facts (Q=2)
Combined, SUFFICIENT

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: Q is less than 10. Is Q a prime number?   [#permalink] 27 Nov 2017, 12:25
Display posts from previous: Sort by

# 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®.