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

 It is currently 13 Oct 2019, 18:37

### 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

# It is given that p, q, and r are positive integers, where p is an odd

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 27 Oct 2017
Posts: 1256
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
It is given that p, q, and r are positive integers, where p is an odd  [#permalink]

### Show Tags

13 Oct 2018, 10:04
5
00:00

Difficulty:

75% (hard)

Question Stats:

35% (02:33) correct 65% (02:35) wrong based on 43 sessions

### HideShow timer Statistics

It is given that p, q, and r are positive integers, where p is an odd number and $$r = p^2 + q^2 + 4.$$ Is $$q^3$$ divisible by 8?
(1) r = 8k -3 where k is a positive integer.
(2) When (r-p+1) is divided by 2, it leaves a remainder.

Weekly Quant Quiz #4 Ques 2

_________________
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 737
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
Re: It is given that p, q, and r are positive integers, where p is an odd  [#permalink]

### Show Tags

13 Oct 2018, 10:11
1
1
According to me (D) should be the answer.

Best,
Attachments

Q4_2 (2).jpeg [ 121.56 KiB | Viewed 523 times ]

_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Intern
Joined: 26 Dec 2017
Posts: 47
Location: India
Concentration: Technology, Marketing
WE: General Management (Internet and New Media)
Re: It is given that p, q, and r are positive integers, where p is an odd  [#permalink]

### Show Tags

13 Oct 2018, 10:16
From question stem we can derive that q will be odd if r is even and q will be even if r is odd.

From Statement - 1:
r = 8k-3 basically means r is always a positive odd integer. This implies q can only be even which means q has 2 as its factor and so we can say q3 is divisible by 8.

From statement - 2:
Because p is odd, and (r-p+1)/2 is also odd we can conclude that r is odd.
This implies q can only be even which means q has 2 as its factor and so we can say q3 is divisible by 8.
Senior Manager
Joined: 18 Jan 2018
Posts: 308
Location: India
Concentration: General Management, Healthcare
Schools: Booth '22, ISB '21, IIMB
GPA: 3.87
WE: Design (Manufacturing)
Re: It is given that p, q, and r are positive integers, where p is an odd  [#permalink]

### Show Tags

13 Oct 2018, 10:27
given p is odd , and r = p^2+q^2+4

statement : 1 ==>r = 8k -3 where k is a positive integer

it does not give any information about Q , so insuffient .

Statement 2 :When (r-p+1) is divided by 2, it leaves a remainder.
r-p+1 is not divisible by 2 , so it says that r-p+1 is a odd number
r-p+1 = Odd
==> r-p = Odd+1 = Even
==> given p is Odd
==> r = Even + p(Odd)
==> r = Even +Odd = Odd
So now we have P ( Odd ) , r(Odd)
so r = Odd is never divisible by 8 . Sufficient , So OA is B
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4976
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: It is given that p, q, and r are positive integers, where p is an odd  [#permalink]

### Show Tags

13 Oct 2018, 10:27
It is given that p, q, and r are positive integers, where p is an odd number and r=p2+q2+4.r=p2+q2+4. Is q3q3 divisible by 8?
(1) r = 8k -3 where k is a positive integer.
(2) When (r-p+1) is divided by 2, it leaves a remainder.

from given eqn 2

no value of r given
q2=r-p2-4 ( is a factor of 8 or not)
From stmnt1: for value of k=1 we get r= 5 and k=2 r= 13

plugging into eqn we get yes and no insufficient

from stmtn2

IMO C
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
RC Moderator
Joined: 24 Aug 2016
Posts: 790
GMAT 1: 540 Q49 V16
GMAT 2: 680 Q49 V33
Re: It is given that p, q, and r are positive integers, where p is an odd  [#permalink]

### Show Tags

13 Oct 2018, 10:29
r=p^2+q^2+4 p odd p^2 odd p^2 +4 odd

(1) r = 8k -3 where k is a positive int------ Suff
r-3 even, r odd
p^2+q^2+1 even , p^2+q^2 odd, q^2 even , q even , q=2a hence q^3 = 8a^3

(2) When (r-p+1) is divided by 2, it leaves a remainder. - Suff
r-p even , r odd ( as p odd) ====>similar to 1==>q^3 = 8a^3

Ans D
_________________
Please let me know if I am going in wrong direction.
Thanks in appreciation.
Booth Moderator
Joined: 11 Feb 2018
Posts: 294
Location: India
Concentration: General Management, Finance
GMAT 1: 690 Q47 V37
GMAT 2: 710 Q50 V36
GMAT 3: 750 Q50 V42
Re: It is given that p, q, and r are positive integers, where p is an odd  [#permalink]

### Show Tags

13 Oct 2018, 12:28
The answer is fine.But how the hell do we solve this question in under 2 mins..?

Posted from my mobile device
Retired Moderator
Joined: 27 Oct 2017
Posts: 1256
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
It is given that p, q, and r are positive integers, where p is an odd  [#permalink]

### Show Tags

13 Oct 2018, 20:30
Hi redskull1
Please see the explanations above, you will understand the solution.
If you still have any doubt, feel free to tag me

redskull1 wrote:
The answer is fine.But how the hell do we solve this question in under 2 mins..?

Posted from my mobile device

_________________
It is given that p, q, and r are positive integers, where p is an odd   [#permalink] 13 Oct 2018, 20:30
Display posts from previous: Sort by