It is currently 18 Nov 2017, 11:08

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If p is an integer and p* = p^2 + 2, what is the value of integer k?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132595 [0], given: 12326

If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 12 Sep 2017, 23:35
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (01:13) correct 40% (01:34) wrong based on 48 sessions

HideShow timer Statistics

Kudos [?]: 132595 [0], given: 12326

Senior Manager
Senior Manager
User avatar
G
Joined: 02 Jul 2017
Posts: 269

Kudos [?]: 79 [0], given: 65

Location: India
GMAT ToolKit User CAT Tests
Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 13 Sep 2017, 00:42
Given: p is an integer and p* = p^2 + 2,
Find: k

(1) When k + 2 is divided by 5 the remainder is 2.
so basically (k+2) = 5a +2 => k=5a
basically says k can be any value -> 0,5,10,15 ..

Not sufficient

(2) 18 < k* < 35
given p* =p^2+2
k* = k^2 +2

=> 18 <k* <35
=> 18<k^2+2<35
=> 16<k^2<33
As here k is an integer (for p* given p is an integer), so possible value of k = 5 or k=-5
Not sufficient

1+2
It will gives us: k=5. sufficient

Answer: C

Last edited by Nikkb on 13 Sep 2017, 04:36, edited 2 times in total.

Kudos [?]: 79 [0], given: 65

Intern
Intern
User avatar
S
Joined: 25 Jul 2011
Posts: 44

Kudos [?]: 5 [0], given: 1058

Location: India
Concentration: Strategy, Operations
GMAT 1: 740 Q49 V41
GPA: 3.5
WE: Engineering (Energy and Utilities)
CAT Tests
Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 13 Sep 2017, 04:23
Bunuel wrote:
If p is an integer and p* = p^2 + 2, what is the value of k?

(1) When k + 2 is divided by 5 the remainder is 2.
(2) 18 < k* < 35




consider (1)...

When k + 2 is divided by 5 the remainder is 2.
So, basically ..k is divisible by 5...
now as k is integer...(positive, negative or zero)..following values of k are possible
k=......,-8,-3, 0,5,10... and so on...

Remember that 0 is divisible by all integers except 0 itself
also...we can not assume k to be positive integer necessarily...

So, (1) alone is not sufficient....remove option A and D.....

consider (2)...

18 < k* < 35

given that If p is an integer and p* = p^2 + 2..
so here...k*=k^2+2

So..
18 < k^2+2< 35
or
16 < k^2< 33

or k^2=25 for integer k...
but here again...
k= +5 or -5

(2) alone is not sufficient....remove option B .....

consider (1) and (2) simultaneously we get ..
k=......,-8, -3, 0,5,10...
k= +5 or -5

combining we get..
k= +5
hence (1) and (2) together sufficient...

Correct choice=C
_________________

Please hit kudos button below if you found my post helpful..TIA


Last edited by devarshi9283 on 13 Sep 2017, 04:49, edited 1 time in total.

Kudos [?]: 5 [0], given: 1058

Director
Director
avatar
G
Joined: 21 May 2013
Posts: 539

Kudos [?]: 48 [0], given: 492

CAT Tests
Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 13 Sep 2017, 04:39
devarshi9283 wrote:
Bunuel wrote:
If p is an integer and p* = p^2 + 2, what is the value of k?

(1) When k + 2 is divided by 5 the remainder is 2.
(2) 18 < k* < 35




consider (1)...

When k + 2 is divided by 5 the remainder is 2.
So, basically ..k is divisible by 5...
now as k is integer...(positive, negative or zero)..following values of k are possible
k=......,-10, -5, 0,5,10... and so on...

Remember that 0 is divisible by all integers except 0 itself

So, (1) alone is not sufficient....remove option A and D.....

consider (2)...

18 < k* < 35

given that If p is an integer and p* = p^2 + 2..
so here...k*=k^2+2

So..
18 < k^2+2< 35
or
16 < k^2< 33

or k^2=25 for integer k...
but here again...
k= +5 or -5

(2) alone is not sufficient....remove option B .....

consider (1) and (2) simultaneously we get ..
k=......,-10, -5, 0,5,10...
k= +5 or -5

or
k= +5 or -5
hence (1) and (2) together not sufficient...So remove D

Correct choice=E


I think it should be C-How did you get remainder 2 when -3 is divided by 5?

Last edited by KS15 on 13 Sep 2017, 04:42, edited 1 time in total.

Kudos [?]: 48 [0], given: 492

Senior Manager
Senior Manager
User avatar
G
Joined: 02 Jul 2017
Posts: 269

Kudos [?]: 79 [0], given: 65

Location: India
GMAT ToolKit User CAT Tests
Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 13 Sep 2017, 04:41
devarshi9283 wrote:


consider (1)...

When k + 2 is divided by 5 the remainder is 2.
So, basically ..k is divisible by 5...
now as k is integer...(positive, negative or zero)..following values of k are possible
k=......,-10, -5, 0,5,10... and so on...

Remember that 0 is divisible by all integers except 0 itself

So, (1) alone is not sufficient....remove option A and D.....



k=......,-10, -5, 0,5,10.. and so on...

If we consider k = -5
than k+2 = -5+2 =-3
If we divide -3 by 5 reminder will be -3 and not 2. So here k cannot be -5

If we cant to work in negative number: we can say -7 / 5 = -1 quotient and reminder 2 => k+2 = -7 => k=-9
So for k+2 =5a+2
we can get -ve numbers for k = -4, -9, -14.... etc..

Kudos [?]: 79 [0], given: 65

Director
Director
avatar
G
Joined: 21 May 2013
Posts: 539

Kudos [?]: 48 [0], given: 492

CAT Tests
Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 13 Sep 2017, 04:46
Nikkb wrote:
devarshi9283 wrote:


consider (1)...

When k + 2 is divided by 5 the remainder is 2.
So, basically ..k is divisible by 5...
now as k is integer...(positive, negative or zero)..following values of k are possible
k=......,-10, -5, 0,5,10... and so on...

Remember that 0 is divisible by all integers except 0 itself

So, (1) alone is not sufficient....remove option A and D.....






k=......,-10, -5, 0,5,10.. and so on...

If we consider k = -5
than k+2 = -5+2 =-3
If we divide -3 by 5 reminder will be -3 and not 2. So here k cannot be -

If we cant to work in negative number: we can say -7 / 5 = -1 quotient and reminder 2 => k+2 = -7 => k=-9
So for k+2 =5a+2
we can get -ve numbers for k = -4, -9, -14.... etc..




I did not get what you are saying.
Statement 2: K can be 5 or -5
Statement 1: K can be 10 etc etc but not negative. Using both, should the answer not be C i.e k=5?

Kudos [?]: 48 [0], given: 492

Senior Manager
Senior Manager
User avatar
G
Joined: 02 Jul 2017
Posts: 269

Kudos [?]: 79 [0], given: 65

Location: India
GMAT ToolKit User CAT Tests
Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 13 Sep 2017, 04:53
KS15 wrote:


I did not get what you are saying.
Statement 2: K can be 5 or -5
Statement 1: K can be 10 etc etc but not negative. Using both, should the answer not be C i.e k=5?



Yes, i was just trying to tell " devarshi9283" that value of k =0,5, 10.... etc
By statement 1 we cannot say k = -10, -5...

So by 1 and 2... k =5 and Answer is C..
Same thing i wrote in my descriptive solution above.

:)

Kudos [?]: 79 [0], given: 65

Intern
Intern
User avatar
S
Joined: 25 Jul 2011
Posts: 44

Kudos [?]: 5 [0], given: 1058

Location: India
Concentration: Strategy, Operations
GMAT 1: 740 Q49 V41
GPA: 3.5
WE: Engineering (Energy and Utilities)
CAT Tests
If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 13 Sep 2017, 04:54
KS15 wrote:
Nikkb wrote:
devarshi9283 wrote:


consider (1)...

When k + 2 is divided by 5 the remainder is 2.
So, basically ..k is divisible by 5...
now as k is integer...(positive, negative or zero)..following values of k are possible
k=......,-10, -5, 0,5,10... and so on...

Remember that 0 is divisible by all integers except 0 itself

So, (1) alone is not sufficient....remove option A and D.....



k=......,-10, -5, 0,5,10.. and so on...

If we consider k = -5
than k+2 = -5+2 =-3
If we divide -3 by 5 reminder will be -3 and not 2. So here k cannot be -

If we cant to work in negative number: we can say -7 / 5 = -1 quotient and reminder 2 => k+2 = -7 => k=-9
So for k+2 =5a+2
we can get -ve numbers for k = -4, -9, -14.... etc..




I did not get what you are saying.
Statement 2: K can be 5 or -5
Statement 1: K can be 10 etc etc but not negative. Using both, should the answer not be C i.e k=5?





Sorry guys...I did a calculation mistake...the possible negative values for k as negative integer would be -3,-8...and so on which will give a reminder 2 when divided by 5..
My bad...edited my previous post...correct answer would be C....but yes..I think we have to consider negative integer values of k also in eqn 1...I request Bunuel to shed more light onto this...
_________________

Please hit kudos button below if you found my post helpful..TIA


Last edited by devarshi9283 on 13 Sep 2017, 04:57, edited 1 time in total.

Kudos [?]: 5 [0], given: 1058

Director
Director
avatar
G
Joined: 21 May 2013
Posts: 539

Kudos [?]: 48 [0], given: 492

CAT Tests
Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 13 Sep 2017, 04:56
Guys,

Please give me 1 kudo each :)

Kudos [?]: 48 [0], given: 492

Senior Manager
Senior Manager
avatar
B
Joined: 15 Jan 2017
Posts: 295

Kudos [?]: 21 [0], given: 674

Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 17 Sep 2017, 12:29
St 1: K +2/5 = quotient + 2; so K is multiple of 5
But that can be any number. So NS

st 2: 18<k<35
I wrote down all the values that lies between them.
And then checked what value satisfies K square plus 2. Only 27 does (25 + 2)

so, 1) + 2) K is multiple of 5 with quotient 2; so value is k = 5 (root of 25). Ans C

Kudos [?]: 21 [0], given: 674

Manager
Manager
avatar
B
Joined: 02 Nov 2015
Posts: 176

Kudos [?]: 26 [0], given: 121

GMAT 1: 640 Q49 V29
Premium Member CAT Tests
Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 17 Sep 2017, 21:57
Madhavi1990 wrote:
St 1: K +2/5 = quotient + 2; so K is multiple of 5
But that can be any number. So NS

st 2: 18<k<35
I wrote down all the values that lies between them.
And then checked what value satisfies K square plus 2. Only 27 does (25 + 2)

so, 1) + 2) K is multiple of 5 with quotient 2; so value is k = 5 (root of 25). Ans C

Hello Madhavi1990,

May you pls explain by cannot we take negative value of K ??

Imo we can consider the negative value of K as well and so the answer should be E.

What I understand is that if -3 is divided by 5, then the remainder is 2..

Thanks in advance..

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app

Kudos [?]: 26 [0], given: 121

Senior Manager
Senior Manager
avatar
B
Joined: 15 Jan 2017
Posts: 295

Kudos [?]: 21 [0], given: 674

Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 18 Sep 2017, 00:47
kumarparitosh123 wrote:
Madhavi1990 wrote:
St 1: K +2/5 = quotient + 2; so K is multiple of 5
But that can be any number. So NS

st 2: 18<k<35
I wrote down all the values that lies between them.
And then checked what value satisfies K square plus 2. Only 27 does (25 + 2)

so, 1) + 2) K is multiple of 5 with quotient 2; so value is k = 5 (root of 25). Ans C

Hello Madhavi1990,

May you pls explain by cannot we take negative value of K ??

Imo we can consider the negative value of K as well and so the answer should be E.

What I understand is that if -3 is divided by 5, then the remainder is 2..

Thanks in advance..

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app


Hi, I took a value which is multiple of 5 and added 2
So -15 +2 / 5 --> -3 + 2
or -20 + 2 --> -4 + 2
Either way, there are multiple values so A is insuff

When trying with 1) and 2) we know that it has to be positive (with the addition of st 2) and satisfying given condition. So C

Kudos [?]: 21 [0], given: 674

Manager
Manager
avatar
B
Joined: 02 Nov 2015
Posts: 176

Kudos [?]: 26 [0], given: 121

GMAT 1: 640 Q49 V29
Premium Member CAT Tests
Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 18 Sep 2017, 01:05
Madhavi1990 wrote:
kumarparitosh123 wrote:
Madhavi1990 wrote:
St 1: K +2/5 = quotient + 2; so K is multiple of 5
But that can be any number. So NS

st 2: 18<k<35
I wrote down all the values that lies between them.
And then checked what value satisfies K square plus 2. Only 27 does (25 + 2)

so, 1) + 2) K is multiple of 5 with quotient 2; so value is k = 5 (root of 25). Ans C

Hello Madhavi1990,

May you pls explain by cannot we take negative value of K ??

Imo we can consider the negative value of K as well and so the answer should be E.

What I understand is that if -3 is divided by 5, then the remainder is 2..

Thanks in advance..

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app


Hi, I took a value which is multiple of 5 and added 2
So -15 +2 / 5 --> -3 + 2
or -20 + 2 --> -4 + 2
Either way, there are multiple values so A is insuff

When trying with 1) and 2) we know that it has to be positive (with the addition of st 2) and satisfying given condition. So C

I feel it ha been mentioned in statement 2 that K* has to be positive and not K..
So even if we consider k=-5 , then also K * will be 27 and if k=5, then also it will be 27.

Moreover, the value of K* need to be between 18 and 35 and not K..


Note: I don't know where I m missing but this is what I have understood till now. May be some experts can shed some light on my misunderstanding.

Thanks in advance.

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app

Kudos [?]: 26 [0], given: 121

Intern
Intern
avatar
Joined: 04 Mar 2017
Posts: 3

Kudos [?]: 0 [0], given: 6

Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 18 Sep 2017, 01:19
value of integer k?

(1) Not Sufficient

(2) could be -5 or +5 when substituting -5/+5 in the equation . Not Sufficient

(c) on combining, only 5 is possible. (-5+2 divided by 5 gives remainder -3 ; we need remainder 2)

C

Kudos [?]: 0 [0], given: 6

Manager
Manager
avatar
B
Joined: 02 Nov 2015
Posts: 176

Kudos [?]: 26 [0], given: 121

GMAT 1: 640 Q49 V29
Premium Member CAT Tests
Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]

Show Tags

New post 18 Sep 2017, 03:44
akshay93 wrote:
value of integer k?

(1) Not Sufficient

(2) could be -5 or +5 when substituting -5/+5 in the equation . Not Sufficient

(c) on combining, only 5 is possible. (-5+2 divided by 5 gives remainder -3 ; we need remainder 2)

C

Hi
If I am not mistaken, if -3 is divided by 5 , the remainder will be 2 ...
It's something about negative remainder.

@bunuel.. @pushpitkc,... kindly correct me if I am wrong...

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app

Kudos [?]: 26 [0], given: 121

Re: If p is an integer and p* = p^2 + 2, what is the value of integer k?   [#permalink] 18 Sep 2017, 03:44
Display posts from previous: Sort by

If p is an integer and p* = p^2 + 2, what is the value of integer k?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.