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If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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12 Sep 2017, 22:35
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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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12 Sep 2017, 23:42
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, 03:36, edited 2 times in total.



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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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13 Sep 2017, 03:23
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 itselfalso...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 5combining we get.. k= +5 hence (1) and (2) together sufficient... Correct choice=C
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Last edited by devarshi9283 on 13 Sep 2017, 03:49, edited 1 time in total.



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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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13 Sep 2017, 03:39
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 itselfSo, (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 5or k= +5 or 5 hence (1) and (2) together not sufficient...So remove D Correct choice=E I think it should be CHow did you get remainder 2 when 3 is divided by 5?
Last edited by KS15 on 13 Sep 2017, 03:42, edited 1 time in total.



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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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13 Sep 2017, 03:41
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..



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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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13 Sep 2017, 03:46
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?



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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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13 Sep 2017, 03:53
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.



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If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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13 Sep 2017, 03:54
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...
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Last edited by devarshi9283 on 13 Sep 2017, 03:57, edited 1 time in total.



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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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13 Sep 2017, 03:56
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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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17 Sep 2017, 11:29
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



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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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17 Sep 2017, 20:57
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 S850LC using GMAT Club Forum mobile app



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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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17 Sep 2017, 23:47
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 S850LC using GMAT Club Forum mobile appHi, 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



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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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18 Sep 2017, 00:05
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 S850LC using GMAT Club Forum mobile appHi, 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 S850LC using GMAT Club Forum mobile app



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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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18 Sep 2017, 00:19
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



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Re: If p is an integer and p* = p^2 + 2, what is the value of integer k? [#permalink]
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18 Sep 2017, 02:44
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 S850LC using GMAT Club Forum mobile app




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