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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, 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.

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, 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.

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, 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..

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, 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?

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, 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.

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

Show Tags

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.

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

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.