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12 Sep 2017, 23:35
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C
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Difficulty:
75%
(hard)
Question Stats:
44% (01:51) correct
56%
(01:47)
wrong
based on 230
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If p is an integer and p* = p^2 + 2, what is the value of integer k?
(1) When k + 2 is divided by 5 the remainder is 2.
(2) 18 < k* < 35
(1) When k + 2 is divided by 5 the remainder is 2.
(2) 18 < k* < 35
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
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
devarshi9283
Joined: 25 Jul 2011
Last visit: 06 Oct 2025
Posts: 54
Given Kudos: 1,059
Location: India
Concentration: Strategy, Operations
Schools: NUS '20 (D) Jones '20 (A$) Mays '20 (A$) Jindal '20 (A$) Cox '20 (A$) Kenan-Flagler '20 (WL)
GMAT 1: 740 Q49 V41
GPA: 3.5
WE:Engineering (Energy)
Schools: NUS '20 (D) Jones '20 (A$) Mays '20 (A$) Jindal '20 (A$) Cox '20 (A$) Kenan-Flagler '20 (WL)
GMAT 1: 740 Q49 V41
Posts: 54
Updated on: 13 Sep 2017, 04:49
Originally posted by devarshi9283 on 13 Sep 2017, 04:23.
Last edited by devarshi9283 on 13 Sep 2017, 04:49, edited 1 time in total.
Last edited by devarshi9283 on 13 Sep 2017, 04:49, edited 1 time in total.
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Bunuel
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
