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If k = (n + 2)(n - 2), where n is an integer value greater

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If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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New post Updated on: 23 Feb 2014, 13:28
1
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A
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E

Difficulty:

  45% (medium)

Question Stats:

64% (01:47) correct 36% (01:56) wrong based on 436 sessions

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If k = (n + 2)(n - 2), where n is an integer value greater than 2, what is the value of k?

(1) k is the product of two primes
(2) k < 100

My approach:
Given that K=(N+2)(N-2) and according to statement 1 K is the product of two prime numbers then (N+2) = prime and (N-2)= prime. I interpret that to mean that N is two intervals away from 2 prime numbers, the only example I could think of to fit this description would be (5+2)(5-2) (7)(3) = 21. What other prime numbers would fit this description? Where am I going wrong on this statement? Should I just assume that there will be more prime numbers to fit this premise? Am I supposed to remember prime numbers past 100? I see the second statement says that K<100 and I realize that the statement is clearly insufficient on its own so I selected "A."

OA is "E"

Can someone explain where I am going wrong with this one?

Thanks in advance.

Originally posted by msbandi4321 on 23 Feb 2014, 13:20.
Last edited by Bunuel on 23 Feb 2014, 13:28, edited 1 time in total.
Renamed the topic, edited the question, and moved to DS forum.
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Re: If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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New post 23 Feb 2014, 13:49
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4
msbandi4321 wrote:
If k = (n + 2)(n - 2), where n is an integer value greater than 2, what is the value of k?

(1) k is the product of two primes
(2) k < 100

My approach:
Given that K=(N+2)(N-2) and according to statement 1 K is the product of two prime numbers then (N+2) = prime and (N-2)= prime. I interpret that to mean that N is two intervals away from 2 prime numbers, the only example I could think of to fit this description would be (5+2)(5-2) (7)(3) = 21. What other prime numbers would fit this description? Where am I going wrong on this statement? Should I just assume that there will be more prime numbers to fit this premise? Am I supposed to remember prime numbers past 100? I see the second statement says that K<100 and I realize that the statement is clearly insufficient on its own so I selected "A."

OA is "E"

Can someone explain where I am going wrong with this one?

Thanks in advance.


What about 7*11 = 77?
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Re: If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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New post 27 May 2014, 13:05
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Let us begin with B
(n-2) * (n+2) = n^2 - 4
since k<100 we have 96, 77, 60, 45, 32, 21, 12, 5 not sufficient

for A; from the above list we have 7x11, 7x3 in addition to possible numbers >100; hence not sufficient

A & B together we have 77, 21 not sufficient

Therefore E
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Re: If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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New post 23 Feb 2014, 14:10
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I'm not sure how I missed that Bunuel. I guess I must have been thinking of N as a prime number as well. Thanks!
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Re: If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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New post 20 Nov 2014, 00:32
msbandi4321 wrote:
I'm not sure how I missed that Bunuel. I guess I must have been thinking of N as a prime number as well. Thanks!


That's exactly what I did too. Darn that's a tricky one :\
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Re: If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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New post 30 Mar 2017, 14:23
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msbandi4321 wrote:
If k = (n + 2)(n - 2), where n is an integer value greater than 2, what is the value of k?

(1) k is the product of two primes
(2) k < 100


I thought testing numbers is the fastest approach...

1. say n=5
n-2=3 (prime)
n+2=7 (prime)
k=21.

say n=9
n-2=7 (prime)
n+2=11 (prime)
k=77

2 outcomes. not sufficient.


2. doesn't give us much information - k can have multiple values


1+2. values in 1 still are possible - E is the answer.
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If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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New post 10 Sep 2018, 00:37
Bunuel wrote:
msbandi4321 wrote:
If k = (n + 2)(n - 2), where n is an integer value greater than 2, what is the value of k?

(1) k is the product of two primes
(2) k < 100

My approach:
Given that K=(N+2)(N-2) and according to statement 1 K is the product of two prime numbers then (N+2) = prime and (N-2)= prime. I interpret that to mean that N is two intervals away from 2 prime numbers, the only example I could think of to fit this description would be (5+2)(5-2) (7)(3) = 21. What other prime numbers would fit this description? Where am I going wrong on this statement? Should I just assume that there will be more prime numbers to fit this premise? Am I supposed to remember prime numbers past 100? I see the second statement says that K<100 and I realize that the statement is clearly insufficient on its own so I selected "A."

OA is "E"

Can someone explain where I am going wrong with this one?

Thanks in advance.


What about 7*11 = 77?


Thanks. So is the approach here to name n 1 through 9 and see what K we get? or rather it is see that (2) provides info on K < 100 therefore go back to (1) and check till 100?
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Re: If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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New post 10 Sep 2018, 01:57
msbandi4321 wrote:
If k = (n + 2)(n - 2), where n is an integer value greater than 2, what is the value of k?

(1) k is the product of two primes
(2) k < 100

My approach:
Given that K=(N+2)(N-2) and according to statement 1 K is the product of two prime numbers then (N+2) = prime and (N-2)= prime. I interpret that to mean that N is two intervals away from 2 prime numbers, the only example I could think of to fit this description would be (5+2)(5-2) (7)(3) = 21. What other prime numbers would fit this description? Where am I going wrong on this statement? Should I just assume that there will be more prime numbers to fit this premise? Am I supposed to remember prime numbers past 100? I see the second statement says that K<100 and I realize that the statement is clearly insufficient on its own so I selected "A."

OA is "E"

Can someone explain where I am going wrong with this one?



Thanks in advance.



OA: E

Given: \(k = (n + 2)(n - 2)\) and \(n>2\)

(1) \(k\) is the product of two primes

Difference between Two primes would be \((n+2)-(n-2)= n+2-n+2=4\), Primes number can \({3,7};{7,11};\).....
as there is no unique value of \(k\) , \(k\) can be \(21,77\) or ......
So Statement \(1\) alone is not sufficient.

(2) \(k < 100\)

\(k\) can be \(1,2,3,4\)...............
There is no unique value of \(k\) , so Statement \(2\) alone is not sufficient.

Combining (1) and (2), we get
\(k\) can be 21 or 77, so combining (1) and (2) also is insufficient to give unique value of \(k\)
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Re: If k = (n + 2)(n - 2), where n is an integer value greater &nbs [#permalink] 10 Sep 2018, 01:57
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