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

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Intern
Joined: 27 Jun 2013
Posts: 3
If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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Updated on: 23 Feb 2014, 13:28
1
10
00:00

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?

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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Joined: 02 Sep 2009
Posts: 50711
Re: If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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23 Feb 2014, 13:49
5
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?

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Concentration: Operations, General Management
GMAT 1: 710 Q49 V38
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Re: If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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27 May 2014, 13:05
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2
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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Joined: 27 Jun 2013
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Re: If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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23 Feb 2014, 14:10
3
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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Joined: 11 Oct 2014
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GMAT Date: 11-24-2014
Re: If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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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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30 Mar 2017, 14:23
3
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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GMAT 1: 580 Q44 V26
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If k = (n + 2)(n - 2), where n is an integer value greater  [#permalink]

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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. 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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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?

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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