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If k = (n + 2)(n - 2), where n is an integer value greater
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msbandi4321
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If k = (n + 2)(n - 2), where n is an integer value greater [#permalink] New post  Updated on: 06 Jun 2021, 13:20
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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:
Show Spoiler
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.
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Originally posted by msbandi4321 on 23 Feb 2014, 13:20.
Last edited by Bunuel on 06 Jun 2021, 13:20, edited 2 times in total.
Renamed the topic, edited the question, and moved to DS forum.
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Bunuel
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Re: If k = (n + 2)(n - 2), where n is an integer value greater [#permalink] New post  23 Feb 2014, 13:49
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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

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] 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] 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] 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] 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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Re: If k = (n + 2)(n - 2), where n is an integer value greater [#permalink] New post  10 Sep 2018, 01:57
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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

My approach:
Show Spoiler
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 [#permalink] New post  24 May 2019, 10:36
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Given: k = (n+2)(n-2) = n²-4, int n > 2
Question: k = ?

(1) k is the product of two primes
I thought about listing out the prime numbers to 100 and seeing what fit (n+2)(n-2) but decided this would take way too long.
Instead I made a chart using n²-4 to check:
n | n² | - 4 | product of 2 pn?
3 | 9 | 5 | No
4 | 16 | 12 | No
5 | 25 | 21 | YES --- 3*7
6 | 36 | 32 | No
7 | 49 | 45 | No
8 | 64 | 60 | No
9 | 81 | 77 | YES --- 7*11

2 Answers, can't determine value of k, insufficient.

(2) k < 100
Totally useless in determining what k actually is. Insufficient.

(3)
Combining together doesn't help because we still have 2 possibilities for k that will satisfy both statements.
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Re: If k = (n + 2)(n - 2), where n is an integer value greater [#permalink] New post  05 Sep 2020, 17:14
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1) k is the multiple of two primes with a gap of 4
Lets write down the prime numbers till 20
2,3,5,7,9,11,13,17,19
Primes with gap of 4 are:
3,7
7.11
13.17
So k could be the multiplication of these three numbers

2) tells us that k should be less than 100 so it could be any numbers with a gap of 4 ( including the primes stated above)

1+2 combined still is insufficient as k could be 3.7=21 or 7*11=77 as both are less than 100

So e is the answer

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Re: If k = (n + 2)(n - 2), where n is an integer value greater [#permalink] New post  15 Sep 2020, 04:23
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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



[quote]

Solution:

Statement One Alone:

k is the product of two primes

If k is the product of two primes, then n must be odd. If n = 5, then k = 7 x 3 = 21. If n = 9, then k = 11 x 7 = 77. Since we already have two different values for k, statement one alone is not sufficient.

Statement Two Alone:

k < 100

Since there are many integer values less than 100, so statement two alone is not sufficient.

Statements One and Two Together:

From statements one and two, we see that k can still be either 21 or 77, so the two statements together are still not sufficient.

Answer: E

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Re: If k = (n + 2)(n - 2), where n is an integer value greater [#permalink] New post  06 Jun 2021, 13:09
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This question is basically asking, "are there more than two primes that are 4 apart and have a product of less than 100?"

The answer is yes: 3 times 7 is 21, and 7 times 11 is 77.
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Re: If k = (n + 2)(n - 2), where n is an integer value greater [#permalink] New post  14 Sep 2021, 11:02
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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
Since k is a product of 2 prime numbers, n+2 and n-2 should be prime numbers. We can also conclude that the difference between these two prime numbers should be 4.
Lets consider the prime numbers (3,7) , ( 7,11) , (13,17 ) (19,23) and so on. In all of these pairs, the difference between the prime numbers is 4.

K = 3 * 7

k = 7 * 11

K = 13 *17

Since different values of k is possible, Statement 1 alone is insufficient.

(2) k < 100
Statement 2 alone is also insufficient as different values of k are possible which is less than 100.

Even if you combine both statements, 2 values of k are possible.
K = 3 * 7 and k = 7 * 11
Hence its insufficient.
Option E is the right answer.

Thanks,
Clifin J Francis,
GMAT SME
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Re: If k = (n + 2)(n - 2), where n is an integer value greater [#permalink]
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