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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: 23 Feb 2014, 13:28
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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: ::
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 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] 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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If k = (n + 2)(n - 2), where n is an integer value greater [#permalink] 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] 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: ::
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  19 Apr 2019, 12:52
Bunuel

What is the best approach to solving this problem? I get the solution but is there any approach other than assuming values of n starting from 1? In such cases, ita difficult to know till what value of n should we test till. I tested it till 8 and then guessed A would be correct
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Re: If k = (n + 2)(n - 2), where n is an integer value greater [#permalink] New post  12 May 2019, 13:52
jyotsnamahajan wrote:

What is the best approach to solving this problem? I get the solution but is there any approach other than assuming values of n starting from 1? In such cases, ita difficult to know till what value of n should we test till. I tested it till 8 and then guessed A would be correct


But you only have to test some values (lets say 2) to reach at multiple values to be the answer, then its insuff

For ex

1) says that n>2 then: n= 5 we have 7*3= 21 and n=9 we have 11*7= 77

2 different values that satisfy the condition, hence insuff

2) k<100 ns

1+2) still it could be 21 or 77 (both k<100) hence insuff --> E
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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  11 Mar 2020, 01:59
My thought process was the following:

Given:
n>2

Find: k

Statement 1: K is the product of two primes
k has to be odd, since n>2 and the sum/difference of n with 2 has to be a prime number
so, if n is 3, n-2=1, n+2=5
if n is 5, n-2=3, n+2=7
Both of these work, so statement 1 is insufficient

Statement 2: K<100
(n+2)(n-2)<100
n^2-4<100
n^2<104
n<104^1/2
n<~11
Multiple options, so statement 2 is insufficient

Combined:
Statement 1: n can be 3, 5, 7...
Statement 2: n<~11
Still insufficient
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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
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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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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