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

Question

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.

syntnghosh · Accepted Answer

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

Bunuel · Answer

What about 7*11 = 77?

mvictor · Answer

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.

msbandi4321 · Answer

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!

sidrsharma · Answer

That's exactly what I did too. Darn that's a tricky one :\

Princ · Answer

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

energetics · Answer

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.

Saraskarki · Answer

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

Posted from my mobile device

ScottTargetTestPrep · Answer

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

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

mcelroytutoring · Answer

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.

CrackverbalGMAT · Answer

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

AnkurGMAT20 · Answer

Bunuel , GMAT Prep question. Please tag it.

Bunuel · Answer

______________________
Done. Thank you!

Afn24 · Answer

Posted from my mobile device

My method

bumpbot · Answer

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

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