Can the positive integer n be written as the sum of two different posi

Question

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is even.
(2) n is less than 10.

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Archit3110 · Answer

#1
n is even
n=8 ; 3+5 yes or 8+0
insufficient
#2
n is less than 10
insufficient as many values are possible
from 1 &2
n is 8 #1 already discussed
option E

bellbell · Answer

"Can the positive integer n be written as the sum of two different positive prime numbers?"
=> as long as it can be written by 02 diff positive prime numbers then it should be ok right?
For example, 8 can be written as 8+0 but also 3+5 => so it's still a YES, doesn't matter how many other combinations there are, as long as there's 01 combination that satisfy as SUM of 02 diff prime numbers then it should be fine, or am I understanding the question wrong?
Thanks.

SoSolid · Answer

Statement 1) n is even. 
If n = 4 then 2 + 2 = 4 and n is not the sum of two different primes
If n = 8 then 5 + 3 = 8 and n is the sum of two different primes
Insufficient

Statement 2) n is less than 10
if n = 4 then 2 + 2 = 4 and n is not the sum of two different primes
If n = 8 then 5 + 3 = 8 and n is the sum of two different primes
Insufficient.

Statement 1 and 2 taken together)
Using the statements above we still don't know if n is the sum of two different primes.
Answer choice E.

vivek920368 · Answer

I think the language of the question is misleading.

It only asks, Can it be done? yes, it could be written as the sum of two primes.
nowhere is it mentioned or hinted that sum should not be achieved with non-primes.

what am I missing here?  carcass

Carcass · Answer

Not sure, I am.

If I read the stem "can I write the number n and it will contain two primes ?

yes 7+3=10 or 5+3=8

No 6=2+4

6 is even but not has two primes in it

The stem also opens up to use many combinations and actually no restrictions.

Not sure if it is the best question in the world but surely I saw things worse than that

Bunuel · Answer

There is nothing wrong with the question (apart from the redundant word "positive" in the stem). When combining the statements we get that n is 2, 4, 6, or 8. If n is 2, 4, or 6, then the answer is NO: n CANNOT be written as the sum of two different primes. If n is 8, then the answer is YES: n CAN be written as the sum of two different primes (8 = 5 + 3). So, we have two different answers to the question and thus the answer is E. If (2) were n is less than 8 (instead of "n is less than 10"), then the answer would have been C. Because none of the possible values of n (2, 4, and 6) can be written as the sum of two different primes. Similar questions to practice: https://gmatclub.com/forum/can-the-posi ... 66085.html (OG) https://gmatclub.com/forum/can-the-posi ... 38813.html https://gmatclub.com/forum/is-the-posit ... 69034.html https://gmatclub.com/forum/can-the-posi ... 91460.html https://gmatclub.com/forum/is-positive- ... 47007.html https://gmatclub.com/forum/can-the-posi ... 27401.html Hope it helps.

Vasu49 · Answer

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is even.
(2) n is less than 10.

A 
n = 2; No
n = 4; No
n = 6; No
n = 8;  Yes  (5+3)
Hence,  Not sufficient .
B
n = 1; No
n = 2; No
n = 3; No
n = 4; No
n = 5;  Yes  (3+2)
Hence,  Not sufficient .
C - Both together i.e n = (2,4,6,8)
n = 2; No
n = 4; No
n = 6; No
n = 8; Yes(5+3)
Again  Not sufficient.

We do not know the value of n. If that is known, we can conclude the question with a specific Yes or a No. From C, we get n as 2, 4, 6 and 8. If 8 was excluded then all other values can not be written as a sum of two different prime numbers. 
 Hence, the answer is E.

bumpbot · Answer

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Can the positive integer n be written as the sum of two different posi

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