Data Sufficiency

If n is an integer between 10 and 99, is n < 80 ?
(1) The sum of the two digits of n is a prime number.
(2) Each of the two digits of n is a prime number.




I think B but it says C..

well there atleast two numbers 32 and 52.

Calista.

Hi Magical Cook,

Well, I would say B too, there is no two digit number greater than 80 that has both its integer prime, so n has to be less that 80 .. btw what is the source of the question

Regards

Hmm. This is from gmatprep. so, answer should be correct but I dont understand why it's C..

I dont see how the ans can be C

If n is an integer between 10 and 99, is n < 80 ?

(2) Each of the two digits of n is a prime number.

for this stmt to be false we need to deduce that both n<80

& n GE (greater than or equal to) 80
are possible

n<80 we have 73

but for n GE (greater than or equal to) 80, we will have values
80-89 (first digit is eight) 90-99 (first digit 9) so none of these numbers would satisfy stmt 2

however is there a possibility that a soln can be incorrect in gmatprep?

Magical_cook, ur Qs is -

If n is an integer between 10 and 99, is n <80> 80
or = 21, 23, ... When n < 80
So not A or D.
If we go by 2,
n = any prime number at unit's digit with 3, 5 and 7 but neither 8 nor 9 as ten's digit .

Now by this, we can conclude by B that the best option to chose is B. Guys am I correct?

wow if the answer is C it means that I have to study a lot more.. I do think its B?

For example, as Each of the two digit needs to be a prime number and 8 and 9 is not a prime, there couldn't be any number which satisfies this condition if the number is bigger than 80... as there will always be one number which is not prime..

Agree as well that it should be B for the reasoning's noted.

First thing I did was to reframe the question:
10<n<99, is n<80?

For (2) Each of the two digits of n is a prime number:
I listed some #'s that only have prime #'s for each of the two digits, such as, 22, 33, 55, 77, etc. From this I deduced that the largest number n could be is 77, thus n<80. SUFF

For (1) The sum of the two digits of n is a prime number.
This was a little more tedious, I listed all possible combo's in my own short way:
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9

By visualizing this I could use connecting arrows to see what the possibilities are. I could make a combo of a # below 80, such as, if n = 74 -> then 7+4 = 11, a prime number, and thus n<80 (and still maintaining 10<n<99).
Also, I could make a combo of a # greater than 80, such as, if n = 83 -> 8+ 3 = 11, a prime number, and thus n>80. Since we have n<80 and n>80, INSUFF.

Thus answer is B.

10< n < 99
if both digits are prime.Then 8 and 9 are ruled out.
hence its B.

If its C then something is missing in the question.

answer is B as per the answer in gmatprep...

Are you sure Aniket that the answer is B as per the GMAT prep...

though it should be B as we all have solved it but just check all of you guyz once inorder to know wat is the OA...