Around the World in 80 Questions (Day 3): If m and n are prime numbers

(1) the only even prime is 2, if m>11 then m is odd, and m - 11 is even. An even number multiplied by an integer is even.
The answer is NO. Sufficient.
(2) The only prime number less than 3 is 2, so n = 2, and 2 - n = 0. Any number multiplied by 0 is 0. 0 is even
The answer is NO. Sufficient.

Answer D

If m and n are prime numbers, is (m - 11)(2 - n) an odd number ?

it would be odd number if its Odd*Odd so (m-11) = odd and (2-n)= odd to satisfy

(1) m > 11, prime m greater than 11 would be 13,17, which both are odds, and (m-11) would be 2 and 6, which means (m-11) would be Even. Sufficient to say the formula is not an Odd number.
(2) n < 3, prime n less than 3 can be 2, -2,-3. (2-n) would be 0, 4, and 5. It can be even, odd or zero. Insufficient.

Answer is A

(1) m>11, m is odd => m-11 is even => (m-11)(2-n) is even => no => (1) sufficient.
(2) n<3, n can be odd or even => (2) insufficient.
=>A

m and 11 are odd therefore m-11 is even
2 is even and n is odd therefore 2-n is odd
The product of an odd and an even is even so both answers are sufficient, they only give indication on the sign of the product

If m and n are prime numbers, is (m - 11)(2 - n) an odd number ?

Basic principles:
e-e=even
o-o=even
e-o=odd
o-e=odd

e*e=even
o*o=odd
e*o=even

(1) m > 11
This tells us that m is odd. So m-11 must be even. If m-11 is even, then we know that the answer is even.

Sufficient

(2) n < 3
This tells us that n=2. So, 2-2 is zero, which means the answer is even.

Sufficient.

Answer D

Given m,n are prime.
Asked \((m-11)(2-n)\) is odd ?
S1 :- \(m>11\)
So all number of can only be odd as except \(2\) , all prime numbers are odd.
So expression \(m-11\) will be \(odd-odd\) i.e even.
So \(even*anything\) is even. Thus answer is no. Expression is even.
S1 sufficient.

S2 :- \(n<3\)
n can only be 2, as m,n are prime and only\( 2\) fits the criteria.
thus expression \( 2-n\) will 0. Thus whole expression's value is \(somevalue*0 = 0\). Thus even.
S2 is sufficient.

Answer is D.

If m and n are prime numbers, is (m - 11)(2 - n) an odd number ?

(1) m > 11
States that m is Odd and Positive. i.e m=13,17,19,23..
(m-11) is even.
n can be 2, 3, 5,7...
if n=2, value is 0. Product is 0.
if n>2, (2-n) is odd and negative.
The product will be Even.
Hence the final product can be either 0 or even but not Odd.
Hence Sufficient.


(2) n < 3
this states that n=2.
So (2-n) is 0. the final product is 0 no matter what the value of m is.
Hence the final product is 0.
hence it is sufficient.

Ans D

m & n could be equal to 2,3,5,7, or any other prime numbers.

From Statement 1,we get

m = 13/17/19/.. and so on. Therefore, m is an odd prime number.
Hence, m-11 = odd - odd = even

This implies that (m - 11)*(2 - n) = (Odd- 11)*(2- n) =Even*(2- n)= Even

Statement 1 is sufficient.

From Statement 2, we get

n<3
Therefore, only possible value of n is 2.
(m - 11)*(2 - n) = (m - 11)*(2 - 2) = (m- 11)* 0 = 0 = Even

Statement 2 is sufficient.

IMO OA should be D.

If m and n are prime numbers, is (m - 11)(2 - n) an odd number ?

(1) m > 11
(2) n < 3


A) 1 is not sufficient, even if m =13, n could be equal to 2 and ans. would be 0

Choices remain b, c, and e
B) 2 alone is sufficient, n=2, expression is 0 for any value of m, thus not an odd no.

Is (m-11)(2-n) an odd number?

Given: m and n are prime numbers

Statement 1:

m > 11

If m is greater than 11,m could be 13, 15, 17 and so on.

Case 1:
No info about n. So n could be 2 (only even prime number).
(13-11) (2-2) which gives 0

Since zero is not a prime number, the number can't be prime.

Case 2:
If n is 3,
(13-11)(2-3)
= 2 × -1=-2.
Odd - odd = even
Even × Odd = Even.
In this case the number is even.

Statement 1 :
Yes/ No situation

Statement 1 is not sufficient since we don't have a definite answer.

Statement 2: n < 3

In this case n can only be 2 ( only even prime number) since 1 is not a prime number.

So irrespective of the value of m, the number is zero.

Zero is not a prime number.

We have a definite no as the answer.

So the answer is statement 2 alone is sufficient.

Option B.

Posted from my mobile device

m>11 ==> M is odd , odd-odd= Even , Even *anything is even ; Sufficient
n<3 -==> N is 2 Even-even= even, Even *anything is even ; Sufficient

Answer D

S1:- m>11.
All prime numbers except 2 are odd, so in this case all values of m will be odd.
So, (m-11) = even
And, even* even/odd = even
So, (m-11)(2-n) will be even or zero in case n=2, therefore ans to the question is "no". Hence, S1 is sufficient.

S2:- n<3.
Only case possible will be n=2. In this case (2-n)=0
So, (m-11)(2-n) will be zero always, therefore answer to the question is "no". Hence, S2 is sufficient.

Therefore D is the correct choice.

Posted from my mobile device

Given: m and n are prime numbers
Question: is (m - 11)(2 - n) an odd number ?
(m - 11)(2 - n) odd only if both (m-11) odd and (2-n) odd
(m-11) is odd only when m =2
(2-n) is odd only when n is odd i.e. n >2
Hence the question can be rephrased to "Are both m=2 and n>2?"

(1) m > 11 implies m cant be 2 => the answer is No. sufficient

(2) n < 3 implies n=2 => the answer is No. sufficient

D

IMO D

If m and n are prime numbers, is (m - 11)(2 - n) an odd number ?

(1) m > 11
(2) n < 3

Solu

Here we check if M = even and if N = odd since the product can be ODD only if these 2 conditions are met.

1. M > 11 --> Any prime number greater than 11 is ODD. Hence M is not even and hence SUFFICIENT

2. N < 3 --> Only 2 is prime number which is EVEN. Hence N is not ODD and hence SUFFICIENT

HENCE D

If m and n are prime numbers, is (m - 11)(2 - n) an odd number ?
For (m-11)(2-n) to be odd, both (m-11) and (n-2) have to be odd. Which means, both m have to be even and n have to be odd

(1) m > 11 - SUFFICIENT
m > 11 and being a prime number, m is surely an odd number.
So, (m-11) is even and hence (m - 11)(2 - n) is NOT odd number.

(2) n < 3 - SUFFICIENT
n < 3 and being a prime number, n is surely 2.
So, (2-n) is even and hence (m - 11)(2 - n) is NOT odd number.

Ans is D.

From statement 1:
(1) m > 11
m can be any prime number greater than 11 ( 13,17,19...)
Let E = (m - 11)(2 - n)
For n=2,
E = 0 for every value of m , E=even
For n= 3, m=13
E = -2 (even)
Thus, expression is even.


From statement 2:
(2) n < 3
n = 2 (only prime number less than 3)
m can be any prime integer.
Let E = (m - 11)(2 - n)
E=0.
Thus solution can be determined from both 1 and 2.
Choice D.

St1- m>11 thus m is always odd and hence (m-11)(2-n)= Even * Even/odd= Even Suff
St 2- n=2 Thus (m-11)(0) =0 even Suff

Ans D