If a and b are both prime numbers greater than 10, which of the follow

Question

If a and b are both prime numbers greater than 10, which of the following CANNOT be true?

I. ab is an even number.
II. The difference between a and b equals 117.
III. The sum of a and b is even.

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III

Kudos for a correct  solution .

kvazar · Answer

Properties to use:
1. There is only one even prime number 2, hence any prime greater than 10 is ODD.
2. Product of any two ODD numbers is always ODD.
3. ODD - ODD = EVEN, hence difference between any 2 prime numbers (not including 2) is always EVEN.
4. Sum of any two ODD numbers is always EVEN.

Hence:

I. ab is an even number.  - Impossible, see points 1 and 2 above.

II. The difference between a and b equals 117.  Impossible, see the points 1 and 3 above.

III. The sum of a and b is even.  Correct, see the points 1 and 4 above.

Hence, I and II are not true, Answer  B

GMATinsight · Answer

CONCEPT: Prime Numbers greater than 10 will all be ODD

I. ab is an even number -  Can't be True because both a and b are ODD

II. The difference between a and b equals 117 -  Can't be True because both a and b are ODD and Difference of two Odd No. must be EVEN

III. The sum of a and b is even -  This will be True because both a and b are ODD and Sum of two Odd No. must be EVEN

Answer: Option  B

lipsi18 · Answer

We have a,b prime values>10; so a & b will be odd 
1. Odd* odd = Odd
2. Odd-Odd =even
3. Odd+ Odd = Even
So ab will never be an even number, so 1 is always false. A-b will never be odd number, so 2 is always false. a+b will be always even so 3 is true.

1 and 2 is the right option

Hence answer is B
Thanks,

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

Since a and b are both prime numbers greater than 10, they must both be odd. Therefore ab must be an odd number, so Statement I cannot be true. Similarly, if a and b are both odd, then a - b cannot equal 117 (an odd number). This difference must be even. Therefore, Statement II cannot be true. Finally, since a and b are both odd, a + b must be even, so Statement III will always be true. Since Statements I and II CANNOT be true, but Statement III IS true,  the correct answer is (B) .

EncounterGMAT · Answer

a and b= prime numbers > 10............all numbers will be ODD.

I. ab is an even number. -> odd x odd ≠ even...........not possible
II. The difference between a and b equals 117 -> a-b=odd -> even-odd=odd or odd-even=odd....since a or b is not an even number...........not possible 
III. The sum of a and b is even. -> odd+odd=even.....possible

So answer is  option B

CrackverbalGMAT · Answer

This is actually a ‘Must be False’ question, because, in this question we are trying to establish which questions CANNOT be true. In other words, we are trying to see which statements should be definitely false/always false. 
So, the strategy that we adopt here is to try and make a statement true, once, by taking a simple case or based on odd-even concepts. Whichever statement/s cannot be made true, has to be the answer.

The question says that a and b are both prime numbers greater than 10. Let us recall the fact that 2 is the ONLY even prime number. This means that any prime number greater than 2 will definitely be ODD. This only means that a and b are both odd.

If a and b are odd, their sum will always be even since Odd + Odd = Even. Statement III is always true. But, we are looking for ‘Always false’ statements. Therefore, we shouldn’t consider statement III and any option containing statement III.
Answer options C, D and E can be eliminated.
 
Since a and b are odd, their product will also be ODD always, regardless of what values they take. Statement I is definitely false.

The difference of two odd numbers is always even. Statement II is saying the opposite. Statement II is definitely false.

Answer option A can now be eliminated. The correct answer option is B.

It does not matter whether the question is a ‘Must be true’ or a ‘Must be false’ question. In both cases, the idea is to take cases and use concepts to eliminate statements and hence options, to zero in on the right answer. 
Hope this helps!

bumpbot · Answer

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If a and b are both prime numbers greater than 10, which of the follow

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If a and b are both prime numbers greater than 10, which of the follow

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