If a and b are unique prime integers, which of the following must be e

Hi All,

When a question asks "which of the following MUST be _____", what it's really asking is "which of the following is ALWAYS _____ no matter how many different examples you come up with?" In this way, it's often easy to try to DISPROVE the 4 wrong answers because all that you have to do is find ONE example that breaks the pattern.

In this question, even though the prompt states that A and B have to be unique prime numbers, that "restriction" is actually IRRELEVANT to this question (you could use the same prime number twice, or any two integers for that matter, and still get the correct answer). When an Official GMAT question includes a restriction, it's there for a reason (so you should carefully note the restriction).

We're asked which of the following must be EVEN....We're told that A and B have to be prime numbers. Let's TEST VALUES to prove which answers are NOT necessarily even:

Answer A: A - B.
If A = 3 and B = 2, then 3-2 = 1, which is ODD.
Eliminate A

Answer B: A - 2B
If A = 3 and B = 2, then 3 - 4 = -1 which is ODD.
Eliminate B

Answer D: 2A - B
If A = 2 and B = 3, then 4 - 3 = 1 which is ODD.
Eliminate D

Answer E: AB^2
If A = 3 and B = 5, then 3(5^2) = 75 which is ODD.
Eliminate E

Final Answer:
GMAT assassins aren't born, they're made,
Rich

If a and b are unique prime integers, which of the following must be even?

A. a−b
B. a−2b
C. 2a−2b
D. 2a−b
E. ab^2


OA = C
2a-2b = 2(a-b) will always even (a is not equal to b).

Ans C - 20 Secs

Keyword - MUST BE Even
Any INTEGER multiplied by 2 (even) is ALWAYS Even
Even +/- Even = Even
Option C fits pefectly

VERITAS PREP OFFICIAL SOLUTION

Correct Answer: C

On questions that ask for which solution "must be" something, you can use process of elimination to determine which answer choices don't necessarily fit that category. In this case, for choice A, if either a or b were 2, then the difference would be odd (i.e. 7 - 2 = 5). The same logic holds for choice B, in that if either variable were 2, the difference would again be odd (i.e. 7-2(2) = 7 - 4 = 3). Choice D, again, can be proven incorrect by the same process, but because the first term, 2a, will definitely be even (it's multiplied by 2), then b will have to be odd. Still, we can plug in prime numbers for a and b to reach an odd difference, such as 2(7) - 3 = 14 - 3 = 11. Choice E will be odd unless one of the variables is equal to 2; any other combination of primes will produce an odd value (i.e. 5 * 32 = 45). Choice C must be even, and you may not need to plug in numbers to determine that. If you factor the 2 from each term, you find that the expression is 2(a-b). Because a and be are integers, then the expression will be 2(an integer), which must be even. Therefore, the correct answer is C.

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