If three prime numbers are randomly selected from the prime numbers less than 30 and no prime number can be chosen more than once, what is the probability that the sum of the three prime numbers selected will be even?
Answer Choices
Correct answer marked belowSee the full step-by-step explanation
You can see the correct answer above. Sign in for free to unlock the complete worked solution.
Track your performance and improve
Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.
Unlock the full explanation
Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.
This one got me for a second. I started listing all the triples before realizing there's a much simpler parity argument. Nice question.
Same here. Took me way too long listing combos.
Yeah the parity shortcut is the whole point of the problem.
Quick question: why does the fact that there's only one even prime matter so much here? I get that 2 is even, but I'm not seeing how that decides the answer.
Think about what happens to the sum when you include 2 vs when you don't.
Parity of the sum depends on how many odd numbers you pick.
The wording 'randomly selected' made me pause — do we treat all C(10,3) subsets as equally likely? Once I assumed that, the counting was straightforward.
Yes, each set of 3 distinct primes is equally likely.
A bit tricky for me. I initially picked the answer that matched 'at least one even prime' instead of exactly one, which is wrong since only 2 is even. Good trap.
Classic trap, I almost fell for it too.
What it tests
Your command of divisibility, primes, factors, parity, and how the GMAT tests properties of integers.
Common trap
Forgetting that 1 is not prime, that 0 is divisible by every integer, or that negative numbers flip your assumptions.