If Q is a factor of 18 and T is prime numbers between 2 and 18. What is Q$\cap$T?

Analyze the question: We need the intersection of two sets:

• Q = the factors of 18
• T = the prime numbers between 2 and 18

The intersection (∩) contains only the elements found in both sets.

Concept: A factor of 18 is a number that divides 18 exactly. A prime number has exactly two factors: 1 and itself.

Step 1: List Q (factors of 18) Q = {1, 2, 3, 6, 9, 18}

Step 2: List T (primes between 2 and 18) Primes up to 18 are 2, 3, 5, 7, 11, 13, 17.

• If "between 2 and 18" is read as exclusive, 2 is left out and T = {3, 5, 7, 11, 13, 17}.
• If the problem intends the range to include 2 (as the options suggest), T = {2, 3, 5, 7, 11, 13, 17}.

Step 3: Find the common elements Which members of Q are prime?

• 1: not prime
• 2: prime ✔
• 3: prime ✔
• 6: not prime (2 × 3)
• 9: not prime (3 × 3)
• 18: not prime

So Q ∩ T = {2, 3}.

Note on the wording: Taken strictly, "between 2 and 18" would exclude 2 and give {3}. However, {3} is not among the options, and every option contains 2, so the question intends 2 to be included.

Why the other options are wrong:

• B includes 18, which is not prime.
• C includes 9 = 3 × 3, not prime.
• D includes 6 = 2 × 3, not prime.

Answer: A. (2, 3)

Exam tip: For an intersection question like this, list both sets, then test each element of the smaller set. Here, any option containing a composite number (6, 9, 18) can be eliminated at once, since T only has primes.