Question

Compare Quantity A and Quantity B.
Quantity A: The least prime number greater than 24
Quantity B: The greatest prime number less than 28

• A. Quantity A is greater.
• B. Quantity B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.
• E.

Hint:

For questions involving prime numbers, quickly check for divisibility by small primes like 2, 3, 5, 7. Remember that any even number greater than 2 is not prime. For odd numbers, check divisibility by 3 (sum of digits is divisible by 3) and 5 (ends in 5).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The question requires us to identify two specific prime numbers and then compare them.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Step 2: Detailed Explanation:
Analysis of Quantity A:
We need to find the least prime number that is greater than 24.
Let's check the integers greater than 24 in order:
- 25 is not a prime number because it is divisible by 5 ($5 \times 5 = 25$).
- 26 is not a prime number because it is an even number and divisible by 2 ($2 \times 13 = 26$).
- 27 is not a prime number because it is divisible by 3 and 9 ($3 \times 9 = 27$).
- 28 is not a prime number because it is an even number and divisible by 2 ($2 \times 14 = 28$).
- 29 is a prime number because its only divisors are 1 and 29.
Thus, the least prime number greater than 24 is 29.
So, Quantity A = 29.
Analysis of Quantity B:
We need to find the greatest prime number that is less than 28.
Let's check the integers less than 28 in descending order:
- 27 is not prime (divisible by 3).
- 26 is not prime (divisible by 2).
- 25 is not prime (divisible by 5).
- 24 is not prime (divisible by 2).
- 23 is a prime number because its only divisors are 1 and 23.
Thus, the greatest prime number less than 28 is 23.
So, Quantity B = 23.
Step 3: Comparison:
Now we compare Quantity A and Quantity B.
Quantity A = 29
Quantity B = 23
Since $29>23$, Quantity A is greater than Quantity B.
Step 4: Final Answer:
The correct option is (A) because Quantity A is greater.