ITPEC FE Subject B October 2025 Question 5

Topic: Math & Numbers

From the answer group below, select the correct combination of answers to be inserted into A and B in the program.

Prime numbers are the positive integers that are only divisible by the number itself and 1. Procedure printPrime receives the integer N (N ≥ 1) as an argument and prints the first N prime numbers. For example, printPrime(6) will print “2 3 5 7 11 13”.

[Program]
○ printPrime(integer: N)
integer: count, number, i
boolean: isPrime
count ← 1
number ← 2
while (count ≤ N)
isPrime ← true
for (increase i from 2 to integer part of the square root of number by 1)
if (number mod i = 0)
A
exit the for block
endif
endfor
if (isPrime = true)
output " ", number
B
endif
number ← number + 1
endwhile

Answer group

OptionAB

Explanation

A: isPrime ← false, B: count ← count + 1 — a divisor clears the prime flag, and each prime printed raises the count of primes found.

  • •isPrime is set to true before each number is tested. A divisor between 2 and the square root of number proves it is not prime, so A clears the flag before the for loop is left.
  • •count starts at 1 and the loop runs while count ≤ N, so it holds the number of primes printed so far plus one. Each prime printed must raise it by exactly 1: B is count ← count + 1.

Trace for printPrime(6): 2 and 3 have no candidate divisors and are printed; 4, 6, 8, 9, 10 and 12 each hit a divisor; 5, 7, 11 and 13 pass. After 13 count becomes 7, the loop ends, and 2 3 5 7 11 13 has been printed.

Answer (c)

Why not others:

  • •(a) — never clears isPrime, so every number is printed, and count rises on composites instead of primes: printPrime(6) prints 2 to 12
  • •(b) — the same missing flag, with count raised by the divisor i on each composite
  • •(d) — A is right, but B adds the loop variable i, whose value after the loop has nothing to do with the number of primes found (for 2 and 3 the loop does not run at all)

Key rule: In a search-and-count loop, set the failure flag at the point of failure, and advance the counter only where success is confirmed.

Math & Numbers · AI-written, may contain errors

Practice this exam

This question comes from an official ITPEC past paper. ITPEC Practice is an independent study tool and is not affiliated with ITPEC. See the official FE past-paper collection or Report an issue.