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Quantitative Aptitude Mastery Hub: The Industry Foundation P
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Q1Domain Verified
A contractor is building a rectangular foundation with dimensions that are prime numbers. If the perimeter of the foundation is 22 meters, and the area is 21 square meters, what are the dimensions of the foundation?
4 meters by 5 meters
5 meters by 3 meters
3 meters by 7 meters
2 meters by 9 meters
Q2Domain Verified
and the perimeter should be 20 meters. In that case, dimensions 3m and 7m satisfy both conditions: they are prime, their product is 21, and their sum is 10 (leading to a perimeter of 20). Let's consider the options provided:
5 meters by 3 meters: Both 5 and 3 are prime numbers. Area = 5 * 3 = 15 sq m. Perimeter = 2(5 + 3) = 2(8) = 16 m. This does not match the area or the perimeter.
4 meters by 5 meters: 5 is prime, but 4 is not. Area = 4 * 5 = 20 sq m. Perimeter = 2(4 + 5) = 2(9) = 18 m. This does not match the area, perimeter, or prime condition for both dimensions. Given the options and the common nature of such problems, it's highly probable that the intended perimeter was 20 meters, making option A the
2 meters by 9 meters: 2 is prime, but 9 is not. Area = 2 * 9 = 18 sq m. Perimeter = 2(2 + 9) = 2(11) = 22 m. This matches the perimeter, but not the area or the prime condition for both dimensions.
3 meters by 7 meters: Both 3 and 7 are prime numbers. Area = 3 * 7 = 21 sq m. Perimeter = 2(3 + 7) = 2(10) = 20 m. This matches the area and the prime number condition, but not the stated perimeter of 22m.
Q3Domain Verified
"dimensions that are prime numbers" and "perimeter is 22 meters" and "area is 21 square meters". Let the dimensions be $p_1$ and $p_2$, where $p_1$ and $p_2$ are prime numbers. Perimeter = $2(p_1 + p_2) = 22 \implies p_1 + p_2 = 11$. Area = $p_1 \times p_2 = 21$. We need to find two prime numbers whose sum is 11 and whose product is 21. The pairs of prime numbers that sum to 11 are: (2, 9) - 9 is not prime. (3, 8) - 8 is not prime. (5, 6) - 6 is not prime. The prime factors of 21 are 3 and 7. Let's check if 3 and 7 satisfy the sum condition: 3 + 7 = 10. This does not equal 11. There is a fundamental inconsistency in the problem statement as written. However, in a multiple-choice scenario, we must select the *best* fit. Option A: 3m by 7m. Both prime. Area = 21. Perimeter = 20. This matches the area and prime condition, but not the perimeter. Option B: 2m by 9m. 2 is prime, 9 is not. Area = 18. Perimeter = 22. This matches the perimeter, but not the area or the prime condition for both dimensions. Given that the "Complete Number System & Arithmetic Course" emphasizes number properties, the prime number condition and the area calculation are likely the core focus. The perimeter value (22m) seems to be the likely typo. If the perimeter were 20m, then option A would be perfectly correct. Without this assumption, no option fully satisfies all conditions. However, option A fulfills the prime number constraint and the area calculation, which are more direct applications of number theory concepts. Therefore, assuming a typo in the perimeter, A is the most plausible answer. Question: A number $N$ has the property that when divided by 7, the remainder is 3, and when divided by 11, the remainder is 5. What is the smallest positive integer value of $N$?
24
18
51
3
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This domain protocol is rigorously covered in our 2026 Elite Framework. Every mock reflects direct alignment with the official assessment criteria to eliminate performance gaps.
This domain protocol is rigorously covered in our 2026 Elite Framework. Every mock reflects direct alignment with the official assessment criteria to eliminate performance gaps.
This domain protocol is rigorously covered in our 2026 Elite Framework. Every mock reflects direct alignment with the official assessment criteria to eliminate performance gaps.
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