Mathematical And Numerical Reasoning 2026 Njfp Job

The ratio of good oranges to bad oranges is 5:4. Let the common multiplier be \( k \). Thus, the number of good oranges is \( 5k \) and the number of bad oranges is \( 4k \).
Given that the number of bad oranges is 36:\[ 4k = 36 \]\[ k = 9 \]Now we can find the number of good oranges:\[ \text{Good oranges} = 5(9) = 45 \]To find the total number of oranges in the bag:\[ \text{Total} = \text{Good} + \text{Bad} \]\[ \text{Total} = 45 + 36 = 81 \text{ oranges} \]

Let the age of the son be \( s \). The man's age is therefore \( 4s \). The problem states the difference between their ages is 36 years:\[ 4s - s = 36 \]\[ 3s = 36 \]\[ s = 12 \]So, the son is 12 years old and the father is:\[ 4(12) = 48 \text{ years old} \]The sum of their ages is:\[ \text{Sum} = 48 + 12 = 60 \text{ years} \]

First, we determine the current number of men and women in the 20-member committee using the ratio 3:1.\[ \text{Total parts} = 3 + 1 = 4 \]\[ \text{Number of men} = \frac{3}{4} \times 20 = 15 \]\[ \text{Number of women} = \frac{1}{4} \times 20 = 5 \]We want the new ratio of men to women to be 3:2 by adding \( w \) women, while the number of men remains 15:\[ \frac{15}{5 + w} = \frac{3}{2} \]Cross-multiplying gives:\[ 3(5 + w) = 15 \times 2 \]\[ 15 + 3w = 30 \]\[ 3w = 15 \]\[ w = 5 \]Therefore, 5 women must be added to the committee.

Probability is the ratio of the number of desired outcomes to the total number of possible outcomes. Here, the total number of children (outcomes) is 40. The number of surnames starting with 'O' is 16, and the number starting with 'A' is 9. Since the question asks for the probability of either 'O' or 'A', we sum these two counts:\[ \text{Desired outcomes} = 16 + 9 = 25 \]\[ P(\text{O or A}) = \frac{25}{40} \]Simplifying the fraction by dividing both the numerator and the denominator by 5:\[ \frac{25 \div 5}{40 \div 5} = \frac{5}{8} \]Note: The provided answer C (9/16) is mathematically incorrect based on the data provided (25/40 = 5/8). I have updated the correct answer to reflect the true mathematical solution.

In trigonometry and geometry, angles are defined by their rotational span. A reflex angle is one that has passed a straight line (180°) but has not yet completed a full circle (360°). Therefore, any angle whose measure falls between 180° and 360° is classified as a reflex angle. This is distinct from obtuse angles (90°-180°) and acute angles (less than 90°).

The clock strikes based on the hour, meaning from 1 to 12. We first calculate the number of strikes in a 12-hour cycle by summing the integers from 1 to 12. This is an arithmetic progression where \( n = 12 \), \( a = 1 \), and \( l = 12 \):\[ \text{Sum} = \frac{n}{2}(a + l) \]\[ \text{Sum}_{12} = \frac{12}{2}(1 + 12) = 6 \times 13 = 78 \]Since a 24-hour day consists of two such 12-hour cycles (AM and PM), we multiply the 12-hour total by 2:\[ \text{Total Strikes} = 78 \times 2 = 156 \]

According to the zero exponent rule in mathematics, any non-zero number raised to the power of zero is equal to 1. This can be demonstrated using the quotient law of indices, which states that:\[ \frac{a^m}{a^n} = a^{m-n} \]If we let \( m = n \), then:\[ \frac{a^n}{a^n} = a^{n-n} = a^0 \]Since any non-zero number divided by itself is 1, it follows that \( a^0 = 1 \).

First, we must determine the daily pay for the group of 4 workers. We divide the total amount by the number of days:\[ \frac{160,000}{5} = 32,000 \text{ per day for 4 workers} \]Next, we find the amount paid to a single worker per day by dividing that daily total by 4:\[ \frac{32,000}{4} = 8,000 \text{ per worker per day} \]Finally, to find the daily pay for 5 workers, we multiply the single worker's daily rate by 5:\[ 8,000 \times 5 = 40,000 \]Note: I have updated the correct answer from D to A, as the calculation clearly shows 5 workers earn ₦40,000 in one day.

When comparing fractions that have the same numerator, the rule is that the fraction with the smallest denominator has the largest value. This is because a constant quantity (15) is being divided into fewer parts, making each part larger. Comparing the denominators 17, 18, 19, and 21, we see that 17 is the smallest value. Therefore, 15/17 is the largest fraction in the set.

The Zero Property of Multiplication states that the product of any number and zero is always zero. This is a fundamental law of arithmetic. Whether the number is positive, negative, a fraction, or an 'exact number', multiplying it by 0 results in the total disappearance of value in the product. Symbolically, this is expressed as: \[ a \times 0 = 0 \]