Mathematical And Numerical Reasoning 2026 Njfp Job

This problem can be solved by finding a common difference between the divisors and their respective remainders. Observe the following:
For divisor 8: \( 8 - 6 = 2 \)
For divisor 9: \( 9 - 7 = 2 \)
Since the difference (k) is constant (2), the smallest number is found by calculating the Least Common Multiple (LCM) of the divisors and subtracting that constant difference.
First, find the LCM of 8 and 9:
\( 8 = 2^3 \)
\( 9 = 3^2 \)
\( \text{LCM}(8, 9) = 8 \times 9 = 72 \)
Now, subtract the common difference:\[ \text{Number} = \text{LCM} - k \]\[ \text{Number} = 72 - 2 = 70 \]We can verify this: \( 70 \div 8 = 8 \) remainder 6, and \( 70 \div 9 = 7 \) remainder 7.

To find the cost price (the amount the dealer paid), we use the relationship between Selling Price (SP), Cost Price (CP), and Profit Percentage.
The Selling Price represents 100% of the cost plus the 8% profit, which is 108% of the Cost Price.\[ SP = CP \times \left(1 + \frac{\text{Profit \%}}{100}\right) \]\[ 81 = CP \times 1.08 \]To find the CP:\[ CP = \frac{81}{1.08} \]\[ CP = 75 \]The dealer paid ₦75 for the bicycle.

To convert a decimal to a fraction, we place the digits to the right of the decimal point over the appropriate power of ten based on the number of decimal places. 0.02 has two decimal places, which represents 'two hundredths'.\[ 0.02 = \frac{2}{100} \]Now, we simplify the fraction to its lowest terms by finding the Greatest Common Divisor (GCD) of 2 and 100, which is 2:\[ \frac{2 \div 2}{100 \div 2} = \frac{1}{50} \]Thus, 0.02 expressed as a fraction in its lowest term is 1/50.

Since -2 is the solution (root) of the equation, we substitute \( x = -2 \) into the equation and solve for the unknown variable \( c \).\[ 2(-2) + 1 - 3c = 2c + 3(-2) - 7 \]\[ -4 + 1 - 3c = 2c - 6 - 7 \]\[ -3 - 3c = 2c - 13 \]Now, rearrange the equation to collect the terms involving \( c \) on one side and the constants on the other:\[ -3 + 13 = 2c + 3c \]\[ 10 = 5c \]\[ c = \frac{10}{5} \]\[ c = 2 \]The value of \( c \) that makes the equation true when \( x = -2 \) is 2.

To find the volume of a rectangular tank, we use the formula for the volume of a cuboid:\[ V = \text{length} \times \text{width} \times \text{height} \]Given the dimensions are 6m, 4m, and 3m:\[ V = 6 \times 4 \times 3 = 72\text{m}^3 \]The question asks for one-third of this volume:\[ \text{One-third volume} = \frac{1}{3} \times 72 = 24\text{m}^3 \]Therefore, one-third of the tank's capacity is 24 cubic metres. Note that volume is always measured in cubic units (m³), making option A the only logically and mathematically sound choice.

To find the square root of a mixed fraction, we must first convert it into an improper fraction:\[ 1 \frac{7}{9} = \frac{(1 \times 9) + 7}{9} = \frac{16}{9} \]Now, we take the square root of the improper fraction by taking the square root of the numerator and the denominator separately:\[ \sqrt{\frac{16}{9}} = \frac{\sqrt{16}}{\sqrt{9}} = \frac{4}{3} \]Note: The provided answer key indicated 'Impossible', but the expression is a perfect square of 4/3 (or 1 1/3). I have corrected the options to include the mathematically accurate result of 4/3.

The 'tonne' (also known as a metric ton) is a unit of mass in the metric system. One tonne is defined as being equal to exactly 1,000 kilograms.
To find the number of kilograms in ten tonnes, we use the following calculation:\[ 1 \text{ tonne} = 1,000 \text{ kg} \]\[ 10 \text{ tonnes} = 10 \times 1,000 \text{ kg} \]\[ 10 \text{ tonnes} = 10,000 \text{ kg} \]This conversion is standard in international trade, engineering, and science.

To solve this problem, we first find the value of \( 2x \) from the given equation and then substitute it into the second expression.
Step 1: Solve for \( 2x \) in the first equation:\[ 2x + 5 = 11 \]\[ 2x = 11 - 5 \]\[ 2x = 6 \]Step 2: Substitute the value of \( 2x \) into the expression \( 2x - 5 \):\[ 6 - 5 = 1 \]Therefore, the value of the expression is 1.

We are given the ratio:\[ \frac{a}{b} = 2 \]To find the value of \( \frac{4b}{a} \), we first find the reciprocal of the given ratio:\[ \frac{b}{a} = \frac{1}{2} \]Now, we multiply this result by 4 as required by the expression:\[ 4 \times \left(\frac{b}{a}\right) = 4 \times \frac{1}{2} = 2 \]Thus, the value of the expression is 2.

This is a simple direct proportion problem. First, calculate the cost of a single apple:\[ \text{Cost per apple} = \frac{4}{8} = \text{₦}0.5 \]Now, multiply the unit cost by the required quantity (9 apples):\[ 9 \times 0.5 = \text{₦}4.5 \]Therefore, 9 apples will cost ₦4.5.