Mathematical And Numerical Reasoning 2026 Njfp Job

In geometry, polygons are named according to the number of sides they possess. A quadrilateral has 4 sides, a hexagon has 6 sides, and an octagon has 8 sides. The term 'nonagon' is derived from the Latin word 'nonus' (ninth) and the Greek 'gonon' (angle). Thus, a nonagon is a polygon that consists of exactly nine straight sides and nine vertices.

A fair die has six faces, numbered 1, 2, 3, 4, 5, and 6. The total number of possible outcomes in a single toss is 6.
The odd numbers on a die are 1, 3, and 5. This gives a total of 3 favourable outcomes. The probability \( P \) is calculated using the formula:\[ P(\text{odd}) = \frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}} \]\[ P(\text{odd}) = \frac{3}{6} \]\[ P(\text{odd}) = \frac{1}{2} \]

To find the value of \( x \), we express the given ratio as an equation involving fractions:\[ \frac{2x}{x + 1} = \frac{3}{2} \]By cross-multiplying the terms, we get:\[ 2(2x) = 3(x + 1) \]\[ 4x = 3x + 3 \]Subtracting \( 3x \) from both sides of the equation to isolate \( x \):\[ 4x - 3x = 3 \]\[ x = 3 \]

To solve this, we must first determine the current day. If tomorrow is Sunday, it means that 'Today' is Saturday. To find out what 'Yesterday' was, we count one day back from Saturday. One day before Saturday is Friday. Therefore, if tomorrow is Sunday, yesterday was Friday.

The English spelling of numbers can sometimes be confusing, particularly with the transition from 'four' to 'forty'. While '40' is spelled 'forty' (dropping the 'u'), the number '14' retains the 'u' from the base number 'four'. Thus, the correct orthographic representation is 'Fourteen'. 'Fourth' refers to an ordinal position (4th), and 'Forteen' is a common misspelling.

Angles are classified based on their degree measurements: * Acute angle: Less than 90°. * Right angle: Exactly 90°. * Obtuse angle: Greater than 90° but less than 180°. * Straight angle: Exactly 180°. * Reflex angle: Greater than 180° but less than 360°.

Average speed is defined as the total distance travelled divided by the total time taken.\[ \text{Total Distance} = (d_1 + d_2) \]\[ d_1 = \text{speed}_1 \times \text{time}_1 = x \times 1 = x \text{ km} \]\[ d_2 = \text{speed}_2 \times \text{time}_2 = y \times 2 = 2y \text{ km} \]\[ \text{Total Distance} = x + 2y \text{ km} \]\[ \text{Total Time} = 1 \text{ hour} + 2 \text{ hours} = 3 \text{ hours} \]\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]\[ \text{Average Speed} = \frac{x + 2y}{3} \text{ km/h} \]

To solve this problem, we represent the ages of the three men as \( 3x \), \( 4x \), and \( 5x \) based on the given ratio. The youngest man is \( 3x \) and the oldest is \( 5x \).
The problem states that the difference between the oldest and youngest is 18 years:\[ 5x - 3x = 18 \]\[ 2x = 18 \]\[ x = 9 \]Now, we find the individual ages:\[ \text{Youngest} = 3(9) = 27 \]\[ \text{Middle} = 4(9) = 36 \]\[ \text{Oldest} = 5(9) = 45 \]The sum of their ages is calculated as follows:\[ \text{Sum} = 27 + 36 + 45 = 108 \text{ years} \]

In geometry, angles are classified according to their magnitude. An angle that measures exactly 90° is called a right angle. Any angle that measures more than 0° but less than 90° is defined as an acute angle. Options such as 'greater than 90 degrees but less than 180 degrees' describe an obtuse angle, while 'greater than 180 degrees but less than 360 degrees' refers to a reflex angle.

To identify the smallest fraction, we can convert each into a decimal for direct comparison:\[ 3/4 = 0.75 \]\[ 6/7 \approx 0.857 \]\[ 1/2 = 0.50 \]\[ 6/5 = 1.20 \]Comparing the decimal values \( 0.75 \), \( 0.857 \), \( 0.50 \), and \( 1.20 \), it is clear that 0.50 is the lowest value. Therefore, 1/2 is the smallest fraction in the set.