Practice NAT Quantitative Reasoning questions with answers and explanations.
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Substitute x = 5 into the function.
Then f(5) = 2(5) + 1 = 11.
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The three interior angles of every Euclidean triangle sum to 180°.
This is a fundamental angle property.
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Triangle angles sum to 180°.
The third angle is 180° - 45° - 65° = 70°.
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The discriminant is b² - 4ac.
Here it is 4² - 4(1)(1) = 16 - 4 = 12.
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All three angles are equal and their sum is 180°.
Therefore, each angle is 180° ÷ 3 = 60°.
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A zero discriminant makes the square-root term in the formula zero.
Both solutions therefore coincide.
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The path forms a right triangle with legs 5 and 12.
By Pythagoras, distance is √(25 + 144) = 13 km.
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The first part takes 2 hours and the second takes 1 hour.
The total travel time is 3 hours.
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The speed is 90 × 5/18 = 25 m/s, so total distance is 25 × 24 = 600 m.
Subtracting the train length gives a bridge length of 400 m.
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Downwind speed is 300 km/h and upwind speed is 200 km/h.
Wind speed is half their difference: 50 km/h.
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Subtract 7 from both sides of the equation.
This gives x = 19 - 7 = 12.
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Divide both sides by the coefficient 3.
Thus, x = 27 ÷ 3 = 9.
