Practice NAT Mathematics questions with answers and explanations.
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At 3:00, the minute hand points at 12 and the hour hand at 3.
Three hour intervals correspond to 3 × 30° = 90°.
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At 6:00, the hands point in opposite directions.
Opposite rays form a straight angle of 180°.
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Adding the equations gives twice the larger number: 50 + 14 = 64.
Dividing by 2 gives 32.
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Dividing an inequality by a negative number reverses the sign.
Thus, x > -4.
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Let the son's age be x and father's age 3x.
Then 3x + 10 = 2(x + 10), giving x = 10.
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Absolute value gives distance from zero.
Both 7 and -7 are 7 units from zero.
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Let tens digit be a and units digit b; then a + b = 11 and 9(b - a) = 27.
So b - a = 3, giving a = 4 and b = 7.
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Set x - 3 equal to 5 and -5.
The resulting solutions are x = 8 and x = -2.
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Square the equation: x² + 2 + 1/x² = 25.
Subtracting 2 gives x² + 1/x² = 23.
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Use a² + b² = (a + b)² - 2ab.
Thus, 144 - 70 = 74.
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Add the geometric terms directly.
Their total is 31.
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The first term is 8 and common ratio is 1/2.
The sum is a/(1-r) = 8/(1/2) = 16.
