Practice HAT Quantitative Reasoning questions with answers and explanations.
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Circumference is 2πr.
Thus, 2 × 22/7 × 7 = 44 cm.
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Circle area is πr².
Thus, 22/7 × 49 = 154 cm².
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A 90° arc is one quarter of the circumference.
The circumference is 88 cm, so the arc is 22 cm.
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Sector area is angle/360 × πr².
Thus, 60/360 × 36π = 6π cm².
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By Pythagoras, c² = 6² + 8² = 100.
Thus, c = 10 cm.
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Alternate interior angles formed by parallel lines are equal.
Thus, the matching angle is 65°.
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For a right triangle, the square of the longest side equals the sum of the other squares.
Here, 5² + 12² = 13².
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Complementary angles sum to 90°.
Thus, 90° - 38° = 52°.
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An exterior angle equals the sum of the two remote interior angles.
It is supplementary to the adjacent interior angle.
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Supplementary angles sum to 180°.
Thus, 180° - 125° = 55°.
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A quadrilateral can be divided into two triangles.
Thus, its angle sum is 2 × 180° = 360°.
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Vertically opposite angles are equal.
Therefore, the opposite angle is 72°.
