Practice HAT questions with answers and explanations.
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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 total is 400 people.
Males represent 240/400 × 100 = 60%.
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The increase is 25 on a base of 125.
Thus, 25/125 × 100 = 20%.
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The two largest shares are 35% and 25%.
Their combined share is 60%.
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The digit sum of 568 is 19, which leaves remainder 1 when divided by 9.
Adding 8 makes the digit sum 27, divisible by 9.
