Practice ECAT questions with answers and explanations.
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Absolute value gives distance from zero.
Both 7 and -7 are 7 units from zero.
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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.
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For ax² + bx + c = 0, the sum of roots is -b/a.
Here, -(-9)/1 = 9.
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For ax² + bx + c = 0, the product of roots is c/a.
Here, 20/1 = 20.
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Selection without order uses combinations.
5C2 = 5 × 4 ÷ 2 = 10.
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The total production is 210 units.
Dividing by 4 gives 52.5 units.
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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.
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There are 4 choices for the first digit, then 3, then 2.
Thus, 4 × 3 × 2 = 24.
