Practice HAT questions with answers and explanations.
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The number of arrangements of 5 distinct objects is 5!.
Thus, 5! = 120.
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Use inclusion-exclusion: 80 + 60 - 20.
This gives 120 people who prefer at least one.
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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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There are 4 choices for the first digit, then 3, then 2.
Thus, 4 × 3 × 2 = 24.
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Total expenses are Rs. 100,000.
Salaries are Rs. 50,000, which is 50% of the total.
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There are 5 letters with L repeated twice and E repeated twice.
Distinct arrangements = 5!/(2!2!) = 30.
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A 76 average over 5 tests requires 380 total marks.
The first four total 300, so 80 more marks are needed.
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The sum is 40 and there are 5 values.
The mean is 40 ÷ 5 = 8.
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The decrease is 65 units.
Since 65/650 × 100 = 10%, the decrease is 10%.
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The median is the middle value in ordered data.
The third of five values is 9.
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The total population is 100,000.
The largest town has 45,000, so the fraction is 45/100 = 9/20.
