Practice HAT questions with answers and explanations.
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Since 12 × 13 = 156, subtracting gives 157 - 156 = 1.
Thus, the remainder is 1.
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Each match corresponds to a unique pair of teams.
The number of pairs is 6×5/2 = 15.
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Each handshake is a unique pair of people.
The number of pairs is 8×7/2 = 28.
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Order does not matter when selecting a committee.
The number of selections is 5 choose 2 = 10.
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The prizes are distinct, so order matters.
The number of assignments is 5×4×3 = 60.
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Every student must receive exactly one identical pen.
There is only one distinguishable final distribution.
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Let the son's age be x and the father's age 2x.
Then 3x = 54, so x = 18.
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Fame in acting does not establish expertise in nutrition science.
The endorsement is not reliable scientific evidence.
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An odd number of presses changes the initial state to the opposite state.
Since 17 is odd, the lamp is on.
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Ruling out alternative explanations strengthens the claim that training caused the decline.
The other facts do not address competing causes.
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Those liking at least one are 60 + 50 - 20 = 90.
Therefore, 100 - 90 = 10 like neither.
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More buses reduce congestion only if they replace some private-vehicle trips.
That behavioral change is necessary for the plan's logic.
