Practice ECAT questions with answers and explanations.
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The square root is the number whose square equals 196.
Since 14 × 14 = 196, the answer is 14.
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The digit 7 is in the thousands place.
Therefore, its place value is 7 × 1,000 = 7,000.
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The cube root is the number that gives 729 when cubed.
Since 9³ = 729, the answer is 9.
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A prime number has exactly two positive factors: 1 and itself.
The number 29 is not divisible by 2, 3, or 5.
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The sequence increases by 3 each time.
Adding 3 to 11 gives 14.
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The common factors of 36 and 48 include 1, 2, 3, 4, 6, and 12.
The greatest of these is 12.
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The sum of the first n natural numbers is n(n + 1)/2.
For n = 10, the sum is 10 × 11 ÷ 2 = 55.
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Multiples of 8 are 8, 16, 24, and so on.
The first multiple also divisible by 12 is 24.
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The sum of the first n odd numbers equals n².
For n = 8, the sum is 8² = 64.
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A number is divisible by 9 when the sum of its digits is divisible by 9.
For 5,832, the digit sum is 18.
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The least common multiple of 3 and 4 is 12.
A number divisible by both must therefore be divisible by 12.
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Since 12 × 13 = 156, subtracting gives 157 - 156 = 1.
Thus, the remainder is 1.
