Practice Pakistan questions with answers and explanations.
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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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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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The units digits of powers of 7 cycle as 7, 9, 3, 1.
The fourth power therefore ends in 1.
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The greatest common divisor of 18 and 24 is 6.
Dividing both terms by 6 gives 3/4.
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Convert 2/3 to sixths: 2/3 = 4/6.
Then 4/6 + 1/6 = 5/6.
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Convert 1/4 to 2/8.
Then 7/8 - 2/8 = 5/8.
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Multiply numerators and denominators, then simplify.
(3 × 10)/(5 × 9) = 30/45 = 2/3.
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Dividing by a fraction means multiplying by its reciprocal.
Thus, 4/7 × 3/2 = 12/14 = 6/7.
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The positive factors of 16 are 1, 2, 4, 8, and 16.
Therefore, it has 5 positive factors.
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Dividing 84 by primes gives 84 = 2 × 2 × 3 × 7.
This is 2² × 3 × 7.
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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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A prime number has exactly two positive factors: 1 and itself.
The number 29 is not divisible by 2, 3, or 5.
