116 practice questions covering Prime Time, organised into 1 topics.
116 questions include a written explanation.
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Consider these statements. (i) Every composite number is even. (ii) Every prime number greater than $2$ is odd. Which is or are correct?
AOnly (i)
BBoth (i) and (ii)
CNeither (i) nor (ii)
DOnly (ii)
Show answer and explanation
Correct answer: D - Only (ii)
Statement (i) is false, since $9$ and $15$ are odd composites. Statement (ii) is true, because any even number above $2$ has $2$ as an extra factor and cannot be prime. So only (ii) holds.
Q2
easy
Which of these is a common multiple of $3$ and $5$?
A$25$
B$35$
C$45$
D$21$
Show answer and explanation
Correct answer: C - $45$
Since $45 = 3 \times 15$ and $45 = 5 \times 9$, it is a multiple of both. The number $25$ is a multiple of $5$ only, $21$ of $3$ only, and $35$ of $5$ only.
Q3
medium
How do you test whether a number is divisible by $4$?
ACheck whether it is even
BCheck whether the number formed by its last two digits is divisible by $4$
CCheck whether its digit sum is divisible by $4$
DCheck whether its last digit is divisible by $4$
Show answer and explanation
Correct answer: B - Check whether the number formed by its last two digits is divisible by $4$
Since $100$ is divisible by $4$, only the last two digits matter, as in $316$ where $16$ is divisible by $4$. The last digit alone is not enough, the digit-sum test belongs to $3$ and $9$, and many even numbers such as $6$ are not divisible by $4$.
Q4
medium
How many numbers from $1$ to $50$ are divisible by $10$?
A$10$
B$50$
C$4$
D$5$
Show answer and explanation
Correct answer: D - $5$
The multiples of $10$ up to $50$ are $10, 20, 30, 40$ and $50$, giving $5$. Answering $10$ counts multiples of $5$, $4$ omits one of them, and $50$ counts every number.
Q5
medium
Given $20 = 2 \times 2 \times 5$ and $30 = 2 \times 3 \times 5$, what is their highest common factor?
A$5$
B$10$
C$60$
D$2$
Show answer and explanation
Correct answer: B - $10$
They share one $2$ and one $5$, so the highest common factor is $2 \times 5 = 10$. Answering $5$ or $2$ uses only part of the shared set, and $60$ is their lowest common multiple.
Q6
easy
Which pair of numbers is co-prime?
A$8$ and $12$
B$8$ and $15$
C$9$ and $15$
D$10$ and $25$
Show answer and explanation
Correct answer: B - $8$ and $15$
The factors of $8$ are $1, 2, 4, 8$ and of $15$ are $1, 3, 5, 15$, sharing only $1$. The pair $8$ and $12$ shares $4$, the pair $9$ and $15$ shares $3$, and $10$ and $25$ share $5$.
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