Question

Q1. Explain why 7 x 11 x 13 +13 and 7 x6x5 x 4 x 3 x 2 x 1 +5 are composite numbers.

Q2. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round
of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the
same point and at the same time, and go in the same direction. After how many minutes
will they meet again at the starting point?
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Answer 1

1. 7*11*13+13 here 7*11*13 is odd *odd in which it will give odd and 13 is an odd number.we know that odd + odd will give an even number and an even number which is greater than 2 is an composite number.

2.take lcm

18=2*3*3

12=2*2*3

=2*3*3*2

=36

therefore 36minutes

Answer 2

Answer:

Step-by-step explanation:

Q1.   7×11×13+13  and  7×6×5×4×3×2×1+5

 =13(7×11+1)  and   5(7×6×4×3×2×1+1)

 =13(77+1)    and    5(1008+1)

 =13×78       and    5×1009

⇒both the numbers have more then one factor so it's composite

Q2.  To find the required number of minutes

Let us find the LCM of 18 and 12

We have

18 => 2 × 3 × 3 = 2 × 3²

12.=> 2 × 2 × 3 = 2² × 3

LCM (18,12) => 2² × 3² = 36

After 36 minutes Sonia will be at the starting point after completing 2 rounds of the field and Ravi also be at same point after 3 rounds