Question

Ami and Ria are playing a game where one of them would pick up a card and the other would guess the number.
Ami picked up a card and read the rules to Ria which were:
1. It is an odd number
2. It is a composite number divisible by three different prime numbers.
Which of the following would be Ria's correct guess?

A: 30
B: 75
C: 189
D: 315

Answer 1

Answer:

The answer is 315 ( D )

Step-by-step explanation:

The answer is 315 because 30, 75, 315 are odd number. But they told the number is divisible by 3 different prime number.

But 30 is divisible by 10 which is a composite number. So 30 is wrong.

75 is divisible by 15 but it is composite number. So 75 is wrong.

189 is divisible by three prime numbers but it is even number. So it is wrong.

315 is a odd number and it is divisible by 3, 5 and 7

Hope it helped you.

Answer 2

Concept

A composite number is one which is completely divisible by numbers other than 1 and itself.

Given

Ami picked a card which has a number with the following properties-

1. It is an odd number

2. It is a composite number divisible by three different prime numbers.

Find

we need to find the number

Solution

We have 4 options,

30 , 75, 189, 315

out of these, 30 is immediately eliminated since it is not an odd number.

Now we take 75, its factors are 1, 3, 5, 15, 25 and 75.

Thus, it is only divisible by 2 prime numbers, 3 and 5 so it is not the number on the card.

Now the factors of 189 are 1, 3, 7, 9, 21, 27, 63, and 189

As we can see 189 is also divisible by only 2 prime numbers 3 and 7, thus it is not the correct number

Taking 315,

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105 and 315 are the factors of 315.

Thus, it is divisible by 3 prime numbers- 3, 5 and 7.

Therefore, Ria's correct guess would be 315.

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