Problem Solving

Which of the following are/is prime?

I. 143
II. 147
III. 149

(A) II only
(B) III only
(C) I & II
(D) I & III
(E) I, II, & III

The OA is B.

How can I find the prime number quickly?

VJesus12 wrote:Which of the following are/is prime?

I. 143
II. 147
III. 149

(A) II only
(B) III only
(C) I & II
(D) I & III
(E) I, II, & III

The OA is B.

How can I find the prime number quickly?

Break the numbers down into more manageable/recognizable values.

I: 143 = 130 + 13 --> clearly divisible by 13, as both 130 and 13 are multiples of 13, so 143 is not prime.
II: 147 --> 1 + 4 + 7 = 12. If the sum of the digits of the number is a multiple of 3, then the number itself is a multiple of 3. 147 is not prime.

Since we don't have an option of NONE, we don't even have to test III. It has to be prime. The answer is B

Which of the following are/is prime?

I. 143
II. 147
III. 149

(A) II only
(B) III only
(C) I & II
(D) I & III
(E) I, II, & III

The OA is B.

How can I find the prime number quickly?

Hi VJesus12,
Let's take a look at your question.

We are asked to find the prime number from the options given. We know that a prime number has only two divisors 1 and the number itself.
So to find if a number is a prime number or not we will check if it has any divisor other than 1 and the number itself.

We will look for two shortcuts to reach the solution.
Shortcut 1:
We will test the given numbers for the prime divisors only i.e. 2, 3, 5, 7, 11, 13, ...

Shortcut 2:
We will find the nearest perfect square to the number given. Find its square root and will limit testing till that number.
For example, for 143, the nearest perfect square is 144 and its square root is 12.
So we will limit the testing till 11 because 11 is the last prime number below 12.

It means we need to test 143 for 2, 3, 5, 7 and 11. If 143 is not divisible by any of these it will be a prime number.
Let's check 143.
143 is not divisible by 2.
143 is not divisible by 3.
143 is not divisible by 5.
143 is not divisible by 7
143 is divisible by 11.
Therefore, 143 is not a prime number.

Lets check 147 now.
Nearest perfect square is 169 and its square root is 13.
Therefore we will check 147 for 2, 3, 5, 7 and 11
147 is not divisible by 2.
147 is divisible by 3.
Therefore, 147 is not a prime number.

Let's check 149 now.
Nearest perfect square is 169 and its square root is 13.
Therefore we will check 149 for 2, 3, 5, 7 and 11
149 is not divisible by 2.
149 is not divisible by 3.
149 is not divisible by 5.
149 is not divisible by 7.
149 is not divisible by 11.
149 is not divisible by any of the prime number in the list.
Therefore, 149 is a prime number.

Therefore Option B is correct.

Hope it helps.
I am available if you'd like any follow up.

Piggybacking on David's answer, one neat way of finding a composite number is noticing that it consists of multiples of the same number glued together, so to speak. For example, say we have the number 28144977. We could illuminate that as 28144977, or four multiples of 7. That might not seem like much, but noticing that allows me to break the number down into

28144977 =
28000000 +
140000 +
4900 +
77

or

7 * (4000000 + 20000 + 700 + 11)

So the whole thing must divide by 7.

This won't help you find ANY composite number, but it's a neat trick nonetheless.