Yes, (4) is the answer. If you use 93 to divide by 42 you will also get a remainder of 9. 98 is a multiple of 7. Therefore, 98 - 93 = 5

Erm, I use 42 x 9 = 378, 378 + 9 =387, then I add each given answer to 387 and divide it by 7. I am not sure if I do the correct way.

You have only shown a specific case.

The reasoning is as follows for any number which has a remainder of 9 when divided by 42 :

①
Realise that 42 = 6 x 7

Dividing by 42 can be seen as dividing by 6 first then dividing 7. Or, dividing by 7 first then dividing by 6.

So if a number can be divided by 42, that means you have many groups of 42.

Since each group is made out of six '7's, the number is a multiple of 7 (i.e you have many groups of 7. So it can definitely be divided by 7 as well.

②
As the number leaves a remainder of 9 when divided by 42, that means the rest of it could be divided by 7.

So for this remainder, how to make it divisible by 7 ?

Add or subtract such that you get to a multiple of 7.

From the options given,

We choose 9 + 5 = 14
Then 14 ÷ 7 = 2

So now it can be divided by 7. Since the rest of the number is also divisible by 7, the entire number is divisible by 7.

We do not have to pick any specific number to figure this question out. What you need to master is the logic behind the divisibility

If the question had asked for ' which of the following can be subtracted from the number to make it a multiple of 7?' instead,

Option (2) would be the answer since 9 - 2 = 7, and 7 = 7 x 1

Wow, I will need time to digest this. But thank you so much for your detailed explanation.

Welcome