Ok here is the real big deal of exams such as GRE or GMAT
They apparently test your skills at math or verbal, to know how to read a sentence. However, the real goal is your reasoning skills

Specifically to hit your target in the most efficient way in the less time possible.

In this case, such as Brent showed you, the upfront approach is more difficult.

Instead, testing the answer choices is the best way this time. GRE reward you if you pick the answer correct NOT the most beautiful elegant way to nail it.

Suppose you are the luckiest man in the world and you do zero on math. However, you pick all the questions correctly. For The GRE is fine. Why ?' because your method is efficient and fast even though it is just lucky

Now, to know which approach to take to solve a question instead to go one way rather switch to the fastest lane when you meet an obstacle is probable the most relevant skill you do have to have for the GRE

Hope this helps

When it comes to remainder questions, it's probably best not to treat them as fractions.

For example, notice that 24 divided by 16 leaves a remainder of 8.
However, if you treat this as a fraction (24/16) and then simplify it you get 3/2, in which case 3 divided 2 leaves a remainder of 1.

As you can see, dividing both values by 8, result in a remainder that 1/8 of the original remainder.

In fact, we can say that dividing both values by k, means the NEW remainder is 1/k the original remainder.

Cheers,
Brent

The number equals to:

9a + 5
18b + 14
24c +20

where a,b and c are integer.

We can note that the greatest value is 24c + 20, we can use c=1 and the number is 44 but this doesn't meet the other conditions. If we use c=2m the number is 68 and this value meets the other conditions, so the less value is 68.

We need to find What is the smallest positive integer which when divided by 9, 18, 24 leaves a remainder of 5, 14 and 20 respectively

Number divided by 9 gives 5 remainder => Number - 5 should be a multiple of 9
Number divided by 18 gives 14 remainder => Number - 14 should be a multiple of 18
Number divided by 24 gives 20 remainder => Number - 20 should be a multiple of 24

Let's check each options based on the above conditions and check which one satisfies all of them.

A. 34
34 - 5 = 29 => NOT DIVISIBLE by 9 => NOT POSSIBLE

B. 52
52 - 5 = 47 => NOT DIVISIBLE by 9 => NOT POSSIBLE

C. 62
62 - 5 = 57 => NOT DIVISIBLE by 9 => NOT POSSIBLE

D. 68
68 - 5 = 63 => DIVISIBLE by 9
68 - 14 = 54 => DIVISIBLE by 18
68 - 20 = 48 => DIVISIBLE by 24 => POSSIBLE
We don't need to check further, but I am checking to complete the solution.

E. 72
72 - 5 = 67 => NOT DIVISIBLE by 9 => NOT POSSIBLE

So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Remainders