How many Terminating Zeroes does 200 Have GMAT Problem Solving

Question: How many terminating zeroes does 200! have?

1. 40
2. 48
3. 49
4. 55
5. 64

“How many Terminating Zeroes does 200 Have GMAT Problem Solving”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

We will be solving the problem by giving examples. This is done for anyone who doesn't quite get why the math works the way that it does. Here are some examples to prove the point.

In order to determine the zeros candidates will need to know how many 2 and 5 200! contains. Here, 2 are much more than 5 since every second number is a multiple of 2. That is why when candidates find the multiples of 5, they will get the number of zeros.

If we do 200! = (200)(199)(198)(197)....(2)(1) so we know that it's a gigantic number.

The only reason why it will end in a "string" of 0s is because of all of the multiples of 5 involved.

Suppose we are multiplying integers, there are two ways to get a number that ends in a 0:
1) Is if we multiply a multiple of 5 by an even number
2) Is if we multiply a multiple of 10 by an integer.

(5)(2) = 10 so we get one 0 for every multiple of 5

However, 25 = (5)(5). It has TWO 5s in it, so there will be two 0s.

eg (25)(4) = 100

With 125 = (5)(5)(5), we have THREE 5s, so there will be three 0s.

eg (125)(8) = 1,000

So when we divide 200 by 5.....200/5 = 40 multiples of 5. SOME of those multiples of 5 are multiples of 25 (or 125) though. Each of those special cases has to be accounted for.

25, 50, 75, 100, 125, 150, 175 and 200 are all multiples of 25, so they each include one extra 0 (and 125 includes two extra 0s).

Hence, to find number of terminating zero's count the number of 5's, we will:
200/5 = 40
200/25 = 8
200/125 = 1

So we have 40 + 8 + 1 = 49 zeroes.

Correct Answer: C

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