Problem Solving

What is the last but one digit in the product of the first 75 natural numbers?

a.4 b.2 c.0 d.5

what is the last digit in the product of the first 75 even natural numbers?

a.5 b.7 c.9 d.none

It has to be zero as the product is a multiple of 100 as it contains 75/5+75/25 = 15+3 = 18 zeroes.

For the first one it's C and for the second one it's D I think.

Guys please let me know is this correct.

The answer for the second question is also zero and the option is none.

Can anyone please give a bit detailed explanation??? I am a bit weak in numbers...

kullayappayenugula wrote:What is the last but one digit in the product of the first 75 natural numbers?

a.4 b.2 c.0 d.5

what is the last digit in the product of the first 75 even natural numbers?

a.5 b.7 c.9 d.none

Hi,

I'm happy to explain the concepts, but first it's important to note that the wording of both questions is definitely NOT what you'd see on the GMAT. Also, there are only 4 answer choices and, of course, on the real GMAT there will be 5. Please always post the source of your questions so that serious GMAT studiers know whether or not to pay attention (my advice in this case would be not to do so, although they illustrate some good concepts).

In the first question, we're asked to find the "last but one digit" of a number. In regular math vocabulary, we'd call that the tens digit. The GMAT will never use a phrase like "last but one digit".

Since the number is the product of the first 75 positive integers (natural numbers = counting numbers = positive integers), i.e. 1*2*3*...*75 or, in other words, the value of 75!.

We can answer this question very quickly if we understand a couple of very simple concepts. First, every time you multiply by 10 you add a "0" to the end of a number. Second, when you multiply by a multiple of 10 you also add a "0".

Since 75! includes both 10 and 20, we can think of our product as:

(whole bunch of numbers)*10*20 = some giant number with at least 2 "0"s at the end. Since we only care about the second last digit, no further work is required: choose (C)0.

We can apply the exact same approach to the second question. The first 75 even positive integers includes 10, so we're definitely going to have a 0 at the end of this number as well. Note, "none" isn't the same as "0", another sign that this is a "defective" question.