A number w with two digits to the right of the decimal point is multip

Question

A number w with two digits to the right of the decimal point is multiplied by the number n. How many decimal places are there in the product w*n?

(1) The number n has three digits to the right of the decimal point.
(2) Neither the hundredths digit in w nor the thousandths digit in n is a multiple of 10.

Source:  McGraw Conquering GMAT, page 174, question 8

IanStewart · Answer

If you take a number with three digits after the decimal, and multiply it by a number with two digits after the decimal, all kinds of things can happen. You might multiply 8/25 = 0.32 by 25/8 = 3.125. Then the product is 1, and you have zero digits after the decimal. Or you might multiply 1/100 = 0.01 by 1/1000 = 0.001, and get 0.00001, and have five digits after the decimal, among other possibilities. Those examples both use both statements, so the answer is E.

Based on how they've written Statement 2 (which only says "the last digit after the decimal point in each of w and n is nonzero", since zero is the only digit that can be a multiple of ten), and based on the fact that "C" is their OA, I'm guessing they're trying to count zeros at the end of a decimal as if they're genuine digits. But that's mathematically nonsensical. The only way it even makes sense to talk about how many digits a number has after a decimal is if you ignore any zeros at the end, or else there's an infinite number of possible answers depending on how many zeros you decide to write down. The number 1.600 does not have three digits after the decimal, because if it does, it also has twenty-five if you choose to write it like this: 1.6000000000000000000000000. That number has one digit after the decimal, because it is the number 1.6.

Xin Cho · Answer

Thank you for the reply. I would post the official answer here, frankly the book does not offer one. It merely states the answer choice.

I was quite puzzled by the second statement as well. Even if we assume the answer choice is C, I wonder how can we arrive at the precise answer.

IanStewart · Answer

I thought about that too - I wondered what (incorrect) assumptions they might be making about how math works that could lead them to think C is the right answer here. At first I thought they must be counting any zeros at the end of the product wn (when you do long multiplication using the decimals w and n) as if they were genuine digits. But then there'd be no reason Statement 2 would be relevant; the answer would be A in that case.

I'd be wary about using a source with a question like this, and especially wary about using a source with no answer explanations.

Xin Cho · Answer

Thank you very much for the reply. I really appreciate it.

For most questions, there actually are answers. Frankly, not for this one. Given that McGraw seems to be one of the general providers, I was hoping most of the prompts would be reliable. I had a similar negative experience with Nova's GMAT prep course (book). Thus, it seems to me that unless it is an official material there are bound to be mistakes. Though some sources are more prone than others. Thus, I try to use 3rd party materials rather as a supplement than a core material.

unraveled · Answer

I marked Answer (E).
Here's my reasoning.

Question gives 'w' as number with two digits to the right of decimal. It can be anything.

Statement 1) Number 'n' has three digits to the right of decimal. If 'w' has odd digits at the extreme right in the digits after decimal and 'n' has any digit other than '0' at the extreme right in the digits after decimal, the decimal places obtained for number 'w*n' are five OR if 'w' has even digits(excluding '0') at the extreme right in the digits after decimal and 'n' has '5' as last digit at the extreme right after decimal the decimal places obtained for number 'w*n' are less than five. INSUFFICIENT.
 
Statement 2) 'w' has hundredths digit as a non-multiple of 10 i.e. it can be anything other than '0'. AND 'n' has its thousandths digit as a non-multiple of 10 i.e. it can be anything other than '0' but we don't know how many digits are there after decimal in number 'n'. Thus it can have various answer so 
INSUFFICIENT.

Together 1) and 2) we know that 'n' has three digits after decimals and third digit is non-multiple of '10' i.e. it can be anything other than '0'. But we don't know the extreme right digit of the number 'w' since if its '2' and number 'n' has third digit as '5' then number 'w*n' would have different decimal places than if 'w' has third digit other than '2' and 'n' has third digit other then '5'. 
INSUFFICIENT.

IanStewart · Answer

It occurs to me now that they probably want Statement 2 to say that the final digits of n and w are not  divisors  of 10, rather than "multiples".

Any large book is likely to contain a minor error or two (I've found mistakes in official books too), but there's a difference between a typo that doesn't affect how well you understand the content and a fundamental mathematical error. My books don't contain any mathematical errors (nor any typos I'm aware of), and that is hopefully also true of the books from the most reputable GMAT publishers. You'll find the most realistic practice questions in official books, so relying on them for problems is a good idea, but the official books generally don't do a good job of explain concepts or methods, so you will likely find it worthwhile to find books that do that well.

A number w with two digits to the right of the decimal point is multip

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