Xin Cho
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
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.