sondenso
If x, y, and z are positive integers, what is the remainder when 100x + 10y + z is divided by 7 ?
(1) y = 6
(2) z = 3
We need to determine the remainder of (100x + 10y + z)/7. If we can determine the remainder of 100x/7, 10y/7, and z/7, then we can determine the remainder of (100x + 10y + z)/7.
Statement One Alone:y = 6
Using the information in statement one, we have:
(100x + 60 + z)/7
Although we know the remainder of 60/7 is 4 (note: 60/7 = 8 + 4/7), we still cannot determine the remainder of 100x/7 or z/7. Statement one alone is not sufficient to answer the question.
Statement Two Alone:z = 3
Using the information in statement two, we have:
(100x + 10y + 3)/7
Although we know the remainder of 3/7 is 3, we still cannot determine the remainder of 10y/7 or 100x/7.
Statement two alone is not sufficient to answer the question.
Statements One and Two Together:Using the information from statements one and two, we have:
(100x + 60 + 3)/7 = (100x + 63)/7
Although we know the remainder of 63/7 is 0, we still cannot determine the remainder of 100x/7. Different values of x might yield different remainders. For example, if x = 1, then the remainder of 100/7 is 2, since 100/7 = 14 + 2/7. However, if x = 2, then the remainder of 200/7 is 4, since 200/7 = 28 + 4/7.
Answer: E