The arithmetic mean (average) of a set of 5 numbers is an integer A. Upon being divided by 180, A leaves a remainder of 30. If two of the numbers in the set are decreased by 120 and 180 units respectively, which of the following statements must be true about the new arithmetic mean B of the set?
I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180.
II. When B is divided by 60, the remainder is 30.
III. The value of the decimal digits is greater in the number A/90 than in the number B/90. Options:
A) I only	B) II only	C) III only	D) I and II only	E) I and III only
A = 180n + 30 (n is any non negative integer)   A is 30/210/390...   If the total sum is reduced by 300, with 5 numbers, the average will go down by 60.   B = A - 60   I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180.   B = 180n + 30 - 60 = 180n - 30 = 180(n-1) + 150   Not True. Remainder is 150   II. When B is divided by 60, the remainder is 30.   B = 180(n-1) + 150 = 180(n-1) + 120 + 30   True. B leaves remainder 30 on division by 60.   III. The value of the decimal digits is greater in the number A/90 than in the number B/90.   The decimal part of A is 30/90 = .333   The decimal part of B will be obtained by 150/90 = (90 + 60)/90 =&gt; 60/90 = .666   Not True.   Answer (II only)
<result>B</result>
The arithmetic mean (average) of a set of 5 numbers is an integer A. Upon being divided by 180, A leaves a remainder of 30. If two of the numbers in the set are decreased by 120 and 180 units respectively, which of the following statements must be true about the new arithmetic mean B of the set?
I. The remainder that B leaves upon division by 180 is less than the remainder that A leaves upon division by 180.
II. When B is divided by 60, the remainder is 30.
III. The value of the decimal digits is greater in the number A/90 than in the number B/90.