BTGmoderatorDC wrote:Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the remainders?
(1) The range of the seven remainders is 6.
(2) The seven numbers selected are consecutive integers.
OA B
Source: Official Guide
Let's take each statement one by one.
(1) The range of the seven remainders is 6.
Case 1: Say the seven different numbers are 3, 4, 5, 6, 7, 8, and 9.
Reminders of above numbers, when divided by 7, are 3, 4. 5, 6, 0, 1, and 2. We see that the range of the seven remainders = 6 - 0 = 6. Sum of remainders = 21.
Case 2: Say the seven different numbers are 3, 4, 5, 6, 7, 8, and
14.
Reminders of above numbers, when divided by 7, are 3, 4. 5, 6, 0, 1, and
0. We see that the range of the seven remainders = 6 - 0 = 6. Sum of remainders = 19.
No unique answer. Insufficient.
(2) The seven numbers selected are consecutive integers.
Case 1: Say the seven consecutive numbers are 3, 4, 5, 6, 7, 8, and 9.
Reminders of above numbers, when divided by 7, are 3, 4, 5, 6, 0, 1, and 2.Sum of remainders = 21.
Case 2: Say the seven consecutive numbers are 25, 26, 27, 28, 29, 30 and 31.
Reminders of above numbers, when divided by 7, are 4, 5, 6, 0, 1, 2, and 3. Sum of remainders = 21.
Unique answer. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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