Reminders PRoblem

[ashg84]

Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the reminders?

1) The range of the seven reminders is 6
2) The seven numbers selected are consecutive integers.

IMO - D but OA is B, Please explain..

[Anurag@Gurome]

Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the reminders?

1) The range of the seven reminders is 6
2) The seven numbers selected are consecutive integers.

IMO - D but OA is B, Please explain..

We know that remainder is always non-negative integer less than the divisor, 0 ≤ r < d.
Here divisor = 7, so 0 ≤ r < 7
So, when any integer is divided by 7, then remainder can be 0, 1, 2, 3, 4, 5, or 6, which means 7 values in all.

(1) The range of the seven reminders is 6.
If 7 numbers are 1, 2, 3, 4, 5, 6, 7
Remainder = 1, 2, 3, 4, 5, 6, 0 (range = 6), which implies sum of remainders = 21

If 7 numbers are 7, 14, 21, 28, 35, 42, and 6
Remainder = 0, 0, 0, 0, 0, 0, 6 (range = 6), which implies sum of remainders = 6

No definite answer; NOT sufficient.

(2) The seven numbers selected are consecutive integers.
If 7 numbers are 1, 2, 3, 4, 5, 6, 7
Remainder = 1, 2, 3, 4, 5, 6, 0 (range = 6), which implies sum of remainders = 21

If 7 numbers are 7, 8, 9, 10, 11, 12, 13
Remainder = 0, 1, 2, 3, 4, 5, 6 (range = 6), which implies sum of remainders = 21

So, for any set of 7 consecutive integers, when the integers are divided by 7 the sum of remainders is always 21; SUFFICIENT.

The correct answer is B.

[ashg84]

Oh my God, It was such big reading error..

I read Option 1 as Range of numbers as 6, so i for this to happen, nmbers need to be consecutive and hence i picked this choice

I always make mistakes in reading the question.. Don't know how can i avoid such Silly Mistakes..

Thanks for the reply..

Seven different numbers are selected from the integers 1 to 100, and each number is divided by 7. What is the sum of the reminders?

1) The range of the seven reminders is 6
2) The seven numbers selected are consecutive integers.

IMO - D but OA is B, Please explain..

We know that remainder is always non-negative integer less than the divisor, 0 ≤ r < d.
Here divisor = 7, so 0 ≤ r < 7
So, when any integer is divided by 7, then remainder can be 0, 1, 2, 3, 4, 5, or 6, which means 7 values in all.

(1) The range of the seven reminders is 6.
If 7 numbers are 1, 2, 3, 4, 5, 6, 7
Remainder = 1, 2, 3, 4, 5, 6, 0 (range = 6), which implies sum of remainders = 21

If 7 numbers are 7, 14, 21, 28, 35, 42, and 6
Remainder = 0, 0, 0, 0, 0, 0, 6 (range = 6), which implies sum of remainders = 6

No definite answer; NOT sufficient.

(2) The seven numbers selected are consecutive integers.
If 7 numbers are 1, 2, 3, 4, 5, 6, 7
Remainder = 1, 2, 3, 4, 5, 6, 0 (range = 6), which implies sum of remainders = 21

If 7 numbers are 7, 8, 9, 10, 11, 12, 13
Remainder = 0, 1, 2, 3, 4, 5, 6 (range = 6), which implies sum of remainders = 21

So, for any set of 7 consecutive integers, when the integers are divided by 7 the sum of remainders is always 21; SUFFICIENT.

The correct answer is B.