Answer is B. Here's my explanation.
1. Range is 6.
This statement is insufficient as you can have a range of numbers with six as follows;
{0,0,0,0,0,1,6} or {0,3,4,4,5,5,6}
Range is the difference between the largest and smallest number but that doesn't say anything.
So now we're down to options B,C or E
2. Consecutive numbers.
Since we are choosing 7 consecutive numbers, one of it must be a multiple of 7. So, let's assume its the first number for convenience sake. You can draw a table as follows:
Number Reminder
x - 0
x+1 - 1
x+2 - 2
x+3 - 3
x+4 - 4
x+5 - 5
x+6 - 6
So now you can find out what's asked for.
Hence answer is B.
cebenez wrote:
Question 98 Data Sufficiency
Official GuideSeven 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.
Official Answer: B
But I think its E, let me tell you why.
(1) Range is 6, I believe when the range is 6, it means the numbers are consecutive. Can range be 6 if not consecutive, I do not think so.
Any set with a range of 6 starting with 3 would be have same sum of remainder but different sum of reminder if starting from 2 i.e for set 2 to 8 is different from set 3 to 9.
So -- Not sufficient.
(2) It says the set is consecutive numbers... Now we do not know the range.. but we know that any set of 7 consecutive numbers > 2 has to have a range of 6. So for the same reasons explained in (1) This is also not sufficient.
1 + 2 ) Together we still have the same info. What if the set starts with 2??? Remainders will be R5, R4, R3, R2, R1, R0, R1... right????
If it starts from 3 to 9... It would be R4, R3, R2, R1, R0, R1, R2
Sum of these remainders are different ... So I think E is the answer....but
MGMAT says its B.
MGMT says, (1) is insufficient... but (2) is sufficient because any 7 consecutive nos will have sum of remainders = 21
Can someone explain?