Seven integers are picked at random from the set of all

Question

Seven integers are picked at random from the set of all integers between 10 and 110, inclusive. If each of these integers is divided by 7 and the 7 remainders are all added together, what would be the sum of the 7 remainders?

(1) The range of the remainders is 6.
 
(2) The seven integers are consecutive. 

please explain

v1rok · Answer

(B)

ST1: You can pick 6 numbers divisible by 7 and 1 with a remainder 6, the range is going to be 6. Or you can pick 5 numbers divisible by 7, 1 with ren.1, and 1 with rem.6. The range is tsill 6. And so on. Son, NOT SUFF

ST2. Since numbers are consecutive, a combination of them must prduce the following remainders: 0, 1, 2, 3, 4, 5, 6. So, the sum is 21. /SUFF/

(B)

jamesrwright3 · Answer

Good explanation! 
I have a headache
I am not reading so well tonight

ps_dahiya · Answer

Should be B.

St1: Could pick up 6 divisible by 7 and one with a remainder of 6. OR all consecutive integers: INSUFF

St2: One is divisible by 7 and second will have 1 remainder and third 2 remainder and so on. Sum = 0+1+2+3+4+5+6 = 21: SUFF

heman · Answer

(1) range of remainder = 6
Highest remainder = 6, lowest remainder = 0
#s 14,15,16,17,18,19,20
Sum of Remainders = 0+1+2+3+4+5+6 = 21

#s are 14,15,16,17,18,20,27
Sum of remainders = 0+1+2+3+4+6+6 = 22

BCE

(2) Ints are 10,11,12,13,14,15,16
Sum of remainders = 3+4+5+6+0+1+2=21
Sum will always be 21

Hence B

Heman

Seven integers are picked at random from the set of all

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