Seven different numbers are selected from the....

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factor26: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sun Mar 13, 2011 12:42 pm

Seven different numbers are selected from the....

by factor26 » Wed Dec 07, 2011 6:26 pm

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.

I'm absolutly stuck on this question ... OG answer is B ... insight on this question is much appreciated ... thanks all

Quote

Source: Beat The GMAT — Data Sufficiency | Wed Dec 07, 2011 6:26 pm

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Dec 07, 2011 6:45 pm

factor26 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.

I'm absolutly stuck on this question ... OG answer is B ... insight on this question is much appreciated ... thanks all

(1) Let us assume that the numbers are 1, 2, 3, 4, 5, 6, 7. If we divide these by 7, then the remainders are 3, 6, 5, 2, 1, 4, and 0, whose sum is 21.

In case the numbers are 7, 14, 21, 28, 35, 42, 49, then the remainders are 0, so the sum of remainders is also 0.

We do not get a definite answer; NOT sufficient.

(2) Let us assume that the 1st number is x.
Then the 7 numbers will be x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6
Sum of the remainders = (x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6)/7 = (7x + 21)/7 = x + 3, which is fixed.
So, (2) is SUFFICIENT.

The correct answer is B.

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