maitri_mehta wrote:
Q32:
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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
The first thing to note here is that when a number is divided by 7, it can give one of the following numbers as remainder 0/1/2/3/4/5/6. There can be no other remainder.
Stmnt 1: This implies that one remainder has to be 0 and another has to be 6. That is how we will get the range (greatest - smallest) = 6-0 = 6. But we do not know anything about the other remainders. They could be 1,1,1,1,1 or 1,2,2,6,6 etc. Hence the sum of the remainders is not known.
Stmnt 2: Note that when I divide 10 by 7, I get 3 as remainder. When I divide 11 by 7, I get 4 as remainder. When I divide 12 by 7, I get 5 as remainder. So when I divide consecutive integers by the same number, the remainders will also be consecutive (I will get 3, 4, 5, 6 and then back to 0, 1, 2 as remainders). If the seven numbers selected are consecutive, the remainders will also be consecutive i.e. they will be 0, 1, 2, 3, 4, 5, 6 (or 3, 4, 5, 6, 0, 1, 2 ) or any such sequence. In any case, the sum of the remainders will be 0+1+2+3+4+5+6 = 21. Sufficient.
Answer (B)
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Karishma
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