Math - data sufficiency's question

2008-10-23 8:45 pm

Is the largest of seven consecutive integers an odd number?

(1) The product of the integers is even.
(2) The sum of the integers is zero.

Statement(1)ALONE is sufficient, but statement (2) ALONE is not sufficient.
Statement (2)ALONE is sufficient, but statement 1)ALONE is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

如題，問-
1) 個題目問咩?是否問最大的7個連續數? e.g. 在1234567，7是the largest of seven consecutive integers number?
2) 請解釋答案。

Thanks!

回答 (1)

Danny

2008-10-23 9:47 pm

✔ 最佳答案

答案: Statement (2)ALONE is sufficient, but statement (1)ALONE is not sufficient.

舉例2,3,4,5,6,7,8
相乘為40,320, 係商數 (符合(1))
但最大既數字係8, 唔係單數. 所以statement (1)ALONE 並不足夠.

如符合(2), The sum of the integers is zero, 數列左邊同右邊之和要抵銷, 中間既數字一定係0,
Proof:
設中間既數字係a, 數列為a-3,a-2,a-1,a,a+1,a+2,a+3.
和為 (a-3)+(a-2)+(a-1)+a+(a+1)+(a+2)+(a+3)=0
7a = 0
a = 0
所以數列只能是 -3,-2,-1,0,1,2,3.
最大既數字係3, 係單數. 所以statement (2)ALONE 已經足夠.

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