Is m + z > 0 ?
(1) m - 3z > 0
(2) 4z - m > 0
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.
条件1:m - 3z > 0可以变形为:m+z-z-3z>0 即 m+z>4z,由于不知道z的正负,所以不能确定m+z是否>0.单独不充分;
条件2:4z - m > 0可以变形为:4z-(m+z)+z>0即m+z<5z,同样无法确定正负,单独不充分;
条件1+2:首先将m - 3z > 0和4z - m > 0两个式子相加,得到z>0,由于由上面的两个式子得到m+z>4z,得到m+z>0.充分。
m-3z》0 加上 4z-m》0 得出z》0,z都大于0了,m肯定大于0,所以m+z大于0
(1) m - 3z > 0
(2) 4z - m > 0
1+2 z>0
条件(1)和(2)得出,4z>m>3z,即:4z>3z, 可否得出 Z>0 ? 故,得出 z+m 必定 大于0?
mark。不等式变形及大小比较。
条件1+2:首先将m - 3z > 0和4z - m > 0两个式子相加,得到z>0,由于由上面的两个式子得到m+z>4z,得到m+z>0.充分。
1+2, z>0, 再由1, m>z>0 , suf
(1) m - 3z > 0. Insufficient on its own.
(2) 4z - m > 0. Insufficient on its own.
(1)+(2) Remember we can add inequalities with the sign in the same direction --> \(m-3z+4z-m>0\) --> \(z>0\), so \(z\) is positive. From (1) \(m>3z=positive\), so \(m\) is positive too (\(m\) is more than some positive number \(3z\), so it's positive) --> \(m+z=positive+positive>0\). Sufficient.
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(1)+(2):3z0,z+m>0.
两个条件结合,3z