Is m+z>0?
1) m-3z >0?
2) 4z-m>0?
When I solved this using both statements together, I got 3z<m<4z. But this means m = 3.5z (say)
If z is negative then m + z = 4.5z which is negative
And if z is positive then m+z = 4.5z which is positive
What am I doing wrong?
Thanks
Inequality
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Statement 1: m > 3z.Is m+z > 0?
(1) m-3z > 0
(2) 4z-m > 0
m and z could both be positive, m and z could both be negative.
Insufficient.
Statement 2: m < 4z
m and z could both be positive, m and z could both be negative.
Insufficient.
Statements 1 and 2 combined:
Linking the inequalities, we get:
3z < m < 4z
3z < 4z.
0 < z.
Since z is positive, we know that m -- which is between 3z and 4z -- also is positive.
Thus, m+z > 0.
Sufficient.
The correct answer is C.
The statement in red is not possible.Nijo wrote:Is m+z>0?
1) m-3z >0?
2) 4z-m>0?
When I solved this using both statements together, I got 3z<m<4z. But this means m = 3.5z (say)
If z is negative then m + z = 4.5z which is negative
And if z is positive then m+z = 4.5z which is positive
What am I doing wrong?
Thanks
As shown in my solution above, 3z < m < 4z implies that 0 < z.
Thus, z must be POSITIVE.
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Here's another way to handle the two statements combined....Is m+z>0
(1) m - 3z > 0
(2) 4z - m > 0
Target question: Is m + z > 0?
Statement 1: m - 3z > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: m = 4 and z = 1, in which case m + z is greater than 0
Case a: m = 4 and z = -10, in which case m + z is not greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 4z - m > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: m = 1 and z = 4, in which case m + z is greater than 0
Case a: m = -10 and z = 1, in which case m + z is not greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Rearrange statement 1 to get: -3z + m > 0
Statement 2: 4z - m > 0
Multiply both sides of -3z + m > 0 by 5 to get: -15z + 5m > 0
Multiply both sides of 4z - m > 0 by 4 to get: 16z - 4m > 0
Since both inequality signs are facing the same direction, we can ADD the two green inequalities to get: z + m > 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
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Target question: m + z > 0Is m + z > 0
(1) m - 3z > 0
(2) 4z - m > 0
Statement 1: m - 3z > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: m = 4 and z = 1, in which case m + z is greater than 0
Case a: m = 4 and z = -10, in which case m + z is not greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 4z - m > 0
There are several sets of numbers that meet this condition. Here are two:
Case a: m = 1 and z = 4, in which case m + z is greater than 0
Case a: m = -10 and z = 1, in which case m + z is not greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Rearrange statement 1 to get: -3z + m > 0
Statement 2: 4z - m > 0
Since both inequality signs are facing the same direction, we can add the two given inequalities to get: z > 0
In other words, z is positive.
If z is positive, then 3z is positive, and if 3z is positive then m must be positive (since we know that 3z < m)
If z and m are both positive, then m + z must be greater than 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
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CONCEPT:Is m + z > 0
(1) m - 3z > 0
(2) 4z - m > 0
You can only add inequalities when their signs are in the same direction:
If a>b and c>d (signs in same direction: > and >) --> a+c>b+d.
Example: 4<5 and 3<6 --> 4+3<5+6.
Question : Is m + z > 0 ? Answer must be in the form of YES or NO
Statement 1) m - 3z > 0
m > 3z
Both m and z can be positive or Negative. Hence, INSUFFICIENT
Statement 2) 4z - m > 0
4z > m
Both m and z can be positive or Negative. Hence, INSUFFICIENT
Combining the two statements
Adding the two statements
(M -3Z) + (4Z -M) > 0
i.e. Z>0
Therefore m also must be Positive [as m>3z]
i.e. M+Z > 0
SUFFICIENT
Answer: Option C
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