If zt < -3, we know that we have one positive term and one negative term. If we could prove that z is the negative term, then we could prove sufficiency.
S1) z < 9 doesn't tell us much. z could be between 0 and 9, making t the negative term, or z could be less than 0, making the positive term. z can fall on either side of 4, so S1 is insufficient.
S2) t < -4. We know that z must be the positive term, but we still don't know if it's less than or greater than 4. If t=-5, for instance, z could be 3 or 7 or any other number of possibilities. Insufficient.
When combined, there are still a lot of possibilities. The example used in S2 still applies, so we cannot answer.
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If zt < -3, is z < 4?
(1) z < 9
If z = 2, t = -5, then zt = -10, which is < -3. Here z < 4.
If z = 5, t = -5, then zt = -25, which is < -3. Here z > 4.
No definite answer; NOT sufficient.
(2) t < -4, we can take the same examples as in statement 1.
If z = 2, t = -5, then zt = -10, which is < -3. Here z < 4.
If z = 5, t = -5, then zt = -25, which is < -3. Here z > 4.
No definite answer; NOT sufficient.
Combining statements (1) and (2), we do not get any additional info; NOT sufficient.
The correct answer is E.
(1) z < 9
If z = 2, t = -5, then zt = -10, which is < -3. Here z < 4.
If z = 5, t = -5, then zt = -25, which is < -3. Here z > 4.
No definite answer; NOT sufficient.
(2) t < -4, we can take the same examples as in statement 1.
If z = 2, t = -5, then zt = -10, which is < -3. Here z < 4.
If z = 5, t = -5, then zt = -25, which is < -3. Here z > 4.
No definite answer; NOT sufficient.
Combining statements (1) and (2), we do not get any additional info; NOT sufficient.
The correct answer is E.
Anurag Mairal, Ph.D., MBA
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