If zt < -3, is z < 4 ?
(1) z < 9
(2) t < -4
OA is E
How would you approach ?
Inequalities If zt < -3, is z < 4
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- sachin_yadav
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Target question: Is z < 4 ?sachin_yadav wrote:If zt < -3, is z < 4 ?
(1) z < 9
(2) t < -4
Given: zt < -3
Statement 1: z < 9
Since statement 1 does not FEEL sufficient to me (because we're given information about only 1 value), I'm going to TEST values of z and t (values that satisfy the given conditions).
Case a: t = -5 and z = 1, in which case z IS less than 4
Case b: t = -5 and z = 5, in which case z is NOT less than 4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: t < -4
This statement does not FEEL sufficient either, so let's test some values.
Case a: t = -5 and z = 1, in which case z IS less than 4
Case b: t = -5 and z = 5, in which case z is NOT less than 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Notice that, when testing values, I used values that satisfied BOTH statements.
So, COMBINED, the two statements yield conflicting answers to the target question:
Case a: t = -5 and z = 1, in which case z IS less than 4
Case b: t = -5 and z = 5, in which case z is NOT less than 4
Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
Cheers,
Brent
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S1 tells us z < 9, but we could still have z = 3 or z = 5; NOT SUFFICIENT.
S2 tells us t < 0, so we can divide both sides by t and get z > -3/t. (t's being negative makes the sign switch.) This isn't helpful either: if t = -5, we have z > 3/5; if t = -6, we have z > 3/6, etc. So z is positive, but not necessarily less than 4; NOT SUFFICIENT.
S1+S2 tells us that -3/t < z < 9. We're still in the same jam we were in with just S2 -- if t = -5, we have 3/5 < z < 9; if t = -6, we have 3/6 < z < 9, etc. -- except now we have a ceiling (z < 9). That ceiling is higher than the one we're asked about (z < 4), though, so NOT SUFFICIENT.
S2 tells us t < 0, so we can divide both sides by t and get z > -3/t. (t's being negative makes the sign switch.) This isn't helpful either: if t = -5, we have z > 3/5; if t = -6, we have z > 3/6, etc. So z is positive, but not necessarily less than 4; NOT SUFFICIENT.
S1+S2 tells us that -3/t < z < 9. We're still in the same jam we were in with just S2 -- if t = -5, we have 3/5 < z < 9; if t = -6, we have 3/6 < z < 9, etc. -- except now we have a ceiling (z < 9). That ceiling is higher than the one we're asked about (z < 4), though, so NOT SUFFICIENT.
I think the answer is B and this is my approach:
In the question we know that zt<-3 which means either z or t is negative and the other is positive
Statement 2 mentions that t<-4 which means that t is always negative and so we know that z is positive here.
For zt<-3 z MUST be positive and less than 4 as t is less than -4
so Statement 2 is enough.
What do you think guys wrong with this approach?
Thanks
In the question we know that zt<-3 which means either z or t is negative and the other is positive
Statement 2 mentions that t<-4 which means that t is always negative and so we know that z is positive here.
For zt<-3 z MUST be positive and less than 4 as t is less than -4
so Statement 2 is enough.
What do you think guys wrong with this approach?
Thanks
- DavidG@VeritasPrep
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Here's where you went wrong: For zt<-3 z MUST be positive and less than 4 as t is less than -4Zoser wrote:I think the answer is B and this is my approach:
In the question we know that zt<-3 which means either z or t is negative and the other is positive
Statement 2 mentions that t<-4 which means that t is always negative and so we know that z is positive here.
For zt<-3 z MUST be positive and less than 4 as t is less than -4
so Statement 2 is enough.
What do you think guys wrong with this approach?
Thanks
If t = -5 ad z = 10, tz would be less than -3, right?
[/quote]Here's where you went wrong: For zt<-3 z MUST be positive and less than 4 as t is less than -4
If t = -5 ad z = 10, tz would be less than -3, right?
If t = -5 ad z = 10, tz would be less than -3, right?
You are right! Most certainly, too much studying start affecting my basic math skills.
Thanks anyways
- DavidG@VeritasPrep
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Here's where you went wrong: For zt<-3 z MUST be positive and less than 4 as t is less than -4Zoser wrote:
If t = -5 ad z = 10, tz would be less than -3, right?
[/quote]
You are right! Most certainly, too much studying start affecting my basic math skills.
Thanks anyways
You're in good company Just remember that the killer on the GMAT isn't the high-level stuff. It's the careless mistakes and the questions engineered to look much harder than they are.
Thank you! I started studying a month ago and what you said is totally trueYou're in good company Smile Just remember that the killer on the GMAT isn't the high-level stuff. It's the careless mistakes and the questions engineered to look much harder than they are.
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Two deductions from the inequality zt < -3:sachin_yadav wrote:If zt < -3, is z < 4 ?
(1) z < 9
(2) t < -4
OA is E
How would you approach ?
1. Neither z nor t is 0.
2. One of z and t is positive and the other is negative.
We have to see whether z < 4.
S1: z < 9
If z < 4, the answer is YES; however, if 4 ≤ z < 9, the answer is NO. No unique answer. Insufficient.
S2: t < -4
It means that t is negative, thus z is positive.
Say t = -5, thus per the inequality zt < -3, we have:
z*(-5) < -3
Multiplying the inequality by -1.
=> 5z > 3; notice the sign-reversal of the inequality
=> z > 3/5
If 3/5 < z < 4, the answer is YES; however, if 4 ≤ z, the answer is NO. No unique answer. Insufficient.
S1 and S2:
Even combining both the statements cannot help.
If 3/5 < z < 4, the answer is YES; however, if 4 ≤ z < 9, the answer is NO. No unique answer. Insufficient.
Hope this helps!
-Jay
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Hi All,
This question is based around a couple of Number Properties, which you can use to quickly work through this question without doing too much math.
We're told that (Z)(T) < -3. This means that one of the variables is POSITIVE and the other is NEGATIVE. We're asked if Z < 4. This is a YES/NO question.
1) Z < 9
With this Fact, Z could be less than 4 (a YES answer), 4 exactly (a NO answer) or greater than 4 (a NO answer).
Fact 1 is INSUFFICIENT
2) T < -4
Since T has to be LESS than -4, we know that Z is POSITIVE, but we don't know how big Z actually is. It could be 3 (a YES answer) or 4 (a NO answer).
Fact 2 is INSUFFICIENT
Combined, we already have two TESTs (Z = 3 and Z = 4) that provide different answers, so no more work is necessary.
Combined, INSUFFICIENT
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
This question is based around a couple of Number Properties, which you can use to quickly work through this question without doing too much math.
We're told that (Z)(T) < -3. This means that one of the variables is POSITIVE and the other is NEGATIVE. We're asked if Z < 4. This is a YES/NO question.
1) Z < 9
With this Fact, Z could be less than 4 (a YES answer), 4 exactly (a NO answer) or greater than 4 (a NO answer).
Fact 1 is INSUFFICIENT
2) T < -4
Since T has to be LESS than -4, we know that Z is POSITIVE, but we don't know how big Z actually is. It could be 3 (a YES answer) or 4 (a NO answer).
Fact 2 is INSUFFICIENT
Combined, we already have two TESTs (Z = 3 and Z = 4) that provide different answers, so no more work is necessary.
Combined, INSUFFICIENT
Final Answer: E
GMAT assassins aren't born, they're made,
Rich