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Inequalities If zt < -3, is z < 4

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Jan 24, 2015 7:13 am
sachin_yadav wrote:If zt < -3, is z < 4 ?

(1) z < 9
(2) t < -4
Target question: Is z < 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

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Brent
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by Matt@VeritasPrep » Sun Jan 25, 2015 4:55 pm
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.
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by Zoser » Tue Jan 17, 2017 6:42 am
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
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by DavidG@VeritasPrep » Tue Jan 17, 2017 6:51 am
Zoser 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
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?
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by Zoser » Tue Jan 17, 2017 7:04 am
[/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?

You are right! Most certainly, too much studying start affecting my basic math skills.

Thanks anyways
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by DavidG@VeritasPrep » Tue Jan 17, 2017 7:25 am
Zoser wrote:
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?

You are right! Most certainly, too much studying start affecting my basic math skills.

Thanks anyways
[/quote]

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.
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by Zoser » Tue Jan 17, 2017 9:21 am
You'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.
Thank you! I started studying a month ago and what you said is totally true
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by Jay@ManhattanReview » Wed Jan 18, 2017 9:46 pm
sachin_yadav wrote:If zt < -3, is z < 4 ?
(1) z < 9
(2) t < -4

OA is E

How would you approach ?
Two deductions from the inequality zt < -3:

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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by [email protected] » Thu Jan 19, 2017 10:27 am
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

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