Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Enter The Economist GMAT Tutor’s Brightest Minds competition – it’s completely free! All you have to do is take our online GMAT simulation test and put your mind to the test. Are you ready? This competition closes on December 13th.

Attend a Veritas Prep GMAT Class for Free. With free trial classes you can work with a 99th percentile expert free of charge. Learn valuable strategies and find your new favorite instructor; click for a list of upcoming dates and teachers.

Does GMAT RC seem like an uphill battle? e-GMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days.

The Problem description is not precise, could you provide clear problem solving strategy.

Thanks.

If 2s > 8 and 3t < 9, which of the following could be the value of s-t?

I. -1 II. 0 III. 1

A. None B. I only C. II only D. III only E. II and III

we have two equations.. 2s > 8 .. s>4, so' s' can be 4.1,5,5.05 etc and 3t < 9 .. t<3 so 't'can be 2.9999, 2,-1 etc..

if we take the lowest possible difference between s and t, we will take lowest value of s, which is just above 4 and highest value of t, which is just lower to 3.. s-t >4.0000000001 -2.999999999 .... so s-t>1 therefore all values of -1,0,1 are not possible ans none A hope it helped
_________________

I understand how we get s>4 and t<3, but I'm having a hard time wrapping my head around why t cannot be negative. Can someone please explain?

We don't need to check when t<0 but for the sake of your question, even if t <0 ---> -t>0 and you know that s>0, giving you s-t > 1 for all values of s and t as s>1

Any positive quantity added to a quantity >1 will give you the sum as >1

If 2s > 8 and 3t < 9, which of the following could be the value of s-t?

I. -1 II. 0 III. 1

A. None B. I only C. II only D. III only E. II and III

Given: 2s > 8 Divide both sides by 2 to get: s > 4

Given: 3t < 9 Divide both sides by 3 to get: t < 3

NOTE: If we have two inequalities with the inequality symbols facing in the same direction, we can add the inequalities to learn something new.

So, take t < 3 and multiply both sides by -1 to get: -t > -3[aside: when we divide or multiply both sides of an inequality by a NEGATIVE value, we mist REVERSE the symbol]

We now have: s > 4 -t > -3

When we ADD these two inequalities, we get: s - t > 1

If s - t > 1, then: I) s - t CANNOT equal -1 II) s - t CANNOT equal 0 III) s - t CANNOT equal 1

If 2s > 8 and 3t < 9, which of the following could be the value of s-t?

I. -1 II. 0 III. 1

A. None B. I only C. II only D. III only E. II and III

s>4

t<3 (multiply by -1) --> -t>-3

Add both of them

Thus s-t >4-3

or s-t>1. As none of the options given are greater than 1, the answer is none. A.

pushpitkc any idea why do we multiply t<3 by -1 and s>4 leave as it is ?

thank you

Hi dave13 - I hope you have been slaying Quant dragons. At the least, dump some water on their heads. I'm going to expand a little on pushpitkc 's good answer. BTW, I have to add little dots at times to get terms to line up.

We multiply one of the inequalities by -1 because they have signs that point in different directions. The rule: you cannot add inequalities unless their signs point in the SAME direction.

Another rule: multiplying an inequality by any negative number changes the direction of the sign. Another rule: Multiplying by -1 changes the sign but leaves the numbers and variables the same except with opposite signs.

We are asked to find \(s-t\). If we multiply \((t<3)\)by \(-1,\) we can make \(t\) negative (hang on) AND flip its sign so it points the same way as that of \(s\) We've isolated \(s\) and \(t\) to get: \(s>4\) and \(t<3\)

One sign MUST change so we can add. We change the \(t\) inequality because we will get a sign flip AND a MINUS \(t\) \(s\) + \((-t)\)? Is \((s-t)\)

Mulitply \((t<3)\) by (-1). SIGN flips. \((-1*t)>(-1*3)\) \(-t > -3\)

Now add the two inequalities ··\((s > 4)\) +\((-t>-3)\) ------------------ \(s - t> 1\)

No answer choices are greater than 1. The answer is A. Hope that helps.

Technically, we can subtract (NOT add) inequalities with different signs. The sign on top controls. ··\((t<3)\) -\((s>4)\) ============ \(t-s<-1\) ....Oh yay. Now we get to multiply by -1. We need (s-t), not (t-s). \((-1*t)-(-1*s)<(-1*-1)\) \(-t + s>1\) \(s-t>1.\) Trust me. ADD. _________________

SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has -- Margaret Mead

s is somewhere to the right of 4. t is somewhere to the left of 3. We can see the space between them must be greater than 1. All of the choices are not possible.

gmatclubot

If 2s > 8 and 3t < 9
[#permalink]
22 Mar 2019, 11:44