GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 21:27 GMAT Club Daily Prep

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

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.  If 2s > 8 and 3t < 9

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Intern  Joined: 01 Feb 2013
Posts: 9
Location: United States
Concentration: Finance, Technology
GPA: 3
WE: Analyst (Computer Software)
If 2s > 8 and 3t < 9  [#permalink]

Show Tags

5
11 00:00

Difficulty:   25% (medium)

Question Stats: 72% (01:33) correct 28% (01:31) wrong based on 472 sessions

HideShow timer Statistics

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

_________________
Goal: 25 KUDOZ and higher scores for everyone!

Originally posted by tulsa on 25 Mar 2013, 12:13.
Last edited by tulsa on 25 Mar 2013, 13:30, edited 2 times in total.
Verbal Forum Moderator B
Joined: 10 Oct 2012
Posts: 590
Re: If 2s > 8 and 3t < 9  [#permalink]

Show Tags

9
tulsa wrote:
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.
_________________
General Discussion
Intern  Joined: 22 Jan 2010
Posts: 24
Location: India
Concentration: Finance, Technology
GPA: 3.5
WE: Programming (Telecommunications)
Re: If 2s > 8 and 3t < 9  [#permalink]

Show Tags

4
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

Solution :
----------
2s > 8 => s > 4
3t < 9 => t < 3

The given values can be represented on the number line as follows :

--t-----------3---------------4--------s-----------
|----+ve---|---------1-----|-+ve-+|

So,s-t will be greater than 1.
Correct option is A.
--------------------------------------

Press KUDOS if you like my post.
Intern  Joined: 02 May 2013
Posts: 7
Re: If 2s > 8 and 3t < 9  [#permalink]

Show Tags

Hi,

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

Thanks.
_________________
Kind Regards,

J

"When the going gets tough, the tough get going"
Math Expert V
Joined: 02 Aug 2009
Posts: 7974
Re: If 2s > 8 and 3t < 9  [#permalink]

Show Tags

1
Sapient wrote:
Hi,

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
_________________
Intern  B
Joined: 10 Oct 2014
Posts: 19
GPA: 3.47
WE: Marketing (Advertising and PR)
Re: If 2s > 8 and 3t < 9  [#permalink]

Show Tags

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?
CEO  S
Joined: 20 Mar 2014
Posts: 2597
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
If 2s > 8 and 3t < 9  [#permalink]

Show Tags

1
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

Consider s= 7, t= -5 or -0.3

Both these cases make it s-t >1.

Hope this helps.
Intern  B
Joined: 10 Oct 2014
Posts: 19
GPA: 3.47
WE: Marketing (Advertising and PR)
Re: If 2s > 8 and 3t < 9  [#permalink]

Show Tags

Thank you. I neglected to utilize the fact that s must be positive when testing cases. Appreciate the help
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4007
Re: If 2s > 8 and 3t < 9  [#permalink]

Show Tags

Top Contributor
tulsa wrote:
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

RELATED VIDEOS

_________________
Intern  B
Joined: 30 Nov 2017
Posts: 23
Re: If 2s > 8 and 3t < 9  [#permalink]

Show Tags

2s > 8 and 3t < 9

So, s > 4 and t < 3

Assume
s = 4 + ds
t = 3 - dt

So, s - t = (4 + ds) - (3 - dt)
s - t = 1 + (ds + dt)

So, s - t has to be > 1

None of the given option qualifies.
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2816
Re: If 2s > 8 and 3t < 9  [#permalink]

Show Tags

tulsa wrote:
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 see that s > 4 and that t < 3. Since s is always greater than t, the difference cannot be -1 or zero.

Furthermore, since s > 4 and t < 3, we see that s and t are more than 1 unit apart, so the difference cannot be 1.

Alternate Solution:

Let’s divide each side of 2s > 8 by 2: s > 4

Let’s divide each side of 3t < 9 by -3, paying attention to change the direction of the inequality since we are dividing by a negative number: -t > -3

Let’s add the two inequalities together: s - t > 1

We see that none of the provided numbers is greater than 1.

_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

VP  D
Joined: 09 Mar 2016
Posts: 1230
Re: If 2s > 8 and 3t < 9  [#permalink]

Show Tags

mau5 wrote:
tulsa wrote:
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 Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3335
Location: India
GPA: 3.12
If 2s > 8 and 3t < 9  [#permalink]

Show Tags

1
dave13 wrote:
mau5 wrote:
tulsa wrote:
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 dave13 - We have been asked to find the value of s-t. That's the reason for multiplying the inequality involving t with -1.
_________________
You've got what it takes, but it will take everything you've got
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3548
If 2s > 8 and 3t < 9  [#permalink]

Show Tags

1
dave13 wrote:
mau5 wrote:
tulsa wrote:
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
··$$(s > 4)$$
+$$(-t>-3)$$
------------------
$$s - t> 1$$

Horizontally:
$$s + (-t) = (s-t)$$
$$4 + (-3) = (4-3) = 1$$
The > sign is between, thus $$s - t> 1$$

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.

Choose life.
Manager  B
Joined: 17 Jul 2016
Posts: 54
If 2s > 8 and 3t < 9  [#permalink]

Show Tags

visualizing a number line may be helpful.

--------0----1----2----3----4-----

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. If 2s > 8 and 3t < 9   [#permalink] 22 Mar 2019, 11:44
Display posts from previous: Sort by

If 2s > 8 and 3t < 9

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  