If 2s 8 and 3t

Question

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

BrentGMATPrepNow · Accepted Answer

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 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 Answer: A RELATED VIDEOS https://www.youtube.com/watch?v=Od98BOicIq4 https://www.youtube.com/watch?v=S_fjYmCtvy0

mau5 · Answer

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.

subhendu009 · Answer

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.
--------------------------------------

Sapient · Answer

Hi,

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

Thanks.

chetan2u · Answer

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.
--------------------------------------

ada453 · Answer

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?

ENGRTOMBA2018 · Answer

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.

ada453 · Answer

Thank you. I neglected to utilize the fact that s must be positive when testing cases. Appreciate the help

Nived · Answer

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.

JeffTargetTestPrep · Answer

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. Answer: A

dave13 · Answer

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

thank you

pushpitkc · Answer

dave13  - We have been asked to find the value of s-t. That's the reason for multiplying the inequality involving t with -1.

generis · Answer

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.

Henry S. Hudson Jr. · Answer

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.

bumpbot · Answer

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If 2s > 8 and 3t < 9

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