If r + s 2t, is r t ? (1) t s (2) r s

Question

If r + s > 2t, is r > t ?
 
(1) t > s
 
(2) r > s

lagomez · Answer

answer D

1. 
r + s > 2t
s<t

subtract inequalities and you get r>t so sufficient

2. r>s or r-s>0
r+s>2t

add equations and you get 2r>2t or r>t

MackyCee · Answer

Here, you can manipulate inequalities.

From the givens, we know that:

r+s > 2t

therefore:
(1) 
r+s > 2t
t > s

Inequalities with the same sign can be added / subtracted

=> r + s + t > 2t + s
=> r > t

SUFF

(2)
r + s > 2t
r > s

=> 2r + s > 2t + s
=> 2r > 2t
=> r > t

SUFF

Answer: D

shrouded1 · Answer

r + s > 2t

(1) t > s
So, r+t > r+s > 2t
So, r+t > 2t
So, r>t
Sufficient

(2) r > s
So, r+r > s+r > 2t
So, 2r > 2t
So, r > t
Sufficient

Answer is (d)

calreg11 · Answer

thx lagomez. just forgot that we could add inequalities and equations to help simplify an equation.

Bunuel · Answer

If r + s > 2t, is r > t ?

(1) t > s:

Since the signs of two equations (t > s and r + s > 2t) are the same direction we can sum them:

\(t+(r+s)>s+2t\);

\(r>t\).

Sufficient.

(2) r > s

The same here: since the signs of two equations (r > s and r + s > 2t) are the same direction we can sum them:

\(r+(r+s)>s+2t\);

\(2r>2t\);

\(r>t\).

Sufficient.

Answer: D.

THEORY:

You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\).

Example: \(3<4\) and \(2<5\);

\(3+2<4+5\).

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from).

Example: \(3<4\) and \(5>1\);

\(3-5<4-1\).

Hope it helps.

Diver · Answer

Hi Bunnel, since we don't know the signs of t and s, how can we subtract s on both sides to simplify the inequality R+s+t>S+2T? Am I missing something here?

Bunuel · Answer

You are mixing subtraction/addition with multiplication/division. We are only concerned with sign when we multiply/divide an inequality.

spence11 · Answer

r+s>2t \rightarrow \frac{r+s}{2}>t

So the midpoint of  r  and  s  is greater than  t

The orange line represents possible locations on the number line for  t

Statement 1)

If  t>s  then only the second option is possible, and  r  must be greater than  t

Statement 2)

If  r>s  then only the second option is possible, and again  r  must be greater than  t

Answer  D

tinytiger · Answer

One way to do this is to manipulate the original stem from r-s > 2t (given) into r-t > t-s (another way to see the stem info).

Qn asks if r-s is > 0 --> two ways to know if we can answer yes:

a) if (r-s) > 0 directly, or 
b) if (t-s) > 0 --> therefore (r-t) MUST be > 0

Statement 1: (t-s) > 0 (sufficient)
Statement 2: (r-s) > 0 (sufficient - the question answers its own question)

Answer: D

chrtpmdr · Answer

Sir  Bunuel , do you have a quick list of similar questions at hand?

Bunuel · Answer

9. Inequalities 
     Theory   
 Inequalities Made Easy! 
 Inequalities: Tips and hints 
 Arithmetic with Inequalities 
 Wavy Line Method Application - Complex Algebraic Inequalities 
 Solving Quadratic Inequalities: Graphic Approach 
 Inequalities - Quadratic Inequalities 
 Graphic approach to problems with inequalities 
 Inequalities trick 
 INEQUATIONS(Inequalities) Part 1 
 INEQUATIONS(Inequalities) Part 2 
     Questions   
 Inequality and absolute value questions from my collection 
 DS Questions 
 PS Questions

For more check  Ultimate GMAT Quantitative Megathread

Hope it helps.

avigutman · Answer

Video solution from Quant Reasoning starts at 10:00 Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=2iQ7YkK2oYo

mehtasahil56 · Answer

CAN SOMEONE HELP ME BY DOING THIS BY PLUG IN VALUES?

RastogiSarthak99 · Answer

To be honest, I tried doing this by plugging numbers, but since there is very little info about the nature of r,s,t (integer, fraction, +ve, -ve etc) I took a lot of time.

Therefore I then chose to use the algebraic method.

Never hurts to have many times of weapon in your arsenal!

Let me know if you did manage to plug in values for this

viswanath1 · Answer

I didnt realize that we could get it by adding the equations. i was trying to work with the question stem trying to get it similar to 1 and 2. What particular clue in the question would tell us to add?

Quote:

Bunuel

Bunuel · Answer

The clue is this:

The  direction of the inequalities is the same .

Both statements also give inequalities: 
 (1) t > s
 (2) r > s

Since these inequalities are all in the  “greater than”  direction, you can think of  adding  them together to combine information.

If the signs had been in  opposite directions  (one > and one <), adding wouldn't work, and you’d look to  subtract  instead.

That’s the key clue:

Same direction? Try adding. 
 Opposite direction? Try subtracting.

Legallyblond · Answer

I wanna learn your thought process. how did you know that we should add them up? did you think like okay lets eliminate s?

Bunuel · Answer

Yes. Check this post: https://gmatclub.com/forum/if-r-s-2t-is ... l#p3600367

If r + s > 2t, is r > t ? (1) t > s (2) r > s

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