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Inequalities: If r + s > 2t, is r > t ?
Source: Beat The GMAT — Data Sufficiency |
Lets see, it looks like A to me.
r+s>2t ==> r>2t-s
(1) t>s ==> 2t-s>t (if t=s then 2t-s=t)
r>2t-s>t ==> r>t sufficient
(2) r>s , so what? byitself INSUFFICIENT
r+s>2t ==> r>2t-s
(1) t>s ==> 2t-s>t (if t=s then 2t-s=t)
r>2t-s>t ==> r>t sufficient
(2) r>s , so what? byitself INSUFFICIENT
I think the OA is D
Lets look at the (2)
We know R+S > 2T
-> S > 2T-R .. (1)
(2) S <R
From 1 and 2
2T - R < S <R
therefore
2T - R <R
therefore
T < R
Lets look at the (2)
We know R+S > 2T
-> S > 2T-R .. (1)
(2) S <R
From 1 and 2
2T - R < S <R
therefore
2T - R <R
therefore
T < R
Is the answer A or D ?
My solution:
Given:
r + s > 2t OR
r + s > t + t
Question:
Is r > t
S1:
t > s i.e t = s + a where a is small positive number
r + s > t + t
r + s > s + a + t
r > t + a ---> this means r in fact is bigger then sum of t and another positve number so definitely r > t
SUFF
S2:
r > s i.e r = s + a where a is small positive number
r + s > t + t
r + r - a > t + t
r - a/2 > t ---> which means even after subtracting a small +ve number, r continues to remain bigger then t, so r > t
SUFF
Please let me know official answer as well as a shortcut/approach to such problems.
My solution:
Given:
r + s > 2t OR
r + s > t + t
Question:
Is r > t
S1:
t > s i.e t = s + a where a is small positive number
r + s > t + t
r + s > s + a + t
r > t + a ---> this means r in fact is bigger then sum of t and another positve number so definitely r > t
SUFF
S2:
r > s i.e r = s + a where a is small positive number
r + s > t + t
r + r - a > t + t
r - a/2 > t ---> which means even after subtracting a small +ve number, r continues to remain bigger then t, so r > t
SUFF
Please let me know official answer as well as a shortcut/approach to such problems.
(1) SUFFICIENT: We can combine the given inequality r + s > 2t with the first statement by adding the two inequalities:
r + s > 2t
t > s
r + s + t > 2t + s
r > t
(2) SUFFICIENT: We can combine the given inequality r + s > 2t with the second statement by adding the two inequalities:
r + s > 2t
r > s
2r + s > 2t + s
2r > 2t
r > t
The correct answer is D.
r + s > 2t
t > s
r + s + t > 2t + s
r > t
(2) SUFFICIENT: We can combine the given inequality r + s > 2t with the second statement by adding the two inequalities:
r + s > 2t
r > s
2r + s > 2t + s
2r > 2t
r > t
The correct answer is D.
How do you know when it is a good idea to add inequality equations together?
II wrote:(1) SUFFICIENT: We can combine the given inequality r + s > 2t with the first statement by adding the two inequalities:
r + s > 2t
t > s
r + s + t > 2t + s
r > t
(2) SUFFICIENT: We can combine the given inequality r + s > 2t with the second statement by adding the two inequalities:
r + s > 2t
r > s
2r + s > 2t + s
2r > 2t
r > t
The correct answer is D.
Given that r+s>2tII wrote:If r + s > 2t, is r > t ?
(1) t > s
(2) r > s
1)t>s or -s> -t
add this to the given equation
r+s>2t
-s>-t
---------
r >t
Sufficient
2)r>s or r-s>0
add this to the given equation
r+s>2t
r-s>0
-------
2r>2t
r>t
Sufficient.
This is a Mgmat question and the OA is D
