Target question: Of the numbers q, r, s, and t, which is greatest?

Statement 1: The average (arithmetic mean) of q and r is s
No information is given about t
Statement 1 is NOT SUFFICIENT

Statement 2: The sum of q and r is t.
No information is given about s
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that (q + r)/2 = s
Multiply both sides by 2 to get: q + r = 2s

Statement 2 tells us that q + r = t

There are several values of q, r, s and t that satisfy BOTH statements. Here are two:
Case a: q = -1, r = 1, s = 0 and t = 0. In this case, the answer to the target question is r is the greatest value
Case b: q = 1, r = -1, s = 0 and t = 0. In this case, the answer to the target question is q is the greatest value
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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The mean lies between the two numbers.
So 1 suggests that Q<= S<=R or R<=S<=Q. Clearly we cant tell the relation between Q and R. T is unknown as well . So 1 is insufficient

2) It tells T = R + Q. Not sufficient as we don't know S

Combining 1, 2, We just know S can't be greater than R, Q. But still we dont know for sure about T as for R, Q positive, T will be greates.. but if either R/ Q is negative..T will not be greatest.

Hence it should be E

I most of the time in such cases try couple of scenarios with positive numbers first and later negatives no.

1) Not enough. Only tells us S is between Q and R. No info about T

2) Doesnt tell us anything. Since no info about S

(1+2) : 1 tells us S is between Q & R. 2 gives us very little info. If Q & R are negative, T is less than both, if they are positive T is greater than both. Impossible to know what is the greatest number w/o having this complete information

Answer is (e)
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Plugging in numbers may be useful..
Individual statements are obviously not sufficient..combining both,we have,
let -
Q=4
R=12
Hence,S =12+4/2= 8 =AVERAGE

T=4+12=16....so in this case,T is highest..now,lets take another case..

Q= -4
R= 12
Hence,S = -4+12/2 = 4 = AVERAGE

T= -4+12=8...So,n this case R is highest..so even both of them together not sufficient...



Please consider kudos if my post helped
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from 1: S= (Q+R)/2, S is in between Q and R, Q<S<R or R<S<Q, T can be on any side of this inequality, therefor NSF
from 2: Q+R = T, No info on S at all, so NSF

combining 1 + 2, if Q = -100 and R = 100, then AM of Q and R is 0 = S and T=0 , if we take any other numbers we get different answer.
therefore NSF.

Answer is E

Statement-I (Insufficient)
1. Given that \(\frac{q+r}{2} = s\)
2. But, we have no information on \(t\)

Statement-II (Insufficient)
1. Given that \(q+r = t\)
2. But, we have no information on \(s\)

Combined (Insufficient)
\(\frac{t}{2} = s\) -> \(t = 2s\)

Case-I: \(q = -1\) and \(r = -2\) then \(t = -3\) and \(s = -1.5\) (\(q\) is the greatest)
Case-II: \(q = 1\) and \(r = 2\) then \(t = 3\) and \(s = 1.5\) (\(t\) is the greatest)

Ans. E
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I find the easiest way to solve these problems is to make a number line and plot numbers:

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They can all be 0, hence E.

But if all are 0 we can answer the question, so I think your method is unsatisfactory.

Each statement alone is clearly insufficient.

1+2

If all are +ve, then OfCourse, T is greatest.

But,

(1) The average (arithmetic mean) of q and r is s.

\(q=-5, r=2\), avg = \(-5+2/2= s\)

\(s=-1\)

if \(s=-1\), per the second statement:

2) The sum of q and r is t. --- sum of q and r is \(q+r/2=s --- q+r=2(s)\)

\(2(s)= 2(-1) =-2\)

therefore, \(t= 2(s)= -2\)

hence, in this case r is the greatest.

E is the Answer.

1) Not enough. Only tells us S is between Q and R. We are not in a position to determine T

2) Here there can be a possiblity of any value that can be taken by S
Only options that are left is C and D
Trying all the extreme cases we can figure out one option to eleminate the same being use 0 if it's zreo in
all the cases then we can nail down E
Hence IMO E