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

Question

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

DS81502.01

BrentGMATPrepNow · Accepted Answer

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

krushna · Answer

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

arundas · Answer

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

shrouded1 · Answer

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)

vards · Answer

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

santorasantu · Answer

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

Pritishd · Answer

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

Basshead · Answer

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

ZZhang · Answer

They can all be 0, hence E.

Bambi2021 · Answer

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

ueh55406 · Answer

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.

Crytiocanalyst · 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

KarishmaB · Answer

When comparing numbers with relations given among them, visualise them on a number line. We have the standard number line with 0 in the centre and q, r, s, and t are on it.

We have to find which one is the rightmost number (greatest).

Either statement leaves out information on one variable and hence no statement is sufficient alone. Statement 1 tells us nothing about t and statement 2 tells us nothing about s.

But both together, we know that s is in between q and r. We do not know which is on the right, q or r. 
We also know that t is the sum of q and r. So if both q and r are positive, t is to the right of both. If q and r are negative, t is to the left of both. 
Do we know which is the rightmost number? No. All we can say is that s is not the rightmost number - that's all.

Answer (E)

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

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