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

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tonebeeze
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Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   08 Oct 2010, 19:00
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Of the numbers q, r, s, and t, which is greatest?

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


DS81502.01
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E
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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   19 Dec 2019, 07:49
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tonebeeze wrote:
Of the numbers q, r, s, and t, which is greatest?

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


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

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Brent
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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   08 Oct 2010, 19:48
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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
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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   08 Oct 2010, 22:33
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I most of the time in such cases try couple of scenarios with positive numbers first and later negatives no.
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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   08 Oct 2010, 23:19
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tonebeeze wrote:
Of the numbers Q, R, S, and T, which is greatest?

(1) The average (arithmetic mean) of Q and R is S.

(2) The sum of Q and R is T.

I continue to make careless errors on these types of problems. Is there any testing approaches that people find effective when facing such questions? Any tips would be much appreciated. Thanks!


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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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   13 Sep 2014, 04:37
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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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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   02 Dec 2014, 15:09
tonebeeze wrote:
Of the numbers Q, R, S, and T, which is greatest?

(1) The average (arithmetic mean) of Q and R is S.

(2) The sum of Q and R is T.

I continue to make careless errors on these types of problems. Is there any testing approaches that people find effective when facing such questions? Any tips would be much appreciated. Thanks!



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
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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   28 Oct 2020, 05:44
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tonebeeze wrote:
Of the numbers q, r, s, and t, which is greatest?

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

DS81502.01


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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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   05 Nov 2020, 16:09
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I find the easiest way to solve these problems is to make a number line and plot numbers:
Attachments

qsrt.png
qsrt.png [ 10.31 KiB | Viewed 17412 times ]

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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   02 Jun 2021, 20:56
They can all be 0, hence E.
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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   13 Jun 2021, 17:49
ZZhang wrote:
They can all be 0, hence E.


But if all are 0 we can answer the question, so I think your method is unsatisfactory.
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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   04 Jul 2021, 06:50
tonebeeze wrote:
Of the numbers q, r, s, and t, which is greatest?

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


DS81502.01


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.
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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   11 Jul 2021, 00:03
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
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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink] New post   24 Jul 2023, 09:40
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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink]
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