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

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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink]
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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]
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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

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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink]
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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]
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.

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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink]
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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]
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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 [ 10.31 KiB | Viewed 18934 times ]

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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink]
They can all be 0, hence E.
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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink]
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]
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.

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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink]
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]
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Re: Of the numbers q, r, s, and t, which is greatest? [#permalink]
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