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# Is r>s?

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Math Expert
Joined: 02 Sep 2009
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21 Mar 2017, 03:54
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Difficulty:

65% (hard)

Question Stats:

48% (01:19) correct 52% (01:15) wrong based on 126 sessions

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Is r>s?

(1) r represents the probability that it will rain on Tuesday.
(2) r > 2s

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Joined: 02 Aug 2015
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21 Mar 2017, 07:54
Bunuel wrote:
Is r>s?

(1) r represents the probability that it will rain on Tuesday.
(2) r > 2s

(1) r represents the probability that it will rain on Tuesday - No information about s. Hence not sufficient.

(2) r > 2s
r=4, s=1 - Yes
r=-1, s=-1 - No

(1) + (2) - r has to be positive as it's a probability. Hence sufficient.

Hence C.

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VP
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21 Mar 2017, 07:54
Bunuel wrote:
Is r>s?

(1) r represents the probability that it will rain on Tuesday.
(2) r > 2s

probabilty cant be negative
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21 Mar 2017, 17:17
1
Bunuel wrote:
Is $$r > s$$ ?

(1) r represents the probability that it will rain on Tuesday.
(2) $$r > 2s$$

OFFICIAL SOLUTION

Is $$r > s$$ ? Without looking at the additional information, it's impossible to say, and there's no work that can be done upfront.

On to statement (1)! Rain on Tuesday? Huh? Well if that isn't just the dumbest, randomest, most utterly useless piece of non-information ever...

Statement (1) alone is insufficient.

Statement (2) says that r>2s and at first blush it may seem obvious that if r is more than twice s, then surely r is greater than s itself.
But at this point we should begin to feel like giant suckers. If everything in both statements is that obvious, then what's the point of this problem? What could we be missing? How about negatives. If s<0, then 2s is actually less than s itself, and knowing that r>2s would not establish whether r>s. For instance, if s=−3, then 2s=−6, and if r=−4, then r would be greater than 2s but would not be greater than s.

So actually, it's not obvious that Statement (2) is sufficient; in fact, it's not even true! Statement (2) alone is insufficient.

At this point it might be tempting to go straight to E without even bothering to put the statements together, since statement (1) seemed so incredibly pointless. But that first statement does tell us one critical thing: r cannot be negative; the probability of any event is always a number between 0 and 1.

Now, if s is positive, then 2s>s, and r>2s therefore implies that r>s. If s is 0, then 2s=s, and again r>2s implies that r>s. Finally, if s is negative, then r>s simply based on the fact that r is nonnegative, and any nonnegative number is greater than every negative number. Thus, the two statements together do answer the question by establishing that r>s in every case. C is correct.
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22 Mar 2017, 05:26
Bunuel wrote:
Is r>s?

(1) r represents the probability that it will rain on Tuesday.
(2) r > 2s

ST 1: No data about probability is given. all we know that r is positive
ST 2: for r = positive, if r>2s that means r>s but negative value, not necessarily. for r = -3 and s = -2 r<s but r>2s. INSUFFICIENT

ST 2 & St 2: for positive r if r>2s, that menas r>s. ANSWER

Option C
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23 Mar 2017, 16:03
Bunuel wrote:
Is r>s?

(1) r represents the probability that it will rain on Tuesday.
(2) r > 2s

We need to determine whether r > s.

Statement One Alone:

r represents the probability that it will rain on Tuesday.

Using the information in statement one, we know that r is a number between 0 and 1 inclusive. However, without knowing anything about s, statement one is not sufficient to answer the question.

Statement Two Alone:

r > 2s

Statement two alone is not sufficient to answer the question. For instance, if s = 1 and r = 3, then r is greater than s; however, if s = -2 and r = -2, then r IS NOT greater than s.

Statements One and Two Together:

Using statements one and two, we see that r is a number between 0 and 1 inclusive and that r > 2s. We know that r is nonnegative; however, s could be negative, 0, or positive.

If s is negative, then r is greater than s.

If s is 0, then 2s = s. So r > 2s means r > s.

Finally, if s is positive, then 2s > s, So r > 2s also means r > s.

Thus, r will always be greater than s.

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Re: Is r>s? &nbs [#permalink] 23 Mar 2017, 16:03
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