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Which of the 5 terms p, q, p + q, p – 1, and q + 1 represent

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Which of the 5 terms p, q, p + q, p – 1, and q + 1 represent  [#permalink]

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New post 23 Nov 2012, 16:07
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Question Stats:

32% (02:41) correct 68% (02:39) wrong based on 108 sessions

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Which of the 5 terms p, q, p + q, p – 1, and q + 1, represents the median of these 5 terms?

(1) p > q
(2) p – q < 1

The solution recommends plugging in for each one of these, but that means you'll have to plug in at least 6 times... I don't see how one could do that in less than 2 minutes! I mean you could, but there would have to seamless. You immediately understand the question, immediately start plugging in, and get 0 mistakes.

plug in stat(1), get it S, then try to plug in again and get it IS. (then repeat for Stat(2) and Stat(1+2). Then there is also the possibility you plug in twice and get the same result, leaving you to a false answer.

HELP!
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Re: Which of the 5 terms p, q, p + q, p – 1, and q + 1 represent  [#permalink]

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New post 24 Nov 2012, 23:34
1
anon1 wrote:
Which of the 5 terms p, q, p + q, p – 1, and q + 1, represents the median of these 5 terms?

(1) p > q
(2) p – q < 1

The solution recommends plugging in for each one of these, but that means you'll have to plug in at least 6 times... I don't see how one could do that in less than 2 minutes! I mean you could, but there would have to seamless. You immediately understand the question, immediately start plugging in, and get 0 mistakes.

plug in stat(1), get it S, then try to plug in again and get it IS. (then repeat for Stat(2) and Stat(1+2). Then there is also the possibility you plug in twice and get the same result, leaving you to a false answer.

HELP!


Well you can do it algebraically I think. To get the median we MUST be able to write the elements is ascending/descending order!
For S1
p>q then, then if we want to write the elements is descending order: We CANT because even if p>q we dont know if p-1 > q. Also we dont know if p+q>q+1 as we dont know whether p is postive/negative or a fraction.
So insufficient.
For S2
p<q+1. Again similar problem prevails. We dont know if p+q is less or greater than q+1.
So insuffiecient.
S1+S2
This becomes interesting.
we can see that, p-1>p>q but we still dont know which one between q+1 and p+q is greater. Still the same.
Insufficient.
Hence E
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Re: Which of the 5 terms p, q, p + q, p – 1, and q + 1 represent  [#permalink]

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New post 24 Sep 2014, 09:40
1
anon1 wrote:
Which of the 5 terms p, q, p + q, p – 1, and q + 1, represents the median of these 5 terms?

(1) p > q
(2) p – q < 1

The solution recommends plugging in for each one of these, but that means you'll have to plug in at least 6 times... I don't see how one could do that in less than 2 minutes! I mean you could, but there would have to seamless. You immediately understand the question, immediately start plugging in, and get 0 mistakes.

plug in stat(1), get it S, then try to plug in again and get it IS. (then repeat for Stat(2) and Stat(1+2). Then there is also the possibility you plug in twice and get the same result, leaving you to a false answer.

HELP!


E.

1) p>q

p=1,q=0
terms = 0,0,1,1,1
median is 1 but multiple terms are 1 so which one is the median we cannot know.

2) p-q < 1
p=2 , q=3
1,2,3,4,5 (median 3)
p=(-2),q=(-3)
-5,-3,-3,-2,-2 (median -3)
but same problem as above.

(1)+(2)
p=(-1),q=(-2)
-2,-2,-1,-1,0
same issue here as well.
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Which of the 5 terms x, y, x + y - Statistics - DS  [#permalink]

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New post 11 Aug 2018, 09:21
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Which of the 5 terms x, y, x + y, x – 1, and y + 1, represents the median of these 5 terms?

(1) x > y

(2) x – y < 1
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Re: Which of the 5 terms x, y, x + y - Statistics - DS  [#permalink]

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New post 11 Aug 2018, 10:41
Harshgmat wrote:
Which of the 5 terms x, y, x + y, x – 1, and y + 1, represents the median of these 5 terms?

(1) x > y

(2) x – y < 1


Since these expressions are simple to evaluate, I used substitution.

(1) x > y, make x = 2 and y = 1
The (unordered) list becomes: 2, 1, 2 + 1, 2 - 1, 1 + 1 --> 2, 1, 3, 1, 2
Put them in order: 1, 1, 2, 2, 3 --> "2" is the median.
However, "2" could be "x" or "y + 1"
Therefore, I cannot tell which of the five terms is the median. Insufficient.

(2) x - y < 1, make x = 3 and y = 3
Unordered list: 3, 3, 3 + 3, 3 - 1, 3 +1 --> 3, 3, 6, 2, 4
Ordered list: 2, 3, 3, 5, 6 --> "3" is the median
However, "3" could be "x" or "y"
Therefore, I cannot tell which of the five terms is the median. Insufficient.

Now, if I put them together:
x > y and x - y < 1, make x = 3 and y = 2.5
Unordered list: 3, 2.5, 3 + 2.5, 3 - 1, 2.5 + 1 --> 3, 2.5, 5.5, 2, 3.5
Ordered list: 2, 2.5, 3, 3.5, 5.5
"3" is the median, so in this case, "x" is the median.

Try a different case:
Make x = 1/2 and y = -1/4
Unordered list: 1/2, -1/4, 1/2 + (-1/4), 1/2 - 1, -1/4 + 1 --> 1/2, -1/4, 1/4, -1/2, 3/4
Ordered list: -1/2, -1/4, 1/4, 1/2, 3/4
"1/4" is the median, so in this case, "x + y" is the median.

There is still more than one value that could be the median. Both statements together are insufficient.

Answer: E.
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Re: Which of the 5 terms x, y, x + y - Statistics - DS &nbs [#permalink] 11 Aug 2018, 10:41
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Which of the 5 terms p, q, p + q, p – 1, and q + 1 represent

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