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The numbers of books read by 7 students last year were 10, 5

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The numbers of books read by 7 students last year were 10, 5 [#permalink] New post 11 Jun 2010, 06:44
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The numbers of books read by 7 students last year were 10, 5, p , q , r , 29 and 20. What was the range of the numbers of books read by the 7 students last year?

(1) 5 < p < q
(2) p < r < 15

[Reveal] Spoiler:
How I went ahead 1) Insuff because no info on r
2) Insuff because no info on q

1) & 2) p>5 and p<q and p<r<15 => p=b/w 6 and 13 max value of p =13,min value of p possible = 6
max value of r=14,min value of r=7 Range = Largest-Smallest So 29-5=24.So answer is (C) .Why is this wrong.Please help
[Reveal] Spoiler: OA
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Re: Need help on Range problem in Data Sufficiency [#permalink] New post 11 Jun 2010, 06:55
What about q? There is only one statement that talks about q which says q>p. That doesn't tell us anything about the maximum possible value of q. What if q>29?
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Re: Need help on Range problem in Data Sufficiency [#permalink] New post 28 Aug 2013, 06:53
sjayasa wrote:
What about q? There is only one statement that talks about q which says q>p. That doesn't tell us anything about the maximum possible value of q. What if q>29?



OA E ..Q could be greater than 29..
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink] New post 05 Sep 2013, 07:08
By combining both statements , we may get range of P & R. But we are not getting any maximum possible value of Q. SO E is the correct option
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink] New post 03 Jan 2015, 09:58
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink] New post 03 Jan 2015, 12:20
Expert's post
Hi All,

Note-taking is a MUST on Test Day. Here, with so many numbers and variables to keep track of, missing one small detail could very easily cost you the question (and not taking enough notes is a silly reason to get a question wrong)..

Here, we're given 7 values for the number of books read by 7 students: 5, 10, 20, 29, P, Q and R.

**NOTE: I have arranged the numbers from least to greatest; the variables could be ANY number greater than or equal to 0)**

We're asked for the RANGE of values, which means that we'll need to know the LARGEST - SMALLEST numbers in this set of 7 values.

Fact 1: 5 < P < Q

Since we don't know anything about the values of P, Q and R, it would be easy to say this Fact is insufficient, but here's the PROOF:

IF....
P = 6
Q = 7
R = 8
Range = 29 - 5 = 24

P = 6
Q = 7
R = 100
Range = 100 - 5 = 95
Fact 1 is INSUFFICIENT

Fact 2: P < R < 15

Much like in Fact 1, we don't know the value of P, Q and R. Here's the PROOF that this is insufficient.

IF....
P = 6
R = 7
Q = 8
Range = 29 - 5 = 24

P = 6
R = 7
Q = 50
Range = 50 - 5 = 45
Fact 2 is INSUFFICIENT

Combined, we know...

5 < P < Q
P < R < 15

We can use the SAME TESTs that we used in Fact 2 (above) to prove that the answer is inconsistent.
Combined, INSUFFICIENT

Final Answer:
[Reveal] Spoiler:
E


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Re: The numbers of books read by 7 students last year were 10, 5   [#permalink] 03 Jan 2015, 12:20
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