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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]

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11 Jun 2010, 07:44
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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
[Reveal] Spoiler: OA
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Re: Need help on Range problem in Data Sufficiency [#permalink]

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11 Jun 2010, 07:55
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]

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28 Aug 2013, 07:53
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]

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05 Sep 2013, 08:08
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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]

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03 Jan 2015, 10:58
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink]

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03 Jan 2015, 13:20
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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

[Reveal] Spoiler:
E

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

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13 Jan 2016, 05:23
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink]

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13 Jan 2016, 23:09
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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

In the original condition, there are 3 variables(p,q,r), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2), it becomes 5<p<r<15. However, you don’t know q’s value, which is not sufficient. Therefore, the answer is E.

 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink]

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15 Jul 2016, 09:37
[quote="gautamsubrahmanyam"]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

E
Q's lower limit is known = greater than 5 but upper limit is unknown , so range cannot be calculated
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The numbers of books read by 7 students last year were 10, 5 [#permalink]

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17 Jan 2017, 08:22
clearly both alone are insuff. taking 1 and 2 we don't know about q it can be 6 or more than 29 so diff ans. so ans is E.
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink]

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17 Jan 2017, 08:29
we don't know the value of q from any of the statement, hence ans is E. SIMPLE
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink]

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18 Jan 2017, 11:28
The value of q cannot be ascertained for sure. If it is < 29, then we would know the range, but if it is > 29, then the range will be (p-5)
Re: The numbers of books read by 7 students last year were 10, 5   [#permalink] 18 Jan 2017, 11:28
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