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

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

GMAT assassins aren't born, they're made,
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink]
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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]
[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]
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]
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]
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)
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink]
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This is a question with a very subtle trap laid out for the unsuspecting. This is also a question where you can eliminate some answer options, just by looking at the statements given as part of the question.

The range of a given set of numbers is the difference between the greatest and the smallest numbers. So, essentially, it’s a positional value since it depends on the relative positions of the numbers involved.

At first look, although 29 appears to be the biggest number in the set, we cannot say anything till we know the exact values of p, q and r. Therefore, any statement/combination that gives us unique values/ranges for these variables will help us answer the question.

Statement I is insufficient since it does not provide any information about r. It also does not provide us with complete information about q.
Think about it! At least one of q and r can be greater than 29 and the range will be unknown since we do not the exact values of either q or r.

Answer options A and D can be eliminated. Possible answer options are B, C or E.

Statement II is insufficient because of similar reasons in that, it does not provide any information about q. Neither does it tell us anything about p.
p can be smaller than 5 and q can be greater than 29. p can be greater than 5 and q can be smaller than 29.

Answer option B can be eliminated. Possible answer options are C or E.

Combining statements I and II, the only thing we can say conclusively is that 5<p<15. We still do not know about the positions of q and r.
The combination of statements is also insufficient. Answer option C can be eliminated.

The correct answer option is E.

Hope this helps!
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink]
even with the 2 statements together, q is effectively unbounded. That is the crux of this question.
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink]
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Re: The numbers of books read by 7 students last year were 10, 5 [#permalink]
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