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

Question

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

Show 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

Show Answer

Official Answer

E

If this question felt shaky, try an adaptive mini quiz of similar problems in GMAT Club Forum Quiz →. Free plan gives 5 questions per day.

sjayasa · Answer

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?

SUNGMAT710 · Answer

OA E ..Q could be greater than 29..

monirjewel · Answer

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

EMPOWERgmatRichC · Answer

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:  E

GMAT assassins aren't born, they're made,
Rich

MathRevolution · Answer

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.

LogicGuru1 · Answer

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

vikasp99 · Answer

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.

Nahid078 · Answer

we don't know the value of q from any of the statement, hence ans is E. SIMPLE

malavika1 · Answer

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)

CrackverbalGMAT · Answer

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!

wishmasterdj · Answer

even with the 2 statements together, q is effectively unbounded. That is the crux of this question.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards