The numbers of books read by 7 students ....

[aakhoja]

The numbers of books read by 7 students last year were 10, 5, p, q, r, 29, and 20. What was the range of numbers of books read by the 7 students last year?

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

I am torn between C and E (what a surprise!). Not sure why the answer is E. Can someone please help me understand? Thanks!

[RB_51273]

To know the range you need the maximum and minimum value

Statement one:5<p<q; P and q are greater than 5,P and q not known and can have any value more than;Hence insufficient
Statement two:p<r<15;p and r can have any value less than 15 ,Insufficient

Statement I and II together

5<p and p<15 can ascertain only value of p between 5 and 15,Still value of q and r are not within any limit;Insufficient

Ans:E

Hope it will help

Tks
Ram

[aakhoja]

Ram thanks for a prompt response. Taking both 1 and 2 into account, if you visualize 5 and 15 on a number line, I see p, q, r all between 5 and 15. If thats correct, then it is possible to determine the range. What am I missing? Best regards!

[jenniferdpitts]

q>p - therefore q could be more than 29. This prevents you from knowing the upper limit in the range.

[aakhoja]

q is not bound makes sense for the ans to be 'E'. All we know is that p and q are greater than 5 from (1) and p and r are less than 15 from (2) but we don't know the upper limit on q which can change the range. Thanks for all the help! Happy New Year!

[RonPurewal]

The numbers of books read by 7 students last year were 10, 5, p, q, r, 29, and 20. What was the range of numbers of books read by the 7 students last year?

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

I am torn between C and E (what a surprise!). Not sure why the answer is E. Can someone please help me understand? Thanks!

if we take the two statements together, we can see that p, q, and r are all greater than 5. therefore, the minimum number of books is 5.

since we have the minimum, and the range is just the difference between the minimum and the maximum, it follows that we just have to find the maximum.

if you combine the two statements, we can get
5 < p < r < 15
AND
q is somewhere greater than p
...but that's all we know.
q could be:
* between p and r
* equal to r
* between r and 15
* equal to 15
* greater than 15
if the last of these is true, then the maximum is whatever "q" is, so it's undetermined. therefore, insufficient, so the answer is (e).

[yousuf_azim]

Hello,

U can't define the value of the given variables with give statement:1 or 2

[jnelson0612]

Hello,

U can't define the value of the given variables with give statement:1 or 2

Right. We end up learning that 5<p<r<15, but we are never able to determine q's value. Thus, we can't get a maximum value for our range. It could be 29 is q<29 or it could be infinite, given that q could be huge.