A set S contains five numbers k, k + 1, 2k - 1, 5k + 7 and 6k + 8. If

Question

A set S contains five numbers k, k + 1, 2k - 1, 5k + 7 and 6k + 8. If k is a positive integer, determine its value.

(1) The median of the elements of S is k + 1.

(2) The average of the elements of S is less than 10.

Given OA is A.

My doubt: A is definitely true for k=1. However for k=2, k+1=2k-1, which is also compatible with stmt. 1. This means we have 2 values for k..1 and 2. Then how can A alone be sufficient?

sabineodf · Answer

I got this wrong, eager to see the solution. I worked it out likes this:

Statement 1: insuff

Because k can have several values to meet those conditions (I think?)

if k = 1 
k---k+1---2k-1---5k+7---6k+8
1 2 1 12 14

Median = 2

if k = 2
k---k+1---2k-1---5k+7---6k+8
2 3 3 17 20

Median = 3

So K could be 2 or 3, and probably many more numbers (??)

Statement 2: average of set is less than 10

Using the same examples from above the averages are 6 and 8, both under 10. ---> insuff

Not sure how combining these would help either, but there may very well be a way!

Don't understand how the OA is A...

I would have gone for E on an exam, maybe C.

Moumila · Answer

It's given that the average is less than 10 , so
as per condition 2 :

(k+ k+1 + 2k-1 +5k+7 + 6k+8) / 5 < 10
(15k + 15) /5 <10
3k + 3 < 10
3k < 7 
and k is integer
so k = 1, 2

For k=1, s={1 , 2, 1, 12, 14} and Median= 2 (condition 1 satisfied)

for k=2, s={2, 3, 3, 17, 20} and Median =3 (condition 1 satisfied)

So K=1 and 2

sabineodf · Answer

Yeah but the average being less than 10 is given in statement nr. 2, so how can the answer be "A) Statement 1 alone is sufficient?"

Is there something in the prompt that I'm missing?

sabineodf · Answer

Re-attempting this after some thought:

Placing all values in a number line, it is unclear where k+1 and 2k-1 go, since if k is given different values it is clear that they will shift depending on values for K

akhilbajaj · Answer

sabineodf , for statement 1, why don't you consider the equation as  k+1>=2k-1 
In this case, you would get  k<=2 , which means k=1,2. 
Thus, insufficient.

Please clarify.

sabineodf · Answer

akhilbajaj

I tested the values.

If k = 2, then as you said 2+1=2*2−1 (3=3). But statement 1) tells us that k+1 is the median, and I think that this statement means that it is the  only  median, which is wouldn't be if K=2 because then we have a shared median, which leaves that k=1 since it's the only number that fits the parameters, and gives a unique value for the median.

I'm not 100% sure on this.

PrepTap · Answer

In this question, it is said that k+1 is the median, so you should not assume any extra information.

sabineodf · Answer

K+1 = median

7 values. There must be 3 values on either side of k+1. If k+1 = 2k-1 then they are interchangeable and k+1 is not 100 % the median. But we are given that it IS the median, so that means there must be 2 values either side. I don't think I've made any extreme assumptions/

manishkhare · Answer

Option A :The median of the elements of S is k + 1 .There are 5 elements so two elements on the left and two elements on the right of k+1
so at most k+1>=2k-1 or k+1<=5k+7 .Solving first equation gives us : k<=2 .Second gives k>=6/4 so k=2

Option B : (k +k + 1+2k - 1 +5k + 7 + 6k + 8)/5 < 10 .Solving 3k+3<10 so k<7/3 .k can have values 1,2 So B is not correct .

Hence A is the correct option.

Press Kudos if you like the solution.

Regards,
Manish Khare

teplyam · Answer

I think the solution A would be correct if we changed 5k + 7 to 5k - 7: 
 set S contains five numbers k, k + 1, 2k - 1, 5k - 7 and 6k + 8. If k is a positive integer, determine its value.

A set S contains five numbers k, k + 1, 2k - 1, 5k + 7 and 6k + 8. If

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

A set S contains five numbers k, k + 1, 2k - 1, 5k + 7 and 6k + 8. If

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