GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 17:03 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  A set of 7 different integers has a median of 9, range of 11

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3335
Location: India
GPA: 3.12
A set of 7 different integers has a median of 9, range of 11  [#permalink]

Show Tags

10 00:00

Difficulty:   75% (hard)

Question Stats: 59% (02:17) correct 41% (02:07) wrong based on 94 sessions

HideShow timer Statistics

A set of 7 different integers has a median of 9, a range of 11, and an average of 10. What is
the highest possible value of the lowest integer in the set?

A. 3
B. 4
C. 5
D. 6
E. 8

Source: Experts Global

_________________
You've got what it takes, but it will take everything you've got
Senior Manager  G
Joined: 29 Dec 2017
Posts: 378
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33 GMAT 2: 690 Q47 V37 GMAT 3: 710 Q50 V37 GPA: 3.25
WE: Marketing (Telecommunications)
A set of 7 different integers has a median of 9, range of 11  [#permalink]

Show Tags

2
pushpitkc wrote:
A set of 7 different integers has a median of 9, a range of 11, and an average of 10. What is
the highest possible value of the lowest integer in the set?

A. 3
B. 4
C. 5
D. 6
E. 8

Source: Experts Global

If integers are all different, then max (1st) will be if terms 1,2,3 and 4 (which is median) will be consecutive, so

6,7,8,9,x,y, 6+11.

We have to check, since we know that sum of the set = 7*10=70, hence 6+7+8+9+x+y+17=70, x+y = 23, x can be 10 and y=13 - it works. Answer (D)

Originally posted by Hero8888 on 21 May 2018, 12:25.
Last edited by Hero8888 on 22 May 2018, 12:39, edited 1 time in total.
Current Student B
Affiliations: All Day Test Prep
Joined: 08 May 2018
Posts: 75
Location: United States (IL)
Schools: Booth '20 (A)
GMAT 1: 770 Q51 V49 GRE 1: Q167 V167 GPA: 3.58
Re: A set of 7 different integers has a median of 9, range of 11  [#permalink]

Show Tags

2
A set of 7 different integers has a median of 9, a range of 11, and an average of 10. What is
the highest possible value of the lowest integer in the set?

A. 3
B. 4
C. 5
D. 6
E. 8

Let's call our numbers in ascending order a, b, c, d, e, f, g.

d = median = 9 ----------> a, b, c, 9, e, f, g

We are looking for max "a" can be.

Given that each number is different the absolute max "a" could possibly be is 6. Therefore eliminate E) as an answer choice.

To have an average of 10 the numbers must sum to 70(70/7 = 10). Start by plugging in highest number remaining for "a" to see if it works.

If "a" = 6 then b = 7, c = 8, and g = 17(since range must be 11) ----> 6, 7, 8, 9, e, f, 17
------> to satisfy our requirements that the set sums to 70, e & f need to sum to 23 and each be between 9 - 17. e = 11, f = 12 works to give us a set of: 6, 7, 8, 9, 11, 12, 17

median = 9
range = 11
mean = 10

_________________
University of Chicago Booth School of Business, Class of 2020

Unlimited private GMAT Tutoring in Chicago for less than the cost a generic prep course. No tracking hours. No watching the clock.

Manager  B
Joined: 03 Oct 2016
Posts: 122
Re: A set of 7 different integers has a median of 9, range of 11  [#permalink]

Show Tags

pushpitkc wrote:
A set of 7 different integers has a median of 9, a range of 11, and an average of 10. What is
the highest possible value of the lowest integer in the set?

A. 3
B. 4
C. 5
D. 6
E. 8

Let numbers be:

a, b, c, 9, d, e, f

f-a=11
Avg=10 -> Sum of numbers = 70.

What is the maximum value of a?

a, b and c will be < 9 and d, e and f will be more than 9.

The maximum value of 'a' will be when the decrease of each term less than 9 is minimum.

So, 6, 7, 8, 9, d, e, f

Note: We cannot have all numbers less than 9 be 8 because its given that the numbers are different.

We need to confirm that the remaining 70 - (6+7+8+9) = 40 is sufficient for d, e and f to be different.
We are also given f=a+11=6+11=17 so, now we just need to confirm if d and e can be different and greater than 9.

d+e = 40-f= 40-17=23 clearly, we can have d, e values different and greater than 9 (d+e = 11+12 or 10 + 13).

_________________ Non-Allergic To Kudos Senior Manager  G
Joined: 31 May 2017
Posts: 334
Re: A set of 7 different integers has a median of 9, range of 11  [#permalink]

Show Tags

A set of 7 different integers has a median of 9, a range of 11, and an average of 10. What is
the highest possible value of the lowest integer in the set?

A. 3
B. 4
C. 5
D. 6
E. 8

Step 1: The median of odd set of integers is always the middle number - In this if median is 9 , then 4th digit is 9.

Step 2: If 4th digit is 9 and all digits are different, then numbers smaller than median can be 6,7 and 8.

Step 3: The range is 11 then one option for highest number could be 17 [6+11]

Step 4: The average of 7 numbers are 10 , so sum of 7 digits is 70. From the steps above , we know the numbers can be 6,7,8,9 and 17. The sum of 5 digits is equal to 47.

Now we know that sum is equal to 70 and sum of first 5 digits is 43. From this we get the sum of digits 5 and 6 is equal to 23 [70-47]

the fifth and sixth digits can be 10+13 or 11+12. Both are greater than 9 and lesser than 17 and matches our criteria.

Ans: 6
_________________
Please give kudos if it helps

Resources
| | | | |
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8085
Location: United States (CA)
Re: A set of 7 different integers has a median of 9, range of 11  [#permalink]

Show Tags

pushpitkc wrote:
A set of 7 different integers has a median of 9, a range of 11, and an average of 10. What is
the highest possible value of the lowest integer in the set?

A. 3
B. 4
C. 5
D. 6
E. 8

Since the average is 10, we have a sum of 7 x 10 = 70.

Also, since we need to determine the highest possible value of the lowest integer in the set, we can let that value be 6 so that the 3 numbers less than the median are 6, 7, 8 (recall that all the integers are different and the median is 9). Since the range is 11, the largest number is 6 + 11 = 17. Therefore, so far we have a sum of 6 + 7 + 8 + 9 + 17 = 47. This leaves us a sum of 70 - 47 = 23 for the remaining two numbers. So we can let them to be 11 and 12 (or, 10 and 13). Therefore, we see that it is totally feasible to have 6 as the smallest integer and it will also be the highest possible value for the smallest integer since if we take any integer higher than that, either the median will not be 9 or the numbers will not be all different.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

VP  P
Joined: 07 Dec 2014
Posts: 1222
A set of of 7 different integers has  [#permalink]

Show Tags

aghosh54 wrote:
A set o f 7 different integers has a median of 9, range of 10, and average of 9. What is the lowest possible value of the smallest integer in the set?

A) 6
B) 5
C) 4
D) 3
E) 2

Not getting the concept of such type of questions. Need help.

not really conceptual, but here's how I do it:
then do range:
(9+x)-(9-x)=10→
x=5
subtract 5 from 1st term; add 5 to last term:
4-9-9-9-9-9-14
that works, but we can still go lower
subtract 1 from 1st and last terms, and add 2 to 6th:
3-9-9-9-9-11-13
that works too, and 3 is as low as we can go for 1st term
to get down to 2, we'd have to add 2 to 6th term, which would make it higher than last term, 12
3
D
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3335
Location: India
GPA: 3.12
Re: A set of of 7 different integers has  [#permalink]

Show Tags

aghosh54 wrote:
A set o f 7 different integers has a median of 9, range of 10, and average of 9. What is the lowest possible value of the smallest integer in the set?

A) 6
B) 5
C) 4
D) 3
E) 2

Not getting the concept of such type of questions. Need help.

We need 7 different integers with a range of 10

First integer in the set: x
Last integer in the set: x+10
Since the median is 9, the 4th integer is 9

(If the set has an odd number of elements, the median is the middle value)

The lowest value that the 5th and 6th integers can take is 10 and 11. In order to have
the lowest possible value for the smallest integer, the largest integer will have a value
of 12. So, the set will look like this - 2,b,c,9,10,11,12
In this set, the maximum value of b & c is 15. As the sum is 7*9 = 63(average - 9), b+c = 19.

If the lowest integer were slightly bigger, the set could be 3,7,8,9,11,12,13 whose sum is 63.

Therefore, the lowest possible value of the smallest integer in the set is 3(Option D)
_________________
You've got what it takes, but it will take everything you've got
Director  G
Joined: 09 Mar 2018
Posts: 995
Location: India
Re: A set of 7 different integers has a median of 9, range of 11  [#permalink]

Show Tags

pushpitkc wrote:
A set of 7 different integers has a median of 9, a range of 11, and an average of 10. What is
the highest possible value of the lowest integer in the set?

A. 3
B. 4
C. 5
D. 6
E. 8

Source: Experts Global

Set of 7 different integers

a b c d e f g

d = 9

now a can be 6

D
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: A set of 7 different integers has a median of 9, range of 11   [#permalink] 18 Feb 2019, 00:59
Display posts from previous: Sort by

A set of 7 different integers has a median of 9, range of 11

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  