Set T consist of 19 elements. The average of set T is L.

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 366
Joined: Fri Jun 05, 2015 3:35 am
Thanked: 3 times
Followed by:2 members
Set T consist of 19 elements. The average of set T is L. If a new element is added to the set and the average grows by K%, what is the value of the element?

�. L (1+K/5)
B. L*(K/100) - 20L
C. 20L (1 + K/100)
D. 20 (1+K/100) - 19L
E. L*K/5 - 19L

OA: A

User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Sat Mar 17, 2018 1:31 am
NandishSS wrote:Set T consist of 19 elements. The average of set T is L. If a new element is added to the set and the average grows by K%, what is the value of the element?

�. L (1+K/5)
B. L*(K/100) - 20L
C. 20L (1 + K/100)
D. 20 (1+K/100) - 19L
E. L*K/5 - 19L

OA: A
The value of New element = Old Average + Growth in the average

i,e, Value of New Element = L+(K/100)*20L = L (1+20K/100) = L (1+K/5)

Answer: option A
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Mar 17, 2018 3:37 am
NandishSS wrote:Set T consist of 19 elements. The average of set T is L. If a new element is added to the set and the average grows by K%, what is the value of the element?

�. L (1+K/5)
B. L*(K/100) - 20L
C. 20L (1 + K/100)
D. 20 (1+K/100) - 19L
E. L*K/5 - 19L
Let L = 10 and the added element = 10.
Since the added element (10) is equal to the original average (also 10), the average for the set DOES NOT CHANGE when the new element is added, with the result that K=0%.
The question stem asks for the value of the added element: 10.
Now plug L=10 and K=0 into the answers to see which yields the target value of 10.
Only A works:
L(1 + K/5) = 10(1 + 0/5) = 10.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Master | Next Rank: 500 Posts
Posts: 366
Joined: Fri Jun 05, 2015 3:35 am
Thanked: 3 times
Followed by:2 members

by NandishSS » Sat Mar 17, 2018 4:49 am
GMATGuruNY wrote:
NandishSS wrote:Set T consist of 19 elements. The average of set T is L. If a new element is added to the set and the average grows by K%, what is the value of the element?

�. L (1+K/5)
B. L*(K/100) - 20L
C. 20L (1 + K/100)
D. 20 (1+K/100) - 19L
E. L*K/5 - 19L
Let L = 10 and the added element = 10.
Since the added element (10) is equal to the original average (also 10), the average for the set DOES NOT CHANGE when the new element is added, with the result that K=0%.
The question stem asks for the value of the added element: 10.
Now plug L=10 and K=0 into the answers to see which yields the target value of 10.
Only A works:
L(1 + K/5) = 10(1 + 0/5) = 10.

The correct answer is A.
HI Guru,

Can we take all the elements as 2 in these kinds of question?

What are easiest numbers to plug in?

I plugged in other numbers but struggled :-(

Thanks
Nandish

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Mar 17, 2018 6:07 am
NandishSS wrote:HI Guru,

Can we take all the elements as 2 in these kinds of question?

What are easiest numbers to plug in?

I plugged in other numbers but struggled :-(

Thanks
Nandish
The goal is to plug in easy numbers for L and K.

Let L = 2.
Sum of the original 19 numbers = (count)(average) = 19*2 = 38.
Let K = 50, implying that the average increases 50% from 2 to 3.
Since the average of the resulting set of 20 numbers = 3, the sum of the resulting set of twenty numbers = (count)(average) = 20*3 = 60.
Since the sum increases from 38 to 60, the added element = 60-38 = 22.

The question stem asks for the value of the added element: 22.
Now plug L=2 and K=50 into the answers to see which yields the target value of 22.
Only A works:
L(1 + K/5) = 2(1 + 50/5) = 22.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Thu Mar 22, 2018 2:57 pm
NandishSS wrote:Set T consist of 19 elements. The average of set T is L. If a new element is added to the set and the average grows by K%, what is the value of the element?

�. L (1+K/5)
B. L*(K/100) - 20L
C. 20L (1 + K/100)
D. 20 (1+K/100) - 19L
E. L*K/5 - 19L
We use the formula: average = sum/number, which can be re-expressed as: average x number = sum. Thus, we see that the sum of set T is 19L.

If one element, say x, is added to set T, the new sum is (19L + x), and there are now 20 elements in the set. We can create the equation:

L(1 + K/100) = (19L + x)/20

20L(1 + K/100) = 19L + x

20L + 20LK/100 = 19L + x

L + 20LK/100 = x

L + LK/5 = x

L(1 + K/5) = x

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Legendary Member
Posts: 2218
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members

by swerve » Fri Mar 23, 2018 11:21 am
Hi NandishSS,

We can solve this PS question using Mean = Sum/#

Sum(19) = 19L

Sum(20) = 20*L(1+k/100)

Hence added value = 20L + KL/5 - 19L = L + KL/5. Option A.

Regards!