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

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by NandishSS » Sat Mar 17, 2018 12:44 am
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
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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
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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.
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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
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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.
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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

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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!
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