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# Which of the following procedures is always equivalent to adding 5

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Math Expert
Joined: 02 Sep 2009
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Which of the following procedures is always equivalent to adding 5  [#permalink]

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26 Nov 2015, 05:44
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Difficulty:

65% (hard)

Question Stats:

52% (01:40) correct 48% (01:40) wrong based on 133 sessions

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Which of the following procedures is always equivalent to adding 5 given numbers and then dividing the sum by 5 ?

I. Multiplying the 5 numbers and then finding the 5th root of the product.
II. Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left.
III. Ordering the 5 numbers numerically and then selecting the middle number.

(A) None
(B) I only
(C) II only
(D) III only
(E) I and III

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Re: Which of the following procedures is always equivalent to adding 5  [#permalink]

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26 Nov 2015, 08:07
Let's choose the 5 numbers to be {1, 2, 3, 4, 5}

adding 5 given numbers and then dividing the sum by 5 , that is we find the average .
Average = (1+2+3+4+5)/5 = 3

1.Multiplying the 5 numbers and then finding the 5th root of the product.
Product = 1*2*3*4*5 = 120
Fifth root of 120 is not 3 . (3^5 = 243)

II. Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left.
Sum = 15
2*Sum = 30
then moving the decimal point one place to the left , that is answer is 3

Doubling the sum and moving the decimal point one place to the left is essentially same as by dividing number of terms(5) because we double the sum and then divide by 10 here (5*2)
Always true

III. Ordering the 5 numbers numerically and then selecting the middle number.
Our middle number is 3 , which is same as average . But this will only be true incase the numbers are equally spaced , i.e
have the same common difference.
If the numbers are 1,2,3,4,10 ; then average = 4 , but our middle term = 3 .

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Re: Which of the following procedures is always equivalent to adding 5  [#permalink]

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27 Nov 2015, 22:20
AS Given ,
Adding 5 number and dividing the sum by 5 which can be stated as = Sum/5 = Sum *0.2
From The Given Statements
II- Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left.
=Sum*0.2

Hence C.
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Re: Which of the following procedures is always equivalent to adding 5  [#permalink]

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17 Apr 2019, 09:01
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Re: Which of the following procedures is always equivalent to adding 5   [#permalink] 17 Apr 2019, 09:01
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