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The average of a set of six positive numbers is 30.

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The average of a set of six positive numbers is 30. [#permalink]  17 Sep 2018, 20:30
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66% (00:54) correct 34% (00:40) wrong based on 50 sessions

The average of a set of six positive numbers is 30.

 Quantity A Quantity B The average of the numbers in the set after replacing the smallest number in the set with 0 The average of the remaining numbers in the set after removing the smallest number from the set

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The average of a set of six positive numbers is 30. [#permalink]  17 Sep 2018, 23:34
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Carcass wrote:
The average of a set of six positive numbers is 30.

 Quantity A Quantity B The average of the numbers inthe set after replacing thesmallest number in the setwith 0 The average of the remainingnumbers in the set afterremoving the smallest numberfrom the set

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Now in a set of 6 numbers if the lowest number is replaced by zero than the average of these numbers will be less than the original value.

Now in QTY B if we remove the lowest number then the average of these 5 nos. will always be greater than QTY A

in other words $$\frac{X}{6} < \frac{X}{5}$$ (x = total number which will remain same in both cases)
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Re: The average of a set of six positive numbers is 30. [#permalink]  14 Jan 2019, 00:32
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Expert's post
Lets dumb it down.

the average of 6 POSITIVE INTEGERS is 30, that means that the sum of all 6 numbers is 180

Option A says that we find the average replace the smallest number with 0.
lets say the smallest number is 1

(180-1)/6= 179/6 which is pretty close to 30

Option B says that we find the average after removing the smallest number, that means the sum is now divided by 5
lets also assume the smallest number is 1
(180-1)/5 = 179/5, which is close to 36
in this instance B is greater than A

now lets suppose that the smallest number is 29
(We choose 29 since that's the biggest "small" number it can be,if the average is 30, just make the first 4 numbers 30, the greatest number 31, and the smallest number is 29)

For option A that would be
(180-29)/6= 151/6, which is close to 25

For option B that would be
(180-29)/5 = 151/5, which is close to 30,

in each scenario, B is the greater quality.
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Re: The average of a set of six positive numbers is 30. [#permalink]  14 Jan 2019, 00:42
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Expert's post
Carcass wrote:

The average of a set of six positive numbers is 30.

 Quantity A Quantity B The average of the numbers in the set after replacing the smallest number in the set with 0 The average of the remaining numbers in the set after removing the smallest number from the set

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

The set is the same.

So, the smallest number here will be >0 as all are positive numbers, so when you replace the number with 0, the total will become less than previous and so teh average will also go down.
Now, when you remove the smallest number, the average will never go down. It will remain the same at the least. Don't go by the idea that it will always be less. Because, if all numbers are the SAME, the average will remain the SAME.
It is nowhere given that the numbers are different. You can go wrong if say A was the initial average and B was average after removal of the smallest number..... Here answer will be D and you would choose B wrongly.

so B>A
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: The average of a set of six positive numbers is 30.   [#permalink] 14 Jan 2019, 00:42
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