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# Is the range of them greater than 3?

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Manager
Joined: 27 Dec 2014
Posts: 84
Is the range of them greater than 3? [#permalink]

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12 Dec 2015, 03:00
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The smallest of 7 positive integers is 1. Is the range of them greater than 3?

(1) The average (the arithmetic mean) of them is 4.
(2) The median of them is 4.
[Reveal] Spoiler: OA

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Joined: 06 Oct 2013
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Re: Is the range of them greater than 3? [#permalink]

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12 Dec 2015, 07:55
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gmat2015p wrote:
The smallest of 7 positive integers is 1. Is the range of them greater than 3?
1) The average (the arithmetic mean) of them is 4.
2) The median of them is 4.

Solutions welcome

Solution:

STATEMENT 1) The average (the arithmetic mean) of them is 4.

$$Total/7=4---->Total=28$$

one of them is 1, then sum of remaining integers is 27.
if remaining integers are all 4, then 4*6=24 to get sum of 27 atleast one of them must be greater than 4.

So the range-----> $$integer(>4)-1=integer(>3)$$
SUFFICIENT.

STATEMENT 2) The median of them is 4.

1,2,3,4,4,4,4---> median=4 and range=4-1=3--> ANS: NO.
1,2,3,4,5,6,7--->median=4 and range= 7-1=6--> ANS: YES.

Hence INSUFFICIENT.

ANS. A
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Re: Is the range of them greater than 3? [#permalink]

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13 Dec 2015, 18:18
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Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

The smallest of 7 positive integers is 1. Is the range of them greater than 3?

(1) The average (the arithmetic mean) of them is 4.
(2) The median of them is 4.

In the original condition, there are 7 variables and 1 equation. In order to match with the number of equations, you need 6 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. In 1) & 2), when a question asks ‘greater than,’ you have to find a minimum value(because once find the minimum value, the rest is obviously going to be bigger than the minimum value). So, in order to find the minimum value of the range, the range can be minimum when 1,4,4,4,5,5,5. That is, range=5-1=4>3 -> yes, which is sufficient and therefore the answer is c. This is an integer question which is one of the key questions. When applying 4(A) of the mistake type, you have to find a minimum value in 1). Its range can also be minimum when 1,4,4,4,5,5,5. That is, range=5-1=4>3 -> yes, which is sufficient.
In 2), 1,4,4,4,5,5,5 range=5-1=4>3 -> yes, but 1,4,4,4,4,4,4 range=4-1=3>3 -> no, which is not sufficient.
Therefore, both C and A can be the answer. In this case, A is the answer and therefore A is the answer, You need to get this type of questions correct to reach the score range 50-51.

-> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
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Re: Is the range of them greater than 3? [#permalink]

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07 Jun 2017, 22:50
Statement 1. Smallest integer is 1, and mean = 4. So mean =4, and there is an integer '1' which is lesser than the mean.
Thus there must be at least one more integer which is greater than 4 (so as to balance out the required mean of 4).
So there must be at least one integer >4, thus Range must be > (4-1) or Range must be > 3. Sufficient.

Statement 2. Median is 4, so its possible that the middle term (4th term) is 4, and all further terms are also = 4. In this case, Range = 4-1 = 3.
But its also possible that middle term is 4, and further terms are > 4. In this case Range > 3.
So Insufficient.

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Re: Is the range of them greater than 3? [#permalink]

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08 Feb 2018, 01:43
gmat2015p wrote:
The smallest of 7 positive integers is 1. Is the range of them greater than 3?

(1) The average (the arithmetic mean) of them is 4.
(2) The median of them is 4.

EXTREME CASES ( arrange in increasing order)
1 a b c d e X
plug in abcde =1 each ( for beginning) => X>4
plug in abcde = 4 each => still X = 7

X-1 = 6 , 6>3(range) => sufficient A/D

Median =4
c=4
1 a b 4 d e X
consider 2 possibilities X=4 and X=7 => Range = 3 and 6 in this case => D rejected

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Re: Is the range of them greater than 3?   [#permalink] 08 Feb 2018, 01:43
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