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# If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x

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Math Expert
Joined: 02 Sep 2009
Posts: 56251
If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x  [#permalink]

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16 Aug 2016, 06:07
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35% (medium)

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74% (02:01) correct 26% (02:07) wrong based on 148 sessions

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If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 3x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?

A. 3
B. 4
C. 5
D. 6
E. 8

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Re: If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x  [#permalink]

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16 Aug 2016, 07:32
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Bunuel wrote:
If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 3x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?

A. 3
B. 4
C. 5
D. 6
E. 8

given that x is positive and single digit and based on 4/3*x being one of them, assume x as 3
this gives the list as 4, 6, 3, 5, 7 and when ordered, 3,4,5,6,7 and hence median is 5
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Joined: 12 Sep 2015
Posts: 3848
Re: If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x  [#permalink]

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16 Aug 2016, 07:47
Top Contributor
Bunuel wrote:
If x is a positive, single-digit integer such that (4/3)x, 2x, x, and x + 2, and 3x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?

A. 3
B. 4
C. 5
D. 6
E. 8

The big hints are that x is a 1-digit integer AND (4/3)x, 2x, x, and x + 2, and 3x – 2 are ALL integers
For (4/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9.
Now let's plug each possible value of x into the terms and see which one yields a list of consecutive integers

When x = 3, we get the following terms: (4/3)(3), 2(3), 3, 3 + 2, and 3(3) – 2.
When we evaluate these terms we get: 4, 6, 3, 5 and 7
Rearrange to get: 3, 4, 5, 6, 7. So, when x = 3, we get consecutive integers.
In this case, the MEDIAN = 5
Since 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9)

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Re: If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x  [#permalink]

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25 Sep 2018, 15:31
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Re: If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x   [#permalink] 25 Sep 2018, 15:31
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