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Bunuel
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If the median of Set A above is one less than the mode of Set A, which 27 Feb 2019, 23:38
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D
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25% (medium)

Question Stats:

77% (01:36) correct 23% (01:51) wrong based on 77 sessions

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Set A = {3, 1, 7, 5, 11, x}
If the median of Set A above is one less than the mode of Set A, which of the following is a possible value of x ?

A. 3
B. 5
C. 6
D. 7
E. 9
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D
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If the median of Set A above is one less than the mode of Set A, which 28 Feb 2019, 05:43
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Bunuel
Set A = {3, 1, 7, 5, 11, x}
If the median of Set A above is one less than the mode of Set A, which of the following is a possible value of x ?

A. 3
B. 5
C. 6
D. 7
E. 9
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avg of set = 27+x/6
now mode of set is most repeated term of set
here options can be 3,5,7 only
upon checking with all these options only at 7 we get median = ~ 5.6 ; 6 which is 1 less than mode 7
IMO D
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If the median of Set A above is one less than the mode of Set A, which 27 Mar 2020, 14:30
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I tested the answer choices:

1) Placed the vales in ascending order (smallest to largest)
2) Set this formula as a reminder, Mode = Median + 1
3) Tested the values starting with 3 for "x", mode would be 3, median would be 4, but formula is Mode = Median + 1 so "A" is out
B = Median of 5, and Median of 5, B is out
C = Median of 5.5 and mode of none or all, out
D = Median of 6 and mode of 7, fits , keep
E = No mode, out
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If the median of Set A above is one less than the mode of Set A, which 27 Mar 2020, 16:58
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Bunuel
Set A = {3, 1, 7, 5, 11, x}
If the median of Set A above is one less than the mode of Set A, which of the following is a possible value of x ?

A. 3
B. 5
C. 6
D. 7
E. 9
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The mode of the set is the most common term in that set. Since all of the other numbers in the set only appear once, then in order for the set to have a unique mode, x has to be equal to one of the other numbers in the set. (Otherwise, if x was a different number, all of the numbers in the set would be repeated exactly once, and the set would have more than one mode.)

That lets us eliminate (C) and (E) immediately.

Try the remaining answer choices, and check whether the median is one less than the mode:

(A) if x = 3, the set is 1, 3, 3, 5, 7, 11. The median is (3+5)/2 = 4, and the mode is 3. That's incorrect (we want a median that's 1 less than the mode, not 1 greater.)

(B) if x = 5, the set is 1, 3, 5, 5, 7, 11. The median is (5+5)/2 = 5, and the mode is 5. That's incorrect

(D) if x = 7, the set is 1, 3, 5, 7, 7, 11. The median is (5+7)/2 = 6, and the mode is 7. D is the correct answer.
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If the median of Set A above is one less than the mode of Set A, which 27 Mar 2020, 18:45
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Bunuel
Set A = {3, 1, 7, 5, 11, x}
If the median of Set A above is one less than the mode of Set A, which of the following is a possible value of x ?

A. 3
B. 5
C. 6
D. 7
E. 9
Show more

C and E can be eliminated immediately because if either of them were x, the set would have no mode. From there I went through the values and tested them. 7 is the only one that works, so the answer is (D).
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