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13 Jul 2026, 12:39
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Bunuel
Mode will always be 27 as that's the only number that repeats twice
Avg = 99+x/6
Case 1: 27 30 33
a. Median = 30; Average = 33
99 + x/6 = 33
x = 99
In that case , median = 24. Doesn't match. Eliminate this.
b. Median = 33 ; Avg = 30
x = 180-99
x = 81
In that case, median = 24. Not 33. Eliminate.
Case 2: 21 24 27
a. Median = 24 ; Avg = 21
x = 126 - 99 = 27
Median = 48/2 = 24 ; Valid
b. Median = 21 ; Avg = 24
x = 45 ; median = 24. Eliminate
Case 3: 24 27 30
a. Median = 24 ; Avg = 30
x = 180 - 99 = 81
Median = 24 ; Valid
b. Median = 30 ; Average = 24
This is not possible.
Range = 81 - 27 = 54
Option B
13 Jul 2026, 12:57
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x,6,18,21,27,27
mode=27
so combination can be 21,24,27 or 24,27,30 as median cannot be greater than 27
mean = 99+x / 6
let mode=27, median=24, mean=21, then x=27
let mode=27, median=24, mean=30, then x=81
range = 81-27 =54
Ans B
mode=27
so combination can be 21,24,27 or 24,27,30 as median cannot be greater than 27
mean = 99+x / 6
let mode=27, median=24, mean=21, then x=27
let mode=27, median=24, mean=30, then x=81
range = 81-27 =54
Ans B
13 Jul 2026, 13:05
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My answer is B.) 54
Mode definition- number with highest frequency in the set.
27 has a frequency of 2. So if x is equal to any other numbers in the set then there will be two numbers with a frequency of 2- Not satisfying the condition of UNIQUE mode.
Only unique mode possible= 27.
Mode at 27, mean and median can be (21,24,27) or (24,27,30) or (27,30,33)
For (21,24,27)-
If Mean= 21. For mean to be 21; x= 27. (21*6-(6+18+21+27+27)= x = 27)
Let's check if Median is 24
Median = 6,18,21,27,27,27. Median= (21+27)/2 = 24. VALID
If Mean= 24. For mean to be 24; x= 45. (24*6 - 99) = x = 45
Lets check if median is 21.
Median= 6,18,27,27,45. Median= 24. NOT VALID
For (24,27,30)
If Mean= 24, we know from above x=45
And median is 24 hence NOT VALID
If Mean= 30, x= 81; (30*6-99)
Lets check if median is 24. For any value of x>=27; median =24. VALID
For (27,30,33)
If Mean= 30, x=81 (from above)
Median will be 24 (from above) and not 33. NOT VALID
If mean=33, x= 99 (33*6-99)
As x>=33; median =24. NOT VALID.
VALID values of x=27, 81. Range= 81-27=54
PS. We can notice when x>=27, median is always 24 and x=27 when mean 21; So for all means greater than 21, median will be 24 only.
Hence we can eliminate the calculation. (27,30,33) is not valid because it does not consist of 24 (median). And in other two combinations, only one sequence is valid where median is 24 and mode is 27.
Mode definition- number with highest frequency in the set.
27 has a frequency of 2. So if x is equal to any other numbers in the set then there will be two numbers with a frequency of 2- Not satisfying the condition of UNIQUE mode.
Only unique mode possible= 27.
Mode at 27, mean and median can be (21,24,27) or (24,27,30) or (27,30,33)
For (21,24,27)-
If Mean= 21. For mean to be 21; x= 27. (21*6-(6+18+21+27+27)= x = 27)
Let's check if Median is 24
Median = 6,18,21,27,27,27. Median= (21+27)/2 = 24. VALID
If Mean= 24. For mean to be 24; x= 45. (24*6 - 99) = x = 45
Lets check if median is 21.
Median= 6,18,27,27,45. Median= 24. NOT VALID
For (24,27,30)
If Mean= 24, we know from above x=45
And median is 24 hence NOT VALID
If Mean= 30, x= 81; (30*6-99)
Lets check if median is 24. For any value of x>=27; median =24. VALID
For (27,30,33)
If Mean= 30, x=81 (from above)
Median will be 24 (from above) and not 33. NOT VALID
If mean=33, x= 99 (33*6-99)
As x>=33; median =24. NOT VALID.
VALID values of x=27, 81. Range= 81-27=54
PS. We can notice when x>=27, median is always 24 and x=27 when mean 21; So for all means greater than 21, median will be 24 only.
Hence we can eliminate the calculation. (27,30,33) is not valid because it does not consist of 24 (median). And in other two combinations, only one sequence is valid where median is 24 and mode is 27.
Bunuel
