When the mean of the Set A is divided by the median of the Set B, the

Question

Set A = {20, P, 80}
Set B = {1, 3, 5, 23}

When the mean of the Set A is divided by the median of the Set B, the result is 15.25. What is the remainder when P^4 is divided by the mean of the Set B?

A. 1
B. 3
C. 5
D. 6
E. 7

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Dereno · Answer

Set A = {20, P, 80}

Set B = {1, 3, 5, 23}

Mean of Set A = (100+P)/3

Mean of set B = (1+3+5+23)/4 = 32/4 = 8

Median of Set B = (3+5)/2 = 4

given that :  mean of the Set A is divided by the median of the Set B, the result is 15.25

/4 = 15.25

(100+P)/12 = 15.25

100+P = 183

P= 83

We need to find :  the remainder when P^4 is divided by the mean of the Set B

Mean of Set B = 8

(83/8) remainder is 3.

(3^4) / 8 = (3^2 * 3^2) /8

= ( 9 * 9 ) /8

= 1*1

=  1

Option A

Missinga · Answer

Mean of set A= (20+P+80)/3= (100+P)/3 
Median of set B= (3+5)/2=4 
Mean of set A/ Median of set B = 15.25 
(100+P)/3*4 = 15.25 
100+P= 15.25*3*4=183 
P=183-100=83

Mean of set B= (1+3+5+23)/4=8 
(P^4)/Mean of set B = (83^4)/8 =(83*83*83*83)/8 
When 83 is divided by 8, the remainder is 3. 
So, (83^4)/8 is same as (3^4)/8 =81/8 (It leaves in 1 as remainder)

A

MANASH94 · Answer

Mean of A = (20+P+80)/3
=(100+P)/3

Median of B = average of middle two numbers (3+5)/2=4

Now, as mentioned in the question " when the mean of the Set A is divided by the median of the Set B, the result is 15.25 " 
Hence, ((100+P)/3) / 4 = 15.25
=> (100+P)/12=15.25.
=> 100+P = 183
P=83

Now, Mean of B = (1+3+5+23)/4 = 32/4 = 8.

We need remainder when P^4 = 83 is divided by 8.
I used binomial's theorem to express 83 as (80+3)^4.
Expanding the same we will get (80^4 + 4(80^3)(3) + 6(80^2)(32) + 4(80)(3^3) + 3^4)
The remainder will be dependent on the last term which is 3^4 = 81.
When we divide 81/8 we get a remainder 1. and the other terms of the expression we get the remainders as 0 when divided by 8.

Hence Answer should be A: 1

CLStudyAbroad · Answer

Given in the question:-

Set A = {20, P, 80}
and Set B = {1, 3, 5, 23}

now, median of Set B = (3+5)/2 = 4

Now given, 
Mean of Set A/Median of Set B = 15.25
i.e. Mean of Set A/4 = 15.25 
so, Mean of A = 15.25 * 4 = 61
(20 + P + 80)/ 3 = 61 
100 + P = 183
so, P = 83

Now, mean of Set B = (1+3+5+23)/4 = 8

Now, 83/8 = 10 as quotient and 3 as remainder

so, 3^4 = 81 = 1 = (Mod 8)

Final answer:-Option (A) 1

When the mean of the Set A is divided by the median of the Set B, the

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