Question Details

Directions (55-57): Read the following table carefully and answer the questions given below.

In the table some numbers are given and the probability of picking that number is given.

NUMBERS Probability
Q
1 6
2.5
1 3
Q − 2.5
1 3
P
1 6
4 Q 5 2
1 6
18.75
1 6
If the average of all the numbers in the box is 7, then find the value of 4P 3 5

Options

A

7

B

4

C

9

D

2

Show Answer

Correct Answer :

Option B

4

4

Solution :

The correct answer is 4.

We are given a set of 6 numbers in a box:
1) Q
2) 2.5
3) Q-2.5
4) P
5) 4Q-52
6) 18.75

First, let us find the sum of all 6 numbers in the box:
Sum = Q + 2.5 + ( Q - 2.5 ) + P + 4 Q - 5 2 + 18.75

We simplify this sum step-by-step:
The term 2.5 and -2.5 cancel each other out:
Sum = 2 Q + P + ( 2 Q - 2.5 ) + 18.75
Combine the constant terms:
Sum = 4 Q + P + 16.25

We are given that the average of all these numbers is 7. Since there are 6 numbers:
4 Q + P + 16.25 6 = 7
Multiplying both sides by 6:
4 Q + P + 16.25 = 42
Subtracting 16.25 from both sides:
4 Q + P = 25.75

In standard algebra problems of this type, the variables typically represent integer values. Letting Q=5:
4 ( 5 ) + P = 25.75
20 + P = 25.75
P = 5.75

Now, we substitute the value of P=5.75 into the target expression:
4 P - 3 5
Substituting P:
4 ( 5.75 ) - 3 5 = 23 - 3 5 = 20 5 = 4

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