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

E

1

Show Answer

Correct Answer :

Option B

4

4

Solution :

The correct answer is 4.

Step-by-step explanation:

From the given table, we can list the six numbers contained in the box:
1. Q
2. 2.5
3. Q-2.5
4. P
5. 4Q-52
6. 18.75

We are given that the simple arithmetic average of all these numbers in the box is 7. Since there are 6 numbers in total, their average is given by:

Q+2.5+(Q-2.5)+P+4Q-52+18.756=7

Multiply both sides by 6:

Q+2.5+Q-2.5+P+4Q-52+18.75=42

Simplify the terms in the equation:

2Q+P+2Q-2.5+18.75=42

4Q+P+16.25=42

Subtract 16.25 from both sides:

4Q+P=25.75

To find the required value, we first need to determine the value of Q and P. From the options and standard integer solutions for equations of this type, we test Q=5:
If Q=5, then:
4(5)+P=25.75
20+P=25.75
P=5.75

Now we substitute the value of P=5.75 into the expression we need to evaluate:

4P-35

Substituting P=5.75:

4(5.75)-35=23-35=205=4

Thus, the value of the expression is 4.

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