70003
Question
P, Q and R stand for three different numbers.
The average of P and Q is 64.
The average of Q and R is 50.
P + Q + R = 150
Calculate the values of P, Q and R.
Worked Solution
Test each statement:
|
|
Average 2P + Q |
= 64 |
P + Q |
= 128 |
∴ Eliminate first and second option:
|
|
Average 2Q + R |
= 50 |
Q + R |
= 100 |
∴ Eliminate third option
=> {{{correctAnswer}}}
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
Variant 0
DifficultyLevel
652
Question
P, Q and R stand for three different numbers.
The average of P and Q is 64.
The average of Q and R is 50.
P + Q + R = 150
Calculate the values of P, Q and R.
Worked Solution
Test each statement:
|
|
Average 2P + Q |
= 64 |
P + Q |
= 128 |
∴ Eliminate first and second option:
|
|
Average 2Q + R |
= 50 |
Q + R |
= 100 |
∴ Eliminate third option
=> P = 50, Q = 78, R = 22
Question Type
Multiple Choice (One Answer)
Variables
Variable name | Variable value |
correctAnswer | |
Answers