70004
Question
P, Q and R stand for three different numbers.
The average of P and Q is 30.
The average of Q and R is 45.
P + Q + R = 120
Calculate the values of P, Q and R.
Worked Solution
Test each statement:
|
|
| Average 2P + Q |
= 30 |
| P + Q |
= 60 |
∴ Eliminate first and third option:
|
|
| Average 2Q + R |
= 45 |
| Q + R |
= 90 |
∴ Eliminate second option:
=> {{{correctAnswer}}}
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
Variant 0
DifficultyLevel
650
Question
P, Q and R stand for three different numbers.
The average of P and Q is 30.
The average of Q and R is 45.
P + Q + R = 120
Calculate the values of P, Q and R.
Worked Solution
Test each statement:
|
|
| Average 2P + Q |
= 30 |
| P + Q |
= 60 |
∴ Eliminate first and third option:
|
|
| Average 2Q + R |
= 45 |
| Q + R |
= 90 |
∴ Eliminate second option:
=> P = 30, Q = 30, R = 60
Question Type
Multiple Choice (One Answer)
Variables
| Variable name | Variable value |
| correctAnswer | |
Answers