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Quantitative Aptitude

A+B+C=N (N Fixed)

The number of...

Question

The number of non-negative integral solutions of the equation, x + y + 3z = 33 is

A

120

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B

135

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C

210

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D

520

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Solution

The correct option is C 210
Consider cases when z = 0, 1, 2, . . . . , 11
$\Rightarrow$ x + y = 33, 33, 27, . . .
Total number of solutions of x + y = 33, 30, 27, . .
= 34 + 31 + 28 + . . . + 1 (12 times)
$= \frac{12}{2}$ (1+34) = 210

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