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Question

If r is a real number that r<1 and if a=51-r, then


A

0<a<5

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B

-5<a<5

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C

0<a<10

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D

-10<a<10

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Solution

The correct option is C

0<a<10


Explanation for the correct option:

Given r<1 which implies -1<r<1

From the given relation, we have

a=51-r…1

Multiply the above inequality by -1, we get

1>-r>-1

This can be rewritten as -1<-r<1

Then add 1 in the LHS, RHS, and the variable r, then we have

0<1-r<2

Finally, multiply the inequality by 5,

0<51-r<10

From equation 1,

0<a<10

Hence, the correct option is (C).


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