AP EAMCET · Maths · Statistics
The arithmetic mean of five natural numbers is 40 . The largest exceeds the smallest number by 10 . If \(\alpha\) is the maximum possible value for the largest of these 5 numbers, then the number of positive integral divisors of \(\alpha\) is
- A 12
- B 10
- C 9
- D 5
Answer & Solution
Correct Answer
(B) 10
Step-by-step Solution
Detailed explanation
Let five natural numbers be \(\alpha-10, x, y, z, \alpha\). \[ \begin{aligned} \text { Given, } & \frac{\alpha-10+x+y+z+\alpha}{5}=40 \\ \Rightarrow & \alpha-10+x+y+z+\alpha=200 \\ & x+y+z=210-2 \alpha \end{aligned} \] Now, \(\alpha-10 42 \end{aligned} \]…
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