COMEDK · Maths · 5. Sequences and Series

A number consists of three digits in geometric progression. The sum of the right hand and left hand digits exceeds twice the middle digit by 1 and the sum of left hand and middle digits is two third of the sum of the middle and right hand digits. Then the sum of digits of number is

A 109
B \(\dfrac{1}{4}\)
C 19
D 469

Verified Solution

Answer & Solution

Correct Answer

(C) 19

Step-by-step Solution

Detailed explanation

Let the three digits of the number be \(a/r\), \(a\), and \(ar\), where \(r\) is the common ratio. Since these are digits, \(a/r, a, ar \in \{0, 1, 2, ..., 9\}\). The first condition states that the sum of the right hand and left hand digits exceeds twice the middle digit by 1:…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From COMEDK

Explore more questions on app