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# GP and 2-digit number | PRMO 2017 | Question 16

Try this beautiful problem from the Pre-RMO, 2017 based on GP and 2-digit number.

## GP and 2-digit number - PRMO 2017

Five distinct 2-digit numbers are in geometric progression. Find the middle term.

• is 107
• is 36
• is 840
• cannot be determined from the given information

### Key Concepts

Geometric Progression

2-digit number

Middle term

PRMO, 2017, Question 16

Elementary Algebra by Hall and Knight

## Try with Hints

First hint

Let the numbers be $a, ar, ar^{2}, ar^{3}, ar^{4}$

for all are two digit number r=$\frac{2}{3}$ or $\frac{3}{2}$

Second Hint

where fourth power of integers greater than 3 are 3 digit numbers

Final Step

then five numbers (16,24,36,54,81)

then middle term=36.