How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

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

Check the Answer

Answer: is 36.

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.

Subscribe to Cheenta at Youtube

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.