Question

33 guava trees, 55 banana trees and 88 malta trees need to be planted in rows such that each row contains the same number of trees of one type only. The minimum number of rows in which the trees may be planted is:

• A. 18
• B. 12
• C. 20
• D. 16

Answer 1

Answer:

D. 16

We need the minimum number of rows, with:

• Each row having the same number of trees

• Each row containing only one type of tree

So, we must maximize the number of trees per row → take HCF (GCD) of 33, 55, and 88.

Find HCF

$\gcd(33, 55, 88)$

Prime factors:

• $(33 = 3 \times 11)$

• $(55 = 5 \times 11)$

• $(88 = 8 \times 11 = 2^3 \times 11)$

Common factor = (11)

Number of rows

$\frac{33}{11} = 3,\quad \frac{55}{11} = 5,\quad \frac{88}{11} = 8$

Total rows:
$3 + 5 + 8 = 16$