Question

24 yellow flags and 32 green flags are to be arranged in such a way that maximum number of flags can be accommodated in one row, each row contains flags of only one colour and the number of flags in each row is the same, then we end up with

• A. 6 rows of yellow flags and 8 rows of green flags
• B. 3 rows of yellow flags and 4 rows of green flags
• C. 12 rows of yellow flags and 16 rows of green flags
• D. 4 rows of yellow flags and 4 rows of green flags

Answer 1

The correct option is B 3 rows of yellow flags and 4 rows of green flags

24 yellow and 32 green flags are to be arranged into different rows such that, the number of flags in each row is the same, maximum number of flags are accommodated in each row and none of the rows contains flags of more than one colour.

We have to find the number of flags in each such row. The number of flags in each row has to divide both the numbers 24 and 32 and at the same time, it has to be the maximum possible number.

We find the number of flags in each row by finding the greatest common divisor of the two numbers, 24 and 32


Maximum number of flags = Greatest Common Divisor of 24 and 32
$24=2^3\times 3$
$32=2^5$
GCD of $24$ and $32=2^3=8.$
So, the number of flags in a row is $8.$ Since we have $24$ yellow flags and $32$ green flags, we end up with $(24/8=3)$ rows of yellow flags and $(32/8=4)$ rows of green flags.