Who celebrated his birthday between Y and G?
At most two people celebrated their birthday after G. Neither F nor G celebrated their birthday on 28th of the month. The difference between the days of G and E to celebrate their birthday is 12. X celebrated his birthday immediately before E. No one celebrated their birthday between Y and F, who celebrated his birthday after Y. Z celebrated his birthday after H, who doesn’t celebrate his birthday before X. From above statements, Case-1 : Here G and E celebrated their birthday on 20th and 8th of the month respectively. X celebrated his birthday on 4th of the month. Y and F celebrated their birthday on 12th and 16th of the month respectively. Finally, H and Z celebrated their birthday on 24th and 28th of the month respectively. Thus all the given condition gets satisfied and we get the completed arrangement in Case- Case-2: Here G and E celebrated their birthday on 24th and 12th of the month respectively. X celebrated his birthday on 8th of the month. Y and F celebrated their birthday on 16th and 20th of the month respectively. As per last reference point, H doesn’t celebrate his birthday before X. Thus there is no other date left for H. Thus this case-2 becomes invalid and it can be eliminated. 
I. x2 – 18x + 81 = 0
II. y2 – 3y - 28 = 0
I. 4x² - 15x + 9 = 0
II. 20y² - 23y + 6 = 0
I. x2 – 13x + 36 = 0
II. 3y2 – 29y + 18 = 0
I. 3x2 - 16x - 12 = 0
II. 2y2 + 11y + 9 = 0
I. 5x² + 17x + 6 = 0
II. 2y² + 11y + 12 = 0
...I. 8x² + 2x – 3 = 0
II. 6y² + 11y + 4 = 0
I. x + 1 = 3√ 9261
II. y + 1 = √ 324
I. 117x² + 250x + 117 = 0
II. 54y² -123y + 65 = 0
I. x² + 3x – 154 = 0
II. y² + 5y – 126 = 0
I. 4x2 + 9x - 9 = 0
II. 4y2 - 19y + 12 = 0
