Quantitative Aptitude - Arithmetic Ability Questions

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.

5 min spaces are gained in 6055*5 min  = 5511min 

so, Required time = 5511 min  past 7

The given number series is 3, 11, 80, 291, 803

$$\begin{gathered} 3 \\ 3 + 23 = 3 + 8 = 11 \\ 11 + 43 = 11 + 64 = 75 (not 80) \\ 75 + 63 = 75 + 216 = 291 \\ 291 + 83 = 291 + 512 = 803 \end{gathered}$$

If the period between the two months is divisible by 7, then that two months will have the same calender .

 
(a). Oct + Nov  = 31 + 30 = 61 (not divisible by 7)

(b). Apr + May + Jun + Jul + Aug + Sep + Oct = 30 + 31 + 30 + 31 + 31 + 30 + 31  = 214 (not divisible by 7)

(c). Jun + July + Aug + Sep = 30 + 31 + 31 + 30 = 122 (not divisible by 7)

(d). Apr + May + June = 30 + 31 + 30 = 91 (divisible by 7)

Hence, April and July months will have the same calendar.