Given : a ≯ 1500
I. Given : 19 is a factor of ‘a’.
⇒ ‘a’ is a multiple of 19. There are several multiples of 19, which are not greater than 1500. e.g. 19, 38, 57 and so on.
∴ I alone is not sufficient.
II. Given : 29 divides ‘a’.
∴ ‘a’ is a multiple of 29.
Again, ‘a’ can be 29, 58, 87 and so on.
I & II.
Combining the two statements we have, ‘a’ is a common multiple of 19 and 29.
LCM (19, 29) = 551
Multiples of 551 not exceeding 1500 are 551, 1102. We don’t get a unique value for ‘a’.
∴ I & II together are not sufficient.