If an action began in the past and continues into the present, use the present perfect tense.(Present Perfect = HAVE/ HAS + Past participle).
e.g - We have lived in a big mansion for five days.
(We lived in a big mansion for five days and still live there today)
If an action precedes an earlier past action, use the past perfect tense.(Past Perfect = HAD + Past Participle)
e.g - The play had started by the time we arrived at the theater.
(The earlier past action -- had started - is in the past perfect tense, while the later past action - arrived - is in the simple past tense.)
Otherwise, stick to simple tenses - as GMAT prefers simplicity.
Incorrect - I think that ancient people HAD BELIEVED in many Gods.
Correct - I think that ancient people BELIEVED in many Gods.
In the above sentence the past perfect (had believed) is unnecessary because the sentence involves only one action in the past tense. Therefore, the simple past (believed) is correct.
Note the difference in meanings in the two sentences stated below
When I switched the TV on, the programme started. I was just in time.
When I switched the TV on, the programme had started. I missed the beginning.