GRE Questions

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Four tenths = 0.4

Five thousandths = 0.005

The average is (0.4 + 0.005)/2 = 0.2025

To find the greatest number which divides the numbers 964, 1238 and 1400 leaving the remainders 41, 31 and 51 is nothing but the HCF of (964 - 41), (1238 - 31), (1400 - 51).

Therefore, HCF of 923, 1207 and 1349 is 71.

If yesterday were tomorrow, today is Friday => tomorrow of friday is Saturday.

Hence, it implies that today is Sunday if tomorrow is Saturday.

My father's brother's only sibling is my father. My father's mother is my grandmother. My sister's only brother is myself. So she is my Grandmother.

My fahter's mother's only daughter-in-law is my father's wife i.e. my mother. My mother's daughter is my sister. My sister's father is my father.

First girl facing North
Then she rotates 100 deg clock wise => 10 deg ES
Then again she rotates 190 deg anti clock wise => for 100 deg it is North and more 90 deg means West.
Therefore, the new direction of the girl is West.

Total ages of 80 boys = 15 x 80 = 1200 yrs.
Total age of 16 boys = 15 x 16 = 240 yrs
Total age of 25 boys = 14 x 25 = 350 yrs.
Average age of remaining boys = 1200 - (240+350) / 80 - (25+15) = 610/41 = 15.25 yrs.

we can do this by trial and error method.

Putting x = 2,we get 2²(2² - 1) = 12.
checking with other integers, the above equation always gives a value which is a multiple of 12,
So, x²(x² - 1) is always divisible by 12.