GRE Questions

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Letters of the alphabet used in ancient Rome to represent numbers:

I = 1;

V = 5;

X = 10;

L = 50;

C = 100;

D = 500;

M = 1000.

The numbers one through ten are written I, II, III, IV, V, VI, VII, VIII, IX, and X.

While using punctuations, only one space is used. 

An Umbrella.

Yes, when it is open it can't be fit under a chimney but when it is closed it can be fit down a chimney.

Yep! It's your NAME that belongs to you but is used more by others than you.

In chronology, the sequence of events from the latest to the oldest events or vice versa is laid. In this case, the details of how a particular event or place or thought developed through time is detailed in a chronology. 

Hence, the term chronology is a type of detail.

Here the given series 7  18  42  94  204 follows a pattern that, 

7

7 ×2+4 = 18

18 ×2+6 = 42

42 ×2+10 = 94

94 ×2+16 = 204

Similarly,

4

4 ×2+4 = 12

12 ×2+6 = 30

30 ×2+10 = 70

70 ×2+16 = 156

Hence, the value of P = 156.

Given that x = 2+ 223 + 213

So x - 2 = 223 + 213

Now cubing on both sides, we get

=> x3-8-6x2+12x = 4 + 2 + 6(x-2)

Therefore, x3-6x2+6x = -6 + 8 = 2