Geometry
Point O is the center of the regular octagon ABCDEFGH, and X is the midpoint of the side AB. What fraction of the area of the octagon is shaded?
(A) 7/16
(B) 11/32
(C)23/32
(D)3/8
(E)15/32
Question of the day
Numbers
Let N =123456789…..4344 be the 79-digit number obtained that is formed by writing the integers from 1 to 44 in order, one after the other. What is the remainder when N is divided by 45 ?
Females
- A is the father of two children – B and D who are of different sexes.
- C is B’s spouse.
- E is the same sex as D.
- B and C have the two children – F who is the same sex as B and G who is the same sex as C.
- E’s mother, H who is married to L, is the sister of D’s mother, M.
- E and E’s spouse, I have two children – J and K who are the same sex as I.
Note that no persons have married more than once. Also, there are more number of females than males. How many females are there?
Numbers
For how many values of natural number n, both the numbers 48n + 4 and 27n + 19 are perfect square?
(1) 0
(2) 1
(3) 2
(4) 3
(5) more than 3
Four Men
Four men – Anurag, Varun, Chandan and Dev – are standing in a straight line.
- One man is fair, handsome and unscarred.
- Two men who are not fair, are each standing next to Anurag.
- Varun is the only man standing next to exactly one handsome man.
- Chandan is the only man not standing next to exactly one scarred man.
Who is fair, handsome and unscarred?
See our previous ‘Puzzles of the Day’:
Puzzle of the Day : 21
Puzzle of the Day : 20
Geometry
In a trapezium PQRS, PQ is parallel to RS, PQ = 20 cm, RS = 3 cm, PQR = 30° and QPS = 60°. What is the length of the line joining the midpoints of PQ and RS?
Counting
In how many ways a cube can be painted so that each face is painted either red or white?
A total of 21 cards, consisting of 4 kings, 4 queens, 4 jacks, 4 tens, 4 nines, and 1 joker were dealt to Art, Ben, and Cal. The cards were dealt evenly: 7 per player. Then all jacks, tens, and nines were discarded. At that point:
1. The combined hands consisted of 4 kings, 4 queens, and 1 joker.
2.Art had 2 cards, Ben had 3 cards, and Cal had 4 cards.
3.The man with the most singletons did not have the joker.
4. No man had more than 2 kings.
Who had the joker?
Source : The great book of Puzzles and Teasers.
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