what is next number in pattern below
131 517 192 123 ?
Ans:252
Logic: space them properly as 13 15 17 19 21 23....
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Question: Anna, her brother - Andre, her daughter - Ami, and her son, Adam are tennis players. As a game of doubles
1. Anna's brother is directly across the net from Ami.
2. Adam is diagonally across the net from the worst player's sibling.
3. The best player and the worst player are on the same side of the net.
Answer:
The best player is Andre.
Find out all possible arrangement such that no condition is contradicted.
From (1), there are two possible arrangements. Discarding two arrangements which are identical to following two.
Andre Anna Andre Adam
------------------ AND ------------------
Ami Adam Ami Anna
(I) (II)
From (2), Anna is the worst player in Case I and Adam is the worst player in Case II.
From (3), Andre is the best player in both the cases.
Hence, the best player is Andre.
Question: Elizabeth is engaged.
* Her fiancé is either Arthur, Barry, Colin or Derek.
* Each of the four men and Elizabeth either always tells the truth or always lies.
* Arthur says: "Exactly one of us four men always tells the truth."
* Barry says: "Exactly one of us four men always tells the lies."
* Colin says: "Arthur or Barry is Elizabeth's fiancé."
* Elizabeth says: "My fiancé and I either both always tell truth or both always lie."
Who is Elizabeth's fiancé?
Answer:
Barry is Elizabeth's fiancé.
Analyse the statements made by Colin and Elizabeth first.
From (6), if Elizabeth always tells the truth, then her fiancé always tells the truth and if Elizabeth always lies, then her fiancé always tells the truth. Hence, Elizabeth's fiancé always tells the truth.
Let's assume that statement made by Colin (5) is false. Then Colin lied and Derek is the truth-telling fiancé. But then statement made by Arthur can not be true (if true, then there are 2 truth-tellers which contradicts itself). And it can not be false either (if false, then there are at least 2 truth-tellers, which makes Barry's statement false and
hence there is just a one truth-teller i.e. Derek, again contradiction!!!). Hence statement made by Arthur contradicts itself. So the statement made by Colin is true i.e. Arthur or
Barry is Elizabeth's fiancé.
As statement made by Colin is true, the statement made by Arthur is false. Then because
Elizabeth's fiancé always tells the truth, Barry is Elizabeth's fiancé. Then the statement made by Barry is true and thus Derek always tells the truth.
Thus, Barry is Elizabeth's fiancé. .
Question: A group of fewer than 10 girls found a number of gold-coins which they were able to divide equally among them.
After this division had been done, Lalita - one of the girls, suggested that it would be more equitable to divide the gold-coins by families rather than by individuals. Among the them, there were two groups with two sisters, of course Lalita was not in either group. The rest of the girls were unrelated to each other. A re-division by families would have meant that the gold-coins per family were 5 more than the gold-coins per girl.
The girls argued among themselves over this way of dividing the gold-coins. Before a final decision is made, Ash - one of the girls, decided that she did not want any gold-coins. Her
share was equally divided (without breaking/cutting any gold-coin) among the other girls.
Finally, Lalita decided to withdraw her suggestion of dividing the gold-coins by families.
How many girls were there and how many gold-coins did each girl end up with?
Answer:
There were total 6 girls. Each end up with 12 gold-coins.
The number of gold-coins is evenly divisible by the number of girls as well as the number of families.
Let's assume that N is the number of gold-coins each girl received initially and G is the total number of girls.
Then, total number of gold-coins = NG
If the gold-coins had been divided by families rather than by individuals, the number of recipients would be (G - 2) and each share would be (N + 5).
Again, total number of gold-coins = (N + 5)(G - 2)
But, the total number of the gold-coins is the same.
NG = (N + 5)(G - 2)
NG = NG -2N +5G -10
2N = 5G -10
N = (5/2)G - 5
Now, N and G are the positive integers and also total number of gold-coins must be divisible by G, (G-1) and (G-2). This is because initially there were G girls; then since it was divided family wise, the total number of units, the coins were to be divided would be (G-2) (as two groups had two sisters, so two girls got combined as one group, one per group); and after Ash backed out, there were (G-1) girls.
Now trying different EVEN values for G, starting with 2; there were total 6 girls and 60 gold-coins. The gold-coins are divided among 5 girls and hence each girl ends up with 12 gold-coins.
Question: What are the next two letters in this sequence?
A, B, H, F, M, C, I, G, T, D, O, ?, ?
Answer:
The next letters in the sequence are J, U, E, X etc.
A is the first letter of the alphabet with symmetry about the vertical axis. B is the first letter of the alphabet with symmetry about the horizontal axis. H is the first letter of the alphabet with symmetry about both, the vertical axis and the horizontal axis. F is the first letter of the alphabet with no symmetry.
The sequence then repeats with the second letter of the alphabet with symmetry about the vertical axis, the horizontal axis, both the axes and no axes i.e. M, C, I and G
The third letters of the alphabet are T, D, O and J.
The fourth letters of the alphabet are U, E, X and L.