X and Y are playing a game. There are 11 coins on the table and each player must pick up at least 1 coin but not more than 5 coins. The person picking up the last coin loses. X starts. How many coins should he pick up to ensure a win no matter what strategy Y employs.A. 4B. 3C. 2D. 5What is correct approach to solve such problems???
X and Y are playing a game. There are 11 coins on the table and each player must pick up at least 1 coin but not more than 5 coins. The person picking up the last coin loses. X starts. How many coins should he pick up to ensure a win no matter what strategy Y employs.A. 4B. 3C. 2D. 5What is correct approach to solve such problems???
in this case (who picks last loses), always leave him with (least+max)k + 1 coins --> 6k+1 coin
X and Y are playing a game. There are 11 coins on the table and each player must pick up at least 1 coin but not more than 5 coins. The person picking up the last coin loses. X starts. How many coins should he pick up to ensure a win no matter what strategy Y employs.A. 4B. 3C. 2D. 5What is correct approach to solve such problems???
4;
If x picks 4 coins, then y can pick 1,2,3,4,5 coins in any case x can pick n coins in his/her next turn so that only a coin is left. And in turns will be the winner.
Always try to find a pattern in these kind of question.If there is just 1 coin on the table, then the person whose turn it is will loose.In case of 2, 3, 4, 5, 6 coins, person whose turn it is can pick 1, 2, 3, 4, 5 coins and then win the game.In case of 7 coins no matter what a person does, he will always loose (as he will leave 2 or 3 or .. or 6 coins for the other person)Then for 8 or 9 or 10 or ... or 12, person whose turn it is will always win (as he can leave 7 for the other person)Now, here we have 11 coins on the table. So, if X can manage to leave 7 coins for Y, then he is certain of winning the gameHence, X will pick 4 coins to win the gameHow many numbers n less than 1000 are there such that number of even factors of the n is 3 times the number of odd factors of the n.
ABCD is a square. P is the mid point of AB. The line passing through A and perpendicular to DP intersects the diagonal at Q and BC at R. If AB=2 then PR=_______?A) 1/2B) sqrt(3)/2C) sqrt(2)D) 1E) None of these
How many numbers n less than 1000 are there such that number of even factors of n is 3 times the number of odd factors of n.
n = 2^a * p^b * q^c ......
even factors = a*(b+1)*(c+1)....
odd factors = (b+1)*(c+1)...
acc to ques
a*(b+1)*(c+1)... = 3*(b+1)*(c+1)...
a = 3
N = 8 * odd
highest factors of 8 less than 1000 is 992 = 8 *124
means 62 odd and 62 even factors
so 62
@chillfactor Hemant sir, ur ques in old threads were really fantastic, it would be a grt help if u can come up wid many gud questions which can help us in upcoming XAT
Always try to find a pattern in these kind of question.If there is just 1 coin on the table, then the person whose turn it is will loose.In case of 2, 3, 4, 5, 6 coins, person whose turn it is can pick 1, 2, 3, 4, 5 coins and then win the game.In case of 7 coins no matter what a person does, he will always loose (as he will leave 2 or 3 or .. or 6 coins for the other person)Then for 8 or 9 or 10 or ... or 12, person whose turn it is will always win (as he can leave 7 for the other person)Now, here we have 11 coins on the table. So, if X can manage to leave 7 coins for Y, then he is certain of winning the gameHence, X will pick 4 coins to win the gameHow many numbers n less than 1000 are there such that number of even factors of n is 3 times the number of odd factors of n.
2^0*3^a*5^b*...; odd factors=(a+1)(b+1)... Even factors=a(a+1)(b+1).. a=3 Number will be of type 2*3^a*5^b... Max of such type will be 8*123 We have to count odd numbers from 123 to 1 =62
2^0*3^a*5^b*...; odd factors=(a+1)(b+1)... Even factors=a(a+1)(b+1)..a=3Number will be of type 2*3^a*5^b... Max of such type will be 8*123 We have to count odd numbers from 123 to 3 =61
y till 3...odd number 1 q nhi le rhe ho..dat is 8x1 = 8
Rajiv is a student in a business school. After every test he calculates his cumulative average. QT and OB were his last two tests. 83 marks in QT increased his avg by 2. 75 marks in OB further increased his avg by 1. Reasoning is the next test, if he gets 51 in reasoning, his avg will be_____?
X and Y are playing a game. There are 11 coins on the table and each player must pick up at least 1 coin but not more than 5 coins. The person picking up the last coin loses. X starts. How many coins should he pick up to ensure a win no matter what strategy Y employs.A. 4B. 3C. 2D. 5What is correct approach to solve such problems???
(max+min)k
When last one picks coins it loses.The last coin is left for other person.Subtract one coin from total (11 coins).The winner picks coins coins in such a way that remaining form multiple of (max+min)k
X and Y are playing a game. There are 11 coins on the table and each player must pick up at least 1 coin but not more than 5 coins. The person picking up the last coin loses. X starts. How many coins should he pick up to ensure a win no matter what strategy Y employs.A. 4B. 3C. 2D. 5What is correct approach to solve such problems???
In a certain country the average monthly income is calculated on the basis of 14 months in a calendar year while the average monthly expenditure was to be calculated on the basis of 99 months per year. this leads people having an underestimation of their savings , since there would be an underestimation of the income and an overestimation of the expenditure per month.then
,
1. mr.jack comes back from ussr and convinces his community comprising 273 families to start calculating the average income on the basis of 12 months per year. now if it is know that the average estimated income in his community is (according to old system) 87 rs per month.then what will be the change in the average estimated savings for the country (assume that there are no other change)
a. 251.60 rs b.282.75 rs c. 312.75 rs d . cannot be determined.
2. miss rose comes back from usa and convinces his community comprising 546 families to start calculating the average income and average expenditure on the basis of 12 months per year. now if it is know that the average estimated income on the island is (according to old system) 87 rs per month.then what will be the change in the average estimated savings for the country (assume that there are no other change)
a.251.60 rs b. 565.5 rs c. 625.5 rs d . cannot be determined.
please tell.
still waiting for answer of these so posting it again
X and Y are playing a game. There are 11 coins on the table and each player must pick up at least 1 coin but not more than 5 coins. The person picking up the last coin loses. X starts. How many coins should he pick up to ensure a win no matter what strategy Y employs.A. 4B. 3C. 2D. 5What is correct approach to solve such problems???