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# No wonder Federer lost in his Olympic tennis final, he

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No wonder Federer lost in his Olympic tennis final, he [#permalink]

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06 Aug 2012, 05:46
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No wonder Federer lost in his Olympic tennis final, he previously played an exhausting semifinal match against Del Potro. In the third set, since there was no tie-breaker, after 6:6 they continued to play until one of the players first reached an advantage of 2 games (or in other words, won two consecutive games).
What was the score in the final, decisive third set (which Federer won)?

(1) The square of the average number of games won by Federer and Del Potro is a three digit number of the form BAC, where A,B, and C are non-zero consecutive digits.

(2) Each played less than 50 games, the two numbers representing their final scores are consecutive prime numbers, whose sum is a perfect square.
[Reveal] Spoiler: OA

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Re: No wonder Federer lost in his Olympic tennis final, he previ [#permalink]

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06 Aug 2012, 06:04
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The answer of this Question is quite simple. Although you have to check for a lot of numbers to be sure
In the first part minimum no. of matches can be 14 ( 6+6+2 ) so from 14 move upwards and see square if which number has 3 consecutive numbers .. you will reach 324 at 18 and voila the order of consecutive numbers is BAC same as 324 ! nailed it
after that move forward to square out all other options you have to go only till 31 ! and
Than less that fifty and consecutive prime? and we already know the answer as 18 so breeak it down 6+6+4
4 = 1 + 3 and 1+3 = 4 = 2^2 Bingo !

and Do give kudos if it helps

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Re: No wonder Federer lost in his Olympic tennis final, he previ [#permalink]

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06 Aug 2012, 06:16
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mandyrhtdm wrote:
The answer of this Question is quite simple. Although you have to check for a lot of numbers to be sure
In the first part minimum no. of matches can be 14 ( 6+6+2 ) so from 14 move upwards and see square if which number has 3 consecutive numbers .. you will reach 324 at 18 and voila the order of consecutive numbers is BAC same as 324 ! nailed it
after that move forward to square out all other options you have to go only till 31 ! and
Than less that fifty and consecutive prime? and we already know the answer as 18 so breeak it down 6+6+4
4 = 1 + 3 and 1+3 = 4 = 2^2 Bingo !

and Do give kudos if it helps

I didn't understand your reasoning for (2). And what do you mean by we already know the answer?

Can you do fewer testings for (1)? Any conclusion about the digits or at least one of them that can help?
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Re: No wonder Federer lost in his Olympic tennis final, he previ [#permalink]

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06 Aug 2012, 06:37
EvaJager wrote:
mandyrhtdm wrote:
The answer of this Question is quite simple. Although you have to check for a lot of numbers to be sure
In the first part minimum no. of matches can be 14 ( 6+6+2 ) so from 14 move upwards and see square if which number has 3 consecutive numbers .. you will reach 324 at 18 and voila the order of consecutive numbers is BAC same as 324 ! nailed it
after that move forward to square out all other options you have to go only till 31 ! and
Than less that fifty and consecutive prime? and we already know the answer as 18 so breeak it down 6+6+4
4 = 1 + 3 and 1+3 = 4 = 2^2 Bingo !

and Do give kudos if it helps

I didn't understand your reasoning for (2). And what do you mean by we already know the answer?

Can you do fewer testings for (1)? Any conclusion about the digits or at least one of them that can help?

Nopes the answer is D if you had gone thoroughly through t he explanations you would have found that both statements give the same result.

See i will explain again : 2 says that total number of sets is less than 50 and that the sum of games one by X & Y is a whole square. let x and y be the number of games won by both and we know that to win some one must have one two more consecutive games ?
so we have x + y = z^2 ( statement 2) & x-y = 2 ( Passage) now all you have to determine that these two equations do have a solution. that is it!
as i had solved it using the first statement already so i know the total number of games is 18 ( all three sets ) and therefore games played in the last set = 18-6-6 = 4 and 1 & 3 is the correct value of games already known i just check if i get the same values from statement two.

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Re: No wonder Federer lost in his Olympic tennis final, he previ [#permalink]

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06 Aug 2012, 07:34
mandyrhtdm wrote:
EvaJager wrote:
mandyrhtdm wrote:
The answer of this Question is quite simple. Although you have to check for a lot of numbers to be sure
In the first part minimum no. of matches can be 14 ( 6+6+2 ) so from 14 move upwards and see square if which number has 3 consecutive numbers .. you will reach 324 at 18 and voila the order of consecutive numbers is BAC same as 324 ! nailed it
after that move forward to square out all other options you have to go only till 31 ! and
Than less that fifty and consecutive prime? and we already know the answer as 18 so breeak it down 6+6+4
4 = 1 + 3 and 1+3 = 4 = 2^2 Bingo !

and Do give kudos if it helps

I didn't understand your reasoning for (2). And what do you mean by we already know the answer?

Can you do fewer testings for (1)? Any conclusion about the digits or at least one of them that can help?

Nopes the answer is D if you had gone thoroughly through t he explanations you would have found that both statements give the same result.

See i will explain again : 2 says that total number of sets is less than 50 and that the sum of games one by X & Y is a whole square. let x and y be the number of games won by both and we know that to win some one must have one two more consecutive games ?
so we have x + y = z^2 ( statement 2) & x-y = 2 ( Passage) now all you have to determine that these two equations do have a solution. that is it!
as i had solved it using the first statement already so i know the total number of games is 18 ( all three sets ) and therefore games played in the last set = 18-6-6 = 4 and 1 & 3 is the correct value of games already known i just check if i get the same values from statement two.

(2) states "Each played less than 50 games", it doesn't say the sum of the games is less than 50. And not sets, but games.
When dealing with DS questions, you have to work out the answer solely based on the question stem and the info in a specific statement when considering it alone.
I think you mix up sets with games. It is about the third set, and the number of games each played. How are 1 and 3 relevant?
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Re: No wonder Federer lost in his Olympic tennis final, he previ [#permalink]

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06 Aug 2012, 08:25
for the second part:- as the number of games played is less then 50 and it states that we r looking for consecutive prime nos whose sum is a perfect square . So u start from 11 and 13 as these r the only consecutive prime no after 6. But as they sum up to 24 which is not a perfect square so this cannot be the ans.U move in this manner and u will get that only 19 and 17 as consecutive prime numbers that sum to a perfect square..

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Re: No wonder Federer lost in his Olympic tennis final, he previ [#permalink]

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06 Aug 2012, 08:33
for the second part:- as the number of games played is less then 50 and it states that we r looking for consecutive prime nos whose sum is a perfect square . So u start from 11 and 13 as these r the only consecutive prime no after 6. But as they sum up to 24 which is not a perfect square so this cannot be the ans.U move in this manner and u will get that only 19 and 17 as consecutive prime numbers that sum to a perfect square..

Yes, that's correct.
Just as a curiosity, another pair of consecutive primes whose sum is a perfect square is 71 and 73, sum being $$144 = 12^2$$.
The longest set in the history of tennis was 70:68 at Wimbledon last year between Isner and Mahut. But this is a topic for another forum.

What about statement (1)? Do you have any idea for a shortcut?
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Re: No wonder Federer lost in his Olympic tennis final, he previ [#permalink]

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06 Aug 2012, 08:44
EvaJager wrote:
for the second part:- as the number of games played is less then 50 and it states that we r looking for consecutive prime nos whose sum is a perfect square . So u start from 11 and 13 as these r the only consecutive prime no after 6. But as they sum up to 24 which is not a perfect square so this cannot be the ans.U move in this manner and u will get that only 19 and 17 as consecutive prime numbers that sum to a perfect square..

Yes, that's correct.
Just as a curiosity, another pair of consecutive primes whose sum is a perfect square is 71 and 73, sum being $$144 = 12^2$$.
The longest set in the history of tennis was 70:68 at Wimbledon last year between Isner and Mahut. But this is a topic for another forum.

What about statement (1)? Do you have any idea for a shortcut?

As far as 71 and 73 go,The numbers wont be applicable for this question as the number of games played is less then 50.

And for statement 1 my way is same as the one mentioned above. I dont think theres any shortcut for it.
Hope this cud help ..

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Re: No wonder Federer lost in his Olympic tennis final, he previ [#permalink]

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06 Aug 2012, 09:07
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EvaJager wrote:
for the second part:- as the number of games played is less then 50 and it states that we r looking for consecutive prime nos whose sum is a perfect square . So u start from 11 and 13 as these r the only consecutive prime no after 6. But as they sum up to 24 which is not a perfect square so this cannot be the ans.U move in this manner and u will get that only 19 and 17 as consecutive prime numbers that sum to a perfect square..

Yes, that's correct.
Just as a curiosity, another pair of consecutive primes whose sum is a perfect square is 71 and 73, sum being $$144 = 12^2$$.
The longest set in the history of tennis was 70:68 at Wimbledon last year between Isner and Mahut. But this is a topic for another forum.

What about statement (1)? Do you have any idea for a shortcut?

As far as 71 and 73 go,The numbers wont be applicable for this question as the number of games played is less then 50.

And for statement 1 my way is same as the one mentioned above. I dont think theres any shortcut for it.
Hope this cud help ..

I mentioned 71 and 73 as a curiosity, not as a possible answer for the present question.

Re statement (1): since A, B, C are consecutive digits, their sum is 3B, which means the number BAC is a multiple of 3. Being a perfect square, then it must be divisible by 9, therefore B itself must be a multiple of 3. The only choices are B=3 and B=6 (B cannot 0 and cannot be 9, otherwise C would be 10, not a digit). 324 is a perfect square, but 657 cannot be, as no perfect square ends in 7.
This is shorter than going through all the possibilities for BAC.

Oh, and (1) obviously sufficient. $$324 = 18^2$$, so the score was 19:17.
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Last edited by EvaJager on 06 Aug 2012, 12:19, edited 1 time in total.

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Re: No wonder Federer lost in his Olympic tennis final, he previ [#permalink]

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06 Aug 2012, 11:15
(2) states "Each played less than 50 games", it doesn't say the sum of the games is less than 50. And not sets, but games.
When dealing with DS questions, you have to work out the answer solely based on the question stem and the info in a specific statement when considering it alone.
I think you mix up sets with games. It is about the third set, and the number of games each played. How are 1 and 3 relevant?[/quote]

No Dear I Haven't Mixed up ! Not at all
If each played less than 50 games then out of those 50 lets say federer one x and the other guy one y, then will the sum of x & y be less than 50 or not ?
and in the last set the winner won exactly two consecutive games more than the loser ! ans their sum has to be a perfect square !.
Now if by solving the first statement i know the values i can just check it in the second statement and find if i can get the anwser or not ! Because you are forgetting the fact that both statements have to give the same answer ! i can either solve the second statement and waste time or i can use the answer i got already and test it in it. because if at all second statement is sufficient than it will give the same answer . now that is a FACT ! and it does

By mistake i did use games ans sets interchangeably that was understandble

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Re: No wonder Federer lost in his Olympic tennis final, he [#permalink]

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13 Aug 2012, 11:07
(7,9) and (17,19) are the two pairs below 50 each satisfies the condition.
Putting the value of stmn b in A:
from (17,19) pair we get 324 i.e. BAC , where A,B,c are consecutive integers.

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Re: No wonder Federer lost in his Olympic tennis final, he [#permalink]

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13 Aug 2012, 11:22
soumyaranjandash wrote:
(7,9) and (17,19) are the two pairs below 50 each satisfies the condition.
Putting the value of stmn b in A:
from (17,19) pair we get 324 i.e. BAC , where A,B,c are consecutive integers.

9 is not prime.

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Re: No wonder Federer lost in his Olympic tennis final, he [#permalink]

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23 Jul 2013, 23:56
Quote:
(1) The square of the average number of games won by Federer and Del Potro is a three digit number of the form BAC, where A,B, and C are non-zero consecutive digits.

lets assume that Federer won "a" games and Del potro "b"

So here statement 1 says ((a+b)/2)^2 = BAC where ABC are consecutive.

lets assume (a+b)/2 = x
x^2 = BAC
the minimum no. of games that would have been played is 14(federer 8 and del potro 6) for federer to win the game
Therefore start the value of x from 7(average of 8 and 6)
By trail and error we find x = 18

therefore (a+b)/2 = 18
and also a=b+2(to win, the difference should be 2 games)

Solving this we get a=19 and b=17

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Re: No wonder Federer lost in his Olympic tennis final, he [#permalink]

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