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Pankaj Kamani @pkaman

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# Official Quant Thread for CAT 2011 [Part 8]

Please continue here with all the quant queries and their discussions. link to previous thread :- http://www.pagalguy.com/forum/quantitative-questions-and-answers/72542-official-quant-thread-cat-2011-a.html :cheerio: :cheerio: :c...
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And 2^1008 + 1 = (2^336)^3 + 1 => Divisible by 2^336 + 1
Also, 2^1010 + 1 = (2^2)^505 + 1 => Divisible by 2^2 + 1
How did u get that if u divide by this it will be divided by 2^336 + 1
Ok let's value is 2^2012+1 then????
1) ye to upar se gaya

(a^n + b^n) is divisible by (a+b) if n is odd.
So, I just adjusted some odd power other than 1 for the numbers.

2^2012 + 1 = (2^4)^503 + 1 .... 2012 = 4*503
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Now Submarine and warship both are underwater..we need to find height of the warship over the submarine..
tan30 = height / 50
=> height = 50 * 1/root3
Now after 30 mins the distance is (50-x)
height will remain same..
=> tan60 = 50/(root3) /
=> 50-x = 50 / 3
=> x = 100/3 = 33.33m ?

could anyone make me undestand what is distance between them from the point of observation is 50 km? i am getting it ? you could explain by digram..what is observation point.
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(3) None of them is prime.

3 leaves remainder by 2 as -1.
So, 2^1009 + 1 and 2^1011 + 1 will leave remainder by 3 as (-1+1) = 0

And 2^1008 + 1 = (2^336)^3 + 1 => Divisible by 2^336 + 1
Also, 2^1010 + 1 = (2^2)^505 + 1 => Divisible by 2^2 + 1

And 2^1008 + 1 = (2^336)^3 + 1 => Divisible by 2^336 + 1
Also, 2^1010 + 1 = (2^2)^505 + 1 => Divisible by 2^2 + 1
How did u get that if u divide by this it will be divided by 2^336 + 1
Ok let's value is 2^2012+1 then????
1) ye to upar se gaya

EDIT: are yar neha, ques to diya karo kaha se ques ab
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Take them to be a cyclic trapezium.Of the 4 triangles formed by the diagonals two are equal and the other two are similar.
APB and DPC are equal in area
ADP and BPC are similar
In triangle ABD,
BP:PD = 3:2 [ given area(APD)/area(BPC) = 9/4..sq root will be sides ]
given Area (APD) = 12
Area (ABP):12 = 3:2
=>Area (ABP) = 18

could you clearly explain why APD and BPC are similar?
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1. In an examination having 2 subjects, a student gets 90iles in each subject. What can be the overall maximum and minimum %ile of the student?
2. How many Squares formed by Joining 4 points such that co-ordinate of each point is Intgral (both X And Y). And both X and Y co-ordinate is lies in range .
3. 2^1008+1,2^1009+1,2^1010+1,2^1011+1
which one are prime number?

(1) Minimum percentile will be 80 and maximum will be 100.

Minimum: He has least percentile of 90.
Say he got 10 marks out of 100 in bothe the subject which gives him 90 percentile.
Now say those 10% students ahead of him in each subject score more than 50 in resp. subject. And they are different 10% people.
So, totally 20% people surely have more than 50 marks.

So, he can get 80 percentile. Less than 80 is not possible as students ahead of him must do better than him in at least one section. So, at most 20% such people can be there.

Maximum: He can score 100
Say, he scores 90 and 90 in two subjects. People who are behind him score less than 10 in each. And there are different set of people ahead of him in two sections. So, maximim possible marks of other students are (100+10) = 110. So, he is way ahead of all.

(2) Will try this one after some time

(3) None of them is prime.

3 leaves remainder by 2 as -1.
So, 2^1009 + 1 and 2^1011 + 1 will leave remainder by 3 as (-1+1) = 0

And 2^1008 + 1 = (2^336)^3 + 1 => Divisible by 2^336 + 1
Also, 2^1010 + 1 = (2^2)^505 + 1 => Divisible by 2^2 + 1
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Take them to be a cyclic trapezium.Of the 4 triangles formed by the diagonals two are equal and the other two are similar.
APB and DPC are equal in area
ADP and BPC are similar
In triangle ABD,
BP:PD = 3:2 [ given area(APD)/area(BPC) = 9/4..sq root will be sides ]
given Area (APD) = 12
Area (ABP):12 = 3:2
=>Area (ABP) = 18

could you clearly explain why APD and BPC are similar?
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3. 2^1008+1,2^1009+1,2^1010+1,2^1011+1
which one are prime number?

2^1010+1 ends with 5 so cant be prime

2^1009+1 2^1011 are divisible by 3

2)..20????

1)..80 and 100 waise hi tukka....;)
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3. 2^1008+1,2^1009+1,2^1010+1,2^1011+1
which one are prime number?

2^1008+1 Numbers of the form 2^4n+1 are always primes

P.S : 2^43112609-1 is the largest known prime
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1. In an examination having 2 subjects, a student gets 90iles in each subject. What can be the overall maximum and minimum %ile of the student?

2. How many Squares formed by Joining 4 points such that co-ordinate of each point is Intgral (both X And Y). And both X and Y co-ordinate is lies in range .

3. 2^1008+1,2^1009+1,2^1010+1,2^1011+1
which one are prime number?
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a five digit no divisible by 3 is to be formed using numerical 0,1,2,3,4,5 without repetition . the toal no of ways this can be done is:

1. 122
2. 210
3. 216
4. 217

case 1: no zero
the digits must be 1,2,3,4,5
these can be arranged in 5! = 120 ways
case 2: when we use zero
you can only use 1,2,4,5
number of ways
for zer0 = 4 ways
rest 4! = 24
total = 120+4*24216 ways
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