Official Quant thread for CAT 2013

MBA CAT 2024
28240
@subhakimi said:
Answer is 1/2What we need to take is that the height cannot be less than 1 and so is the baseSo we can take height to be 1 and base to be 1 as well.Then we can draw an obtuse angled triangle and stretch it as far as possible. You need not bother about lengths as the height & base are fixed
What is the least area of a triangle whose vertices have integral co-ordinates and two of the sides are greater than 2013?

Bhai yeh solution iss question ka hai?
28242
@ScareCrow28 said:
Couldn't understand sir, 2 of the lengths are > 2013 na..You have fixed 2 of them as 1, so howcome they satisfy the question?
aisa kuch banega shayad.

correct me if i am wrong
28243
@Iamchaitu said:
A Free 2.5 hour Intensive CAT €“ Workshop for 99th percentile Aspirants byAnil Nair (Mathemagician-Ex Academic Head-CL South)Date: 23 March 2012

Umm, you do know that means he is an ex-mathemagician, right? Seems like he's an old has-been....
@Iamchaitu said:
,India's Most Loved ...... National motivator )

:o Wow, he gets people to join the army or what? National motivator, that's a new one....
@Iamchaitu said:
2.Special Copyrighted and Innovative ways of solving CAT based problems developed from 3500 mathematical books

So he takes material from 3500 books and copyright it? How does that work exactly? Next we'll get Americans patenting turmeric.

Oh, wait, that already happened... http://www1.american.edu/ted/turmeric.htm

@Iamchaitu said:
We are not the best training mentors for the non-serious candidate....

You should consider attending a Critical reasoning class. The above statement is in no way remotely equivalent to what I assume you were trying to say.

@Iamchaitu said:
We just expect students to be serious .

Why so serious?

Since this is Quant thread....a couple of quant questions too! Wouldn't want to spam unnecessarily....unlike some people ^

What is the remainder when 15^17 +16^17 +17^17 +18^17 +19^17 is divided by 34?

Given a hexagon ABCDEF, with sides AB = BC = CD = DE = EF = FA = 31.4 cm, what is the possible range of values that angle ABC can take?

regards
scrabbler
28244
@subhakimi said:
Last one for the night ...Which is the smallest positive integer which can be represented as the sum of two perfect squares in exactly two ways ?
50?
1^2 + 7^2 = 5^2 + 5^2
28245
@scrabbler said:
Umm, you do know that means he is an ex-mathemagician, right? Seems like he's an old has-been.... Wow, he gets people to join the army or what? National motivator, that's a new one.... So he takes material from 3500 books and copyright it? How does that work exactly? Next we'll get Americans patenting turmeric.Oh, wait, that already happened... http://www1.american.edu/ted/turmeric.htmYou should consider attending a Critical reasonning class. The above statement is in no way remotely equivalent to what I assume you were trying to say.Why so serious? Since this is Quant thread....a couple of quant questions too! Wouldn't want to spam unnecessarily....unlike some people ^What is the remainder when 15^17 +16^17 +17^17 +18^17 +19^17 is divided by 34?Given a hexagon ABCDEF, with sides AB = BC = CD = DE = EF = FA = 31.4 cm, what is the possible range of values that angle ABC can take?regardsscrabbler
17?
28246
@scrabbler said:
unnecessarily....unlike some people ^What is the remainder when 15^17 +16^17 +17^17 +18^17 +19^17 is divided by 34?Given a hexagon ABCDEF, with sides AB = BC = CD = DE = EF = FA = 31.4 cm, what is the possible range of values that angle ABC can take?regardsscrabbler
Keh ke leli !!

17^17 mod 34 = 17
28247
@scrabbler said:

Given a hexagon ABCDEF, with sides AB = BC = CD = DE = EF = FA = 31.4 cm, what is the possible range of values that angle ABC can take?regardsscrabbler
i guess it should be 105-120?
28248
@scrabbler said:
What is the remainder when 15^17 +16^17 +17^17 +18^17 +19^17 is divided by 34?
17 ?

17^17 mod 34 = 17
28250
@subhakimi said:
Last one for the night ...Which is the smallest positive integer which can be represented as the sum of two perfect squares in exactly two ways ?
I would think the number is a perfect square itself, so that a^2 + b^2 = d^2 and 0^2 + d^2 = d^2

we take the smallest pythagoras triplet and get
d = 25 = 3^2 + 4^2 = 0^2 + 5^2


28251
@subhakimi said:
What if all the numbers are distinct.
1^2 + 8^2 = 4^2 + 7^2
28252
@subhakimi said:
Last one for the night ...Which is the smallest positive integer which can be represented as the sum of two perfect squares in exactly two ways ?
65 ?

1^2 + 8^2 = 7^2 + 4^2 = 65
28253
@subhakimi said:
What if all the numbers are distinct.
65

49 +16 = 64 +1

regards
scrabbler
28254
@mailtoankit
first see which vertex will affect which all opposite vertices.
like A will affect D and C and so on.

for A we can use 6 colors.

For b, either paint it same as A, or any of the other 5 colors.

let's take the case when B is same as A.

C can be of 5 colors (cannot use A's color)
D also 5.
E 4. (must be different from C and B)
so for 1st case... 6*1*5*5*4 = 600

let's take case 2.
when B can be of 5 colors.
Now,here either C can be of 4 colors , or C same as B.

Suppose C takes 4 colors, then D will also take 4, and E also 4.
=>6 * 5*4*4*4 = 1920

And if C is same as B, C can take only 1 color. D can take 4. and E =5.
=> 6*5*1*4*5= 600


so total ways... 600+600+1920= 3120
28255
@scrabbler said:
. So he takes material from 3500 books and copyright it? How does that work exactly?
same doubt . But this is an Epic one!!
@scrabbler said:
unnecessarily....unlike some people ^What is the remainder when 15^17 +16^17 +17^17 +18^17 +19^17 is divided by 34?
that should be divisible by 17 since it is divisible by 85 and an odd one , so remainder is 1 upon divided by 2.

hence 17k= 2m+1

=17?
28256
@iLoveTorres said:
i guess it should be 105-120?
Dost average is 120....so if one angle goes to 105 (i.e. less than 120) shouldn't some other go to more than 120?

Anyway you are still far from the solution...try again :)

regards
scrabbler
28258
@subhakimi said:
1. First one is of course,17.

Yes, everyone got this right 😃 OA
@subhakimi said:
2. If I can assume concave is also possible then I think it is more than 60 degree and less than 180 degree.Is it correct ?
No. Think harder, this one is devious.

regards
scrabbler
28260
@subhakimi \___-__O__//
28261
@subhakimi said:
Last one for the night ...Which is the smallest positive integer which can be represented as the sum of two perfect squares in exactly two ways ?
65 ??? sir, a^2 + b^2 = c^2 + d^2 --> a^2 - c^2 = d^2 - b^2 --> (a-c)(a+c) = ( d-b)(d+b) so a number which can satisfy both sides has to be a product of 2 odd or 2 even numbers, in 2 different ways,,,
1*3 wont satisfy, 2*4 wont,,, 3*5 does.... hence solving we get a = 4 , b = 7, c = 1 , d = 8
28262
@scrabbler said:

No. Think harder, this one is devious.regardsscrabbler
It can take all values greater than 0 and less than 360
28263
@subhakimi said:
Bache ki na lo sir... positive number bolna bhul gaya toh itne easily kar loge aap Anyways I was looking for 65 actually.No one posted approach ... it can be done by hit & trial , I assume most had done that Try to give it a logical explanation as well
Difference between two squares to be same in two ways (a+b)(a-b) in 2 ways smallest odd case is 15...= 5*3 and 15*1 = (4+1)(4-1) and (8+7)(8-7) so we get two pairs whose diff is same, rearrange and get two whose sum is same .

#trialanderrorworkedfaster :o

regards
scrabbler