Official Quant thread for CAT 2013

MBA CAT 2024
24208
@saurav205 said:
Good Morning Guys,sab kahan gayab ho?When a two digit number is added to another two digit number having the same digits in reverse order, the sum is a perfect square.How many such 2 digit numbers are there?46810
10a+b+10b+a = k^2
11a+11b = k^2
a+b = k^2/11

so basically a+b = 11

hence 8 numbers...
24209
@sachisurbhi said:
N = 3! + 4! ..... + 64!which of the following statements is true regarding N
a) N --perfect square
b)N --perfect cube
c) both A & B
D) neither A nor B
Neither A or B ??
24210
@saurav205 : i think it shud be 10:
11(a+b)=x^2
a+b=11
so (a,b) = (1,10),(2,9),(3,8),(4,7),(5,6),(6,5),(7,4),(8,3),(9,2),(10,1)
total 10
24211
@arunrajput1007 said:
@saurav205 : i think it shud be 10:11(a+b)=x^2a+b=11so (a,b) = (1,10),(2,9),(3,8),(4,7),(5,6),(6,5),(7,4),(8,3),(9,2),(10,1)total 10
a or b can't be 10
24212
@ScareCrow28
@Logrhythm said:
10a+b+10b+a = k^211a+11b = k^2a+b = k^2/11so basically a+b = 11 hence 8 numbers...
So it shud be 8....!!!

24213
@arunrajput1007 said:
@saurav205 : i think it shud be 10:11(a+b)=x^2a+b=11so (a,b) = (1,10),(2,9),(3,8),(4,7),(5,6),(6,5),(7,4),(8,3),(9,2),(10,1)total 10
bhai single digits hai...
24214

last post 5:15 yaani ek ghante pahle hua tha... sorry to spam, but koi toh questions post karo for the hungry QA players...

24215
Each question is followed by two statements, X and Y. Answer each question using the following instructions:Mark (A) If the question can be answered by using the statement X alone but not by using the statement Y alone.Mark (B) If the question can be answered by using the statement Y alone but not by using the statement X alone.Mark (C) If the question can be answered by using either of the statements alone.Mark (D) If the question can be answered by using both the statements together but not by either of the statements alone.Mark (E) If the question cannot be answered on the basis of the two statements.

Let p(x) = x^2 + 40. Then for any two positive integers i and j where i > j, is p(i) + p(j) a composite number?
(X) p(i) €“ p(j) is not a composite number
(Y) p(2i) + p(2j) is a composite number
24216

if the roots of the equation x^10 - 1 = 0 are 1,a,b,c.... i, then what is the value of

(1-a)(1-b)... (1-i) ?
24217
Find the last two digits of 78^379.
24218
@pratskool said:
Find the last two digits of 78^379.
92
24219
@pratskool said:
Each question is followed by two statements, X and Y. Answer each question using the following instructions:Mark (A) If the question can be answered by using the statement X alone but not by using the statement Y alone.Mark (B) If the question can be answered by using the statement Y alone but not by using the statement X alone.Mark (C) If the question can be answered by using either of the statements alone.Mark (D) If the question can be answered by using both the statements together but not by either of the statements alone.Mark (E) If the question cannot be answered on the basis of the two statements.undefinedLet p(x) = x^2 + 40. Then for any two positive integers i and j where i > j, is p(i) + p(j) a composite number?(X) p(i) €“ p(j) is not a composite number(Y) p(2i) + p(2j) is a composite number
(C) If the question can be answered by using either of the statements alone
24220

there is a triangle ABC..dere is a point P inside the triangle such dat its distance from d three sides are 6,8 and 11..find the perimeter of the triangle??

24221
@gs4890 said:
92
approach???
24222
@pratskool if the roots of the equation x^10 - 1 = 0 are 1,a,b,c.... i, then what is the value of
(1-a)(1-b)... (1-i) ?

is dat 2?
24223
@pratskool said:
Find the last two digits of 78^379.
92
24224
@Nihilist1002 said:
@pratskoolif the roots of the equation x^10 - 1 = 0 are 1,a,b,c.... i, then what is the value of(1-a)(1-b)... (1-i) ?is dat 2?
no...

@gs4890

@iLoveTorres said:
92
right answer
24225
@pratskool said:
if the roots of the equation x^10 - 1 = 0 are 1,a,b,c.... i, then what is the value of(1-a)(1-b)... (1-i) ?
the other obvious root is -1 so the value may be 2.? else 0?
24226
@pratskool said:
Find the last two digits of 78^379.
92 ?

78^379 = (2*39)^379 = 2^379*39^379 = 2^9*(2^10)^37*(39^2)^189*39 = 12*24*81*39 = 92
24227
@pratskool said:
if the roots of the equation x^10 - 1 = 0 are 1,a,b,c.... i, then what is the value of(1-a)(1-b)... (1-i) ?

Is it 10?

x^10 - 1 = (x - 1)(x - a)...(x - i) as they are the factors

So (x - a)...(x - i) = (x^10 - 1)/(x - 1)

Now replace x by 1.

RHS will be limit x -> 1, (x^10 - 1)/(x - 1) , a 0/0 form

So apply L'Hospitals Rule: 10x^9 = 10*1 =10

A very important thing to note is all these a,b,c ... i are the 10th roots of unity.

So , a can be w , b can be w^2 ... and so on.

X^n - 1 = 0, gives nth roots of unity.

So roots will be: w,w^2,...,w^n-1 and 1.