Official Quant thread for CAT 2013

MBA CAT 2024
4481
@pankaj1988 said:
If JUNK is written as B5C7B7A11 which word is written as B4C3B7B2?
J = 10 = Bx5
U = 21 = C x 7
N = 14 = B x 7
K = 11 = A x 11

Similarly

Bx4 = 8 = H
Cx3 = 9 = I
Bx7 = 14 = N
Bx2 = 4 = D

regards
scrabbler
4482
@pankaj1988 said:
TIME soln:B4C3B7B2 is coded as HIND
B4 = 2*4 = 8 = H
C3 = 3*3 =9 = I
B7 = 2*7 = 14 =N
B2= 2*2 = 4 = D
4483
sin α + sin β + sin γ = 0

cos α + cos β + cos γ = 0

cos (α − θ) + cos (β − θ) + cos (γ − θ) = ?
OPTIONS

1) sin θ
2) sin^2 θ
3) 0
4) 1 – cos θ
4484
How many numbers from the set A ≡ {11, 111, 1111, …, 111111…20 times} have an odd number of factors?
OPTIONS

1) 4
2) 3
3) 7
4) 9
5) None of these
4485
@pankaj1988 said:
If JUNK is written as B5C7B7A11 which word is written as B4C3B7B2?
J - 10
U - 21
N- 14
K - 11

B5 - 2*5
C7 - 3*7
B7 - 2*7
A11 - 1*11

so
B4C3B7B2
=>
B4 - 2*4=8
C3 - 3*3-9
B7 - 2*7=14
B2 - 2*2=4

so HIND
4486
If x is a natural number which is a perfect square, then the number x^2 ˆ' x must end in:
OPTIONS

1) 0, 2 or 6
2) 0 or 2
3) 0 or 4
4) None of these
4487
@sujamait said:
If x is a natural number which is a perfect square, then the number x^2 ˆ' x must end in:OPTIONS1) 0, 2 or 6 2) 0 or 2 3) 0 or 4 4) None of these
b
4488
@sujamait said:
If x is a natural number which is a perfect square, then the number x^2 ˆ' x must end in:OPTIONS1) 0, 2 or 6 2) 0 or 2 3) 0 or 4 4) None of these
0,2,6???
4489
@sujamait said:
If x is a natural number which is a perfect square, then the number x^2 ˆ' x must end in:OPTIONS1) 0, 2 or 6 2) 0 or 2 3) 0 or 4 4) None of these
is it 1????
4490
@sujamait said:
sin α + sin β + sin γ = 0cos α + cos β + cos γ = 0cos (α − θ) + cos (β − θ) + cos (γ − θ) = ?OPTIONS1) sin θ 2) sin^2 θ 3) 0 4) 1 – cos θ
3) 0
4491

x^2 -x can end in 0,2,6

4492
@sujamait said:
If x is a natural number which is a perfect square, then the number x^2 ˆ' x must end in:OPTIONS1) 0, 2 or 6 2) 0 or 2 3) 0 or 4 4) None of these
Option 1

4493
@sujamait said:
sin α + sin β + sin γ = 0cos α + cos β + cos γ = 0cos (α − θ) + cos (β − θ) + cos (γ − θ) = ?OPTIONS1) sin θ 2) sin^2 θ 3) 0 4) 1 – cos θ
Is it 0?? 0%sure
4494
What is the probability that the product of two integers chosen at random has the same unit digit as the two integers?
4495
@sujamait said:
How many numbers from the set A ≡ {11, 111, 1111, …, 111111…20 times} have an odd number of factors?OPTIONS1) 4 2) 3 3) 7 4) 9 5) None of these
9??
4496
@sujamait said:
If x is a natural number which is a perfect square, then the number x^2 ˆ' x must end in:OPTIONS1) 0, 2 or 6 2) 0 or 2 3) 0 or 4 4) None of these
1?
4497
@sujamait said:
sin α + sin β + sin γ = 0cos α + cos β + cos γ = 0cos (α − θ) + cos (β − θ) + cos (γ − θ) = ?OPTIONS1) sin θ 2) sin^2 θ 3) 0 4) 1 – cos θ
0 ?
4498
@sujamait said:
sin α + sin β + sin γ = 0cos α + cos β + cos γ = 0cos (α − θ) + cos (β − θ) + cos (γ − θ) = ?OPTIONS1) sin θ 2) sin^2 θ 3) 0 4) 1 – cos θ
cos (α − θ) + cos (β − θ) + cos (γ − θ)
=>(cos a*cos θ + sin a*sin θ)+(cos β*cos θ + sin β*sin θ)+(cos γ*cos θ + sin γ*sin θ)
=>cos θ(cos a+cos β+cos γ) + sin θ(sin a+sin β+sin γ)
=>0


@sujamait said:
How many numbers from the set A ≡ {11, 111, 1111, …, 111111…20 times} have an odd number of factors?OPTIONS1) 4 2) 3 3) 7 4) 9 5) None of these
5)none?
4499
@sujamait said:
How many numbers from the set A ≡ {11, 111, 1111, …, 111111…20 times} have an odd number of factors?OPTIONS1) 4 2) 3 3) 7 4) 9 5) None of these
5)none EDITED
4500
@amresh_maverick said:
What is the probability that the product of two integers chosen at random has the same unit digit as the two integers?
3/10 ?