Put Q 1/1, i am ans 1 one:

Assume m male , f female

Using 2: 9.8m + 9.1f = 9.3(m+f) => 0.5m = 0.2f or m/f = 2/5 so B is suff

Using 1. Knowing m=52 doesn't help find f, so that we can locate m/f

Answer to Q1:

From statement 1 u cant find the ratio, because there is one unknown, but we can't form an equation using the unknown. Hence INSUFFICIENT to find an answer.

From statement 2, by applying alligation method, you can find that the ratio of male to female employee is 2/5. The method is listed below.

male emp female emp
9.8 9.1
total avg
9.3

total avg-female avg make avg-total avg
0.2 0.5

Hence the ratio of male to female emp is 2/5. So statement 2 alone is sufficient.

Answer B.

For the 2nd question

We have two equations here:

(s+ 3^1/2)^2 + (t-1)^2=8 ------ 1
and s^2+t^2=4 -------------2

Now expanding equation 1 we have

s^2+ 3+2 (3^1/2) s + t^2 +1 -2t =8
=> s^2 + 2 (3^1/2) s + t^2 -2t = 4

Now subtracting equation 2 from equation 1, we get

2 (3^1/2)s -2t =0
=> 2 (3^1/2)s = 2t
=> 3^1/2 s =t -------------- 3 This is out equation 3

Now substituting the value of t in equation 2 we get

s^2 + (3^1/2 s)^2=4
=> s^2+ 3 s^2=4
=> 4 s^2 =4
=> s^2=1
=> s=1 pr s=-1

-1 is not possible because s is in the 1st quadrant (+ve)

Hence the answer would be B.

Correct me if I am wrong anywhere. And this seems to be a lengthy explanation. If any one has a shorter way to do it, please share.

Answer for the 3rd question:

The question asks us to divide (n-1)(n+1) by 24 and find the remainder r, where n is a positive integer. Now prime factorization of 24 gives 24=2^3 * 3^1. So if we can prove that for any value of n, if the no is divisible by 24, we can claim that the remainder is 0.

Statement 1 says that n is odd. So both (n-1) and (n+1) will be even. But we can't say for certain what the remainder will be when divided by 24. For ex: for n=7, 6*8 is divisible by 24 because it has at least three 2's and one 3's as the prime factors. But for n=9, 8*10 is not divisible by 24 because it doesn't have 3 as its prime factors. Hence INSUFFICIENT.

Statement 2 says that n is not divisible by 3. Hence either n-1 or n+1 has to be divisible by 3, which will ensure that we have at least one 3 as its prime factor. But we can't confirm that it will be divisible by 24, because in case of we take n to be even, both n-1 and n+1 will be odd and we can't have 2 as its prime factors. Hence INSUFFICIENT.

Now combining both statements, we can only take values of n that are odd and not divisible by 3, which will at least have three 2's and one 3 as its prime factors. And hence will be divisible by 24 resulting in a 0 remainder.

So the answer would be 'C'.

banibhusan wrote:For the 2nd question

We have two equations here:

(s+ 3^1/2)^2 + (t-1)^2=8 ------ 1 where is 8 coming from please ?
and s^2+t^2=4 -------------2 where is 2 from ?Now expanding equation 1 we have

s^2+ 3+2 (3^1/2) s + t^2 +1 -2t =8
=> s^2 + 2 (3^1/2) s + t^2 -2t = 4

Now subtracting equation 2 from equation 1, we get

2 (3^1/2)s -2t =0
=> 2 (3^1/2)s = 2t
=> 3^1/2 s =t -------------- 3 This is out equation 3

Now substituting the value of t in equation 2 we get

s^2 + (3^1/2 s)^2=4
=> s^2+ 3 s^2=4
=> 4 s^2 =4
=> s^2=1
=> s=1 pr s=-1

-1 is not possible because s is in the 1st quadrant (+ve)

Hence the answer would be B.

Correct me if I am wrong anywhere. And this seems to be a lengthy explanation. If any one has a shorter way to do it, please share.

Thank you

Sorry for omitting that part. The triangle OPQ is a right angled triangle and PQ is the hypotenuse of it. So PQ^2=OP^2+OQ^2. The value of OP=OQ= ((3^1/2) ^2 + 1^2) ^1/2 = (3+1 ) ^ 1/2 = 4^1/2 = 2. Here O is the origin with the coordinates (0,0).

I hope I am clear now.