I really do not like to post a bunch of questions at a time

Question

I really do not like to post a bunch of questions at a time but seems everybody is ok with this practice. i will post seperately if any. 


1. 200 is 20% less than a number, what is the number:

2. 1/2X = 1/(X + 1/4X), which of the following can be values of X?

3. 10 teachers and 10 students, how many arrangement are possible where there is one teacher more than students.



6. x*y = x + y – xy, Is rs = 0 ?
I. r*s = 0
II. r=s
 


7. x = 10^100, x^x = 10^k, k=?


8. w, n, v are consecutive integers, not in the order, which is the middle integer?

I. n-v = 2
II. w-n < 0

ywilfred · Answer

1. 200 is 20% less than a number, what is the number: 

Let the number be x.
0.8x = 200, then x = 250

ywilfred · Answer

2. 1/2X = 1/(X + 1/4X), which of the following can be values of X? 
1/2x = 4x/(4x^2+1)
4x^2+1 = 8x^2
4x^2-1 = 0
(2x+1)(2x-1) = 0
x = 1/2, -1/2

ywilfred · Answer

3. 10 teachers and 10 students, how many arrangement are possible where there is one teacher more than students. 

So the possibilites are
1 teachers, 0 student = 10
2 teachers, 1 student = 450
3 teachers, 2 students = 5400
4 teachers, 3 students = 25200
6 teachers, 5 students = 52920
7 teachers, 6 students = 25200
8 teachers, 7 students = 5400
9 teachers, 8 students = 450
10 teachers, 9 students = 10

Total = 115040?!

ywilfred · Answer

6. x*y = x + y – xy, Is rs = 0 ? 
I. r*s = 0 
II. r=s 

St1:
r*s = r+s - rs = 0
r+s = rs

Can be:
(r,s) = (0,0) 
(r,s) = (2,2)

Insufficient.

st2:
many possibilites of (r,s). Insufficieint.

Using st1 and st2:
Still can't differentiate if (r,s) is (0,0) or (2,2). Insufficient.

Ans E

ywilfred · Answer

8. w, n, v are consecutive integers, not in the order, which is the middle integer? 

I. n-v = 2 
II. w-n <0> v is middle integer
If w = -10, n = -1, then v = -3 --> v is middle integer.
If w = -10, n = 1, then v = -1 --> v is middle integer.

Sufficient.

Ans C

ywilfred · Answer

7. x = 10^100, x^x = 10^k, k=? 

x^x = 10^100^(10^100)
k = 100^(10^100)= 10^(2*10^100)

k = 2*10^100

Sumithra Sen · Answer

200 is 20% less than a number, what is the number: 

Number is 250

2. 1/2X = 1/(X + 1/4X), which of the following can be values of X? 

X = -1/2 or 1/2

3. 10 teachers and 10 students, how many arrangement are possible where there is one teacher more than students. 

I am very weak in probability ..But here is how I calculated it.. Is there a better link to learn probability well..Always been bad at this

1 0 ----------------------1 

2 1
2 0 ......................................2 
3 0 , 1, 2 .................................3. 
4 0, 1 , 2 ,3....................................4
5 0,1 ,2, 3,4 ......................................5
6 0,1,2,3,4,5...................................... 6
7 0,1,2,3,4,5,6.....................................7
8 0,1,2,3,4,5,6,7....................................8
9 0,1,2,3,4,5,6,7,8....................................9
10 0,1,2,3,4,5,6,7,,8,9.................................10


55 ?

6. x*y = x + y – xy, Is rs = 0 ? 
I. r*s = 0 
II. r=s 

Does X * y mean the same Xy ..Couldnt understand the notations



7. x = 10^100, x^x = 10^k, k=? 

Couldnt solve this.. Help?


8. w, n, v are consecutive integers, not in the order, which is the middle integer? 

I. n-v = 2 
II. w-n < 0

I come up A as sufficient

Because its give that , W, N V are consecutive integers

Postive Eg

0, 1, 2 , N - V = 2 , means W has to be middle 

Negative Eg

-1 0 1 , again , N - V = 2 , means W has to be middle

-4, -3, -2 , N - V = 2 , means ( -2 + 4 = 2) W has to be midle 


Choice B says w - n < 0 

 1 0 2 
 w n v 

 5 4 3 

4 - 5 < 0
3- 4 < 0 

There are 2 possible values that can satisfy w-n <0 in consecutive integers

Hence not a definete answer on what might be the middle number..

gixxer1000 · Answer

7. x = 10^100, x^x = 10^k, k=? 

A. Substitute 10^100 for both x's
10^100^(10^100)=10^k

B. Multiply Exponents 
Eg. (x^2)^3=x^6
10^(100*(10^100))=10^k

C. Now that the bases are the same set the exponents = each other
100*10^100=k

D.Rewrite 100 so the bases are the same
10^2*10^100=k

E.Add exponents
10^102=k

Whatever · Answer

1. 200/80% = X/100%
X = 250

2. 2x = x+1/4x (*4x)
8x^2 = 4x^2 +1
4x^2 = 1
x^2 = 1/4

x = 1/2 or x = -1/2

3. Don't know ... will use POI. Definitely will be big number.

6. 
I. r + s - rs = 0
rs=0 can't answer --> BCE
II. r = s can't answer --> CE
Together: 2s - s^2 = 0
s = 0 or s = 2 can't unswer --> left with E

7. x = 10^100, x^x = 10^k, k=? 
1) x^x = 10^100^10^100 => k = 100^10^100 = 10^(2*10)^100 and I stuck here .. 

8. w, n, v are consecutive integers, not in the order, which is the middle integer? 

I. Suff: n-v = 2 ==> w is in the middle (properties of consecutive integers = difference between 2 cons. int. = 1 ==> v ... diff 1 ... W ... diff 1 ... n)
II. Ins: w-n w<n, but we don't know which one is in the middle - is it n or w?
ANS: A

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