Question 7, 8

7.
k and t are integers and k²-t² is an odd integer, which of the following must be an even integer ?
I. k+t+2 
II. k²+2kt+t²
III. k²+t²  
a) None
b) I only
c) II only
d) III only 
e) I,II and III

Solution:
First, you must find out whether k and t are odd or even.
This problem is all about the results of performing operations on even and odd numbers.  Given that k^2 - t^2 is an odd number, then you know that k^2 is even, and t^2 is odd.
Of course, it could be reverse, but it shouldn't matter because of commutative and associative laws.  
So, you then know that k must be even, and t must be odd.
Even * Even = Even, and Odd * Odd = Odd. 
Now, just go through the statements: 
1: Even + Odd + Even = Odd 
2: Even*Even + Even*Even*Odd + Odd*Odd = Even + Even + Odd = Odd 
3: Even + Odd = Odd 
Answer then is None (A).

8.
A contractor combined x tons of a gravel mixture than contained 10% gravel G, by weight, with y tons of a mixture that contained 2% gravel G, by weight, to produce z tons of a mixture that was 5% gravel G, by weight. What is the value of x?
Y=10
Z=16
Solution:
Mixture 1 :
10% gravel and quantity : x tonnes
Therefore amount of gravel : 0.1x 
Mixture 2 :
2% gravel and y tonnes 
Amount of gravel : 0.02y  
They are mixed to produce a mixture of z tonnes that is 5% gravel 
Hence, 0.1x+0.02y=0.05z 
We need x.  
Statement 1 
y=10 
Now x+y=z 
x+10=z 
Putting it in the equation  0.1x+10*0.02=(x+10)0.05  
We can get x, hence sufficient. 
Statement 2 
z=16
 ==>x+y=16 
And we have  0.1x+0.02y=0.05z 
i.e  0.1x+0.02y=0.05*16 
We can solve for x and y, hence sufficient, 

Hence D