Quantitative questions!! Any help would be appreciated!!

[baseballislife]

1. A certain experiment has three possible outcomes. The outcomes are mutually exclusive and have probabilities p, p/2, and p/4, respectively. What is the value of p?

A. 1/7
B. 2/7
C. 3/7
D. 4/7
E. 5/7

The answer is D. 4/7

2. Which of the following is equal to 6¹⁴/(2⁵)(3⁷)?

A. (2^2)(3^2)
B. (2^7)(3^7)
C. (2^9)(3^2)
D. (2^9)(3^7)
E. (2^9)(3^9)

The answer is D. (2^9)(3^7)

3. The perimeter of square S is 40. Square T is inscribed in square S. What is the least possible area of square T?

A. 45
B. 48
C. 49
D. 50
E. 52

The answer is D. 50

[Pournima Ghule]

Ans:
1)
Total there are 3 possibilities
so outcome will be either p or p/2 or p/4
so OR means addition...
i.e. p+p/2+p/4
which gives 7p/4 => p= 4/7


2. 6¹⁴/(2⁵)(3⁷) =( 2.3 )¹⁴/(2⁵)(3⁷) = (2¹⁴)(3¹⁴)/ (2⁵)(3⁷) = (2^9)(3^7)

3. I am not sure about this answer but in one way it could be deduced like this....
the perimeter of square S is 40 implies each side of S is 10. The way T can be inscribed is one these two extremes: It is precisely the same square or it is a diamond in the square.
If we consider the diamond, then the diagonal of that square would be 10, meaning one of the sides would have a length of 5√2 (coz if diagonal is s then side is s√2 ).
Thus, the perimeter of this square T is 20√2 ≈ 28.28...
therefore this square is smaller, so its area is smaller (area of square T = 50)