Correct answer is option - 2
Explanation: Let angle A be = x
Then angle B = x + 16
And angle C = 2x – 12
Sum of the angles of triangle = 180°.
This gives: x + x + 16 + 2x - 12 = 180° ==> 4x + 4 = 180° ==> 4x = 180° - 4
This implies: 4x = 176° ==> x = 176°/4 ==> x = 44°
Therefore angle A = x = 44°, angle B = 44° + 16 = 60°.
Angle C = 2(44°) – 12 = 76°.

Correct answer is option - 2
Explanation:  Let the money carried by Andrew be = m
Let the price of each apple be = p
Since he can buy 30 apples, it would cost him 30 * p = m ==> m = 30p.
Now if the price of each apple was 10 cents less which gives, (p – 10) then Andrew could buy 10 more apples which means 30 + 10 = 40 apples.
This implies: 40 (p – 10) = m ==> 40p – 400 = 30p.
This gives: 40p – 30p = 400 ==> 10p = 400 ==> p = 40 cents.
This gives:  total money = m = 30p = 30 * 40 = 1200 cents.
$1 = 100 cents ==> 1200 cents means $12.

Correct answer is option - 3
Explanation: Given i⁴⁵⁰ can also be written in terms as i⁴, the advantage being i⁴ = 1.
Hence 450 can be split as 450 = 448 + 2, since 448 is exactly divisible by 4.
This gives: i⁴⁵⁰ = i^{448 + 2} ==> i⁴⁴⁸ * i² ==> (i⁴)¹¹² * i² ==> (1)¹¹² * i²
Hence we get: i² which is equal to -1 as the answer.

Correct answer is option - 3
Explanation: Let the number of books she kept with herself = x.
Then the number of books sold = 20% more than x = x + (20/100)x ==> x + 0.2x = 1.2x.
This gives 1.2x = 18 ==> x = 18/1.2 ==> x = 15.
Hence she kept 15 books with herself without selling.

Correct answer is option - 1
Explanation: Taking the common denominator as (5 – x), we get: [1 + 2(5 – x)]/ (5 – x) = 3.
This implies: (1 + 10 – 2x)/ (5 – x) = 3 ==> (11 – 2x)/ (5 – x) = 3.
Cross-multiplying we get: 11 – 2x = 3 (5 -x) ==> 11 – 2x = 15 – 3x.
This gives: 3x – 2x = 15 – 11 ==> x = 4.

Correct answer is option - 4
Explanation: Midpoint of a line segment joining the points (x₁, y₁) and (x₂, y₂) is = [(x₁ + x₂)/2, (y₁ + y₂)/2].
Let the other unknown endpoint be (x, y).
Then [(2 + x)/ 2, (1 + y)/ 2] = (-4, 6)
Now taking each coordinate separately we get: (2 + x)/2 = -4 ==> 2 + x = -8 ==> x = -10.
Similarly, (1 + y)/ 2 = 6 ==> 1 + y = 12 ==> y = 11.
This gives the other endpoint (x, y) = (-10, 11).

Correct answer is option - 3
Explanation: In order to solve for x, we have to split this absolute value equations in two ways.
(5x - 2) + 1 = 9 ==> (5x – 2) = 9 – 1 ==> 5x – 2 = 8 ==> 5x = 10 ==> x = 10/5 = 2.
Similarly, (5x - 2) + 1 = -9 ==> 5x – 2 = -9 -1 ==> 5x – 2 = -10 ==> 5x = -8 ==> x = -8/5.
Since x = 2 is not in the given options, hence the answer is x = -8/5.