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## GRE Practice - Quantitative Reasoning - Set 22

1. If 6 + 7|x + 4| = 48, then x could equal which of the following?
1. -10
2. -2
3. 2
4. 4
5. 10

Subtract 6 from both sides:
7|x + 4| = 42
|x + 4| = 6
So, (x + 4) = 6 or (x +4) = −6
x = 2 OR -10

1. A certain rectangle has an area of 36 and a perimeter of 26. What is the positive difference between the length and breadth of the rectangle?
1. 4
2. 5
3. 6
4. 9
5. 13

Perimeter = 26 2(L + B) = 26
L = 13 – B
Area = 36
So, (13 – B)B = 36
B2 – 13B + 36 = 0
B2 – 9B – 4B + 36 = 0
B(B – 9) -4(B – 9) = 0
(B – 4) (B – 9) = 0
B= 4, 9
Positive Difference= 9-4 = 5

1. If O is the centre of the circle and its radius of is 8, then what is the area of the shaded region?
1. 32
2. 64
3. 16π – 16
4. 32π – 16
5. 16π − 32

The sector has a central angle of 900 so it represents ¼ of the circle.
Area of sector = ¼ π (8)2 = 16 π
Area of isosceles right triangle AOB = ½ x 8 x 8 = 32
Area of shaded region = Area of sector – area of ΔAOB = 16 π – 32

1. If 2x+4 × 3y-1 = 576, where x and y are integers, what is x + y?

576 = 242 and 24 = 23 x 3
So, 576 = 26 x 32
But 2x+4 × 3y-1 = 576 = 26 x 32
x+4 = 6; x = 2
y – 1 = 2; y = 3
x+y = 5

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