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## GRE Practice - Quantitative Reasoning - Set 25 1. The figure above shows the dimensions of an isosceles triangle in terms of x. What is the area of the triangle?
1. 24
2. 30
3. 48
4. 60
5. 96

2x+3 = 3x-2 [sides opposite to equal angles]
x = 5
Equal sides = 13
Height: 12
Using Pythagoras theorem we get, base of each half-triangle = 5
Using the property that the perpendicular to the base of an isosceles triangle bisects the base: , we get the base = 10
Area = ½ x Base x Height = ½ x 10 x 12 = 60

1. If the perimeter of an isosceles triangle is 40, then which of the following CANNOT be the length of the unequal side?
1. 21
2. 19
3. 17
4. 15
5. 13

Let the 2 equal sides be x each and the unequal side be y Perimeter: 2x + y = 40 Now, in any triangle the sum of two sides must be greater than the third side So x+y >y and x+x > y Or the sum of the equal sides is greater than the unequal side. Which means the sum of the equal sides is greater than 40/2 = 20 In other words, y < 20 In the figure above, If ABCD is a square and AE = EB, then which of the following statements is NOT true?
Select all that apply.

1. DE = CE
2. p = t
3. q = s
4. r = s
5. r = 30

Using Pythagoras theorem:
In ∆AED AE2 + AD2 = DE2
In ∆BEC BE2 + BC2 = CE2
But AD = BC [sides of a square] and AE = BE [Given]
So DE = CE A is TRUE
DE = CE so the angles opposite must also be equal p = t B is TRUE
q=90-p and s = 90 – t so q = s C is TRUE
r = s if BE = BC but BE = ½ BC. D is FALSE
We know in a 30-60-90 triangle, if r = 30 then BE = √3BC but BE = ½ BC. E is FALSE.

1. If √x = 3 and √y = -2, then what is the value of x2 + y2 +2xy in terms of y?
1. 25
2. 49
3. 97
4. 121
5. 169

√x = 3 so x = 9
√y = -2 so y = 4
x2 + y2 +2xy = (x+y)2 = 132 = 169

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