GMAT - Geometry Problems and Questions with Answers

GMAT - Geometry Problems and Questions with Answers

1.    Three tangents of a circle with centre O from  Geometry Problems APB. If o, find

Geometry Problems

A. 60o
    B. 110o
    C. 75o
    D. 140o
    E. None of these

2. A fly is trapped inside a hollow cube. It moves from A to B along the edges of the cube, taking the shortest possible route. It then comes back to A, again along the edges, taking the longest route (without going over any point more than once). If the total distance travelled is 5,040 m, what is the area of a face of the cube?

Geometry Problems

A. 99,225 m2
B. 32,400 m2
C. 3,96,900 m2
D. 46,225 m2
E. None of these

3. In the given parallelogram ABCD, if 3(BE) = 2(DC) and the area of  Geometry ProblemsDQC is 36, find out the area of Geometry ProblemsBQE.

Geometry Problems

A. 16
B. 20
C. 24
D. 18
E. None of these

4. In the given figure, BO and CO are the bisectors of

Geometry Problems

A. 75o
B. 65o
C. 90o
D. 80o
E. None of these

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5.  In the following figure, if PQ = R(P is the centre of the bigger circle) and the shaded area is equal to A, then the radius of the inner circle is equal to

Geometry Problems

A. Geometry Problems

B. Geometry Problems

C. Geometry Problems

D. Geometry Problems

6.  Find the value of x in the following figure.

Geometry Problems

A. 360o – (a + b + c) 
B. b – a – c
C. 180o – c
D. 180o + c
E. None of these

7. If O is the centre of the circle then find the value of (x + y).

Geometry Problems

A. 35
B. 20
C. 70
D. 90
E. None of these

8. If C is the center of two concentric circles as shown in the figure and mo, then find m

Geometry Problems

A. 50o
B. 80o    
C. 100o
D. 130o
E. 135o

9. In the given figure if B is the midpoint of AC then find m + n +5/2.

Geometry Problems

A. 0
B. 1
C. 2
D. -1
E. -2

10. If A (–2, –1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram, find the values of a + b.

A. 3
B. 4
C. 5
D. 6
E. 8

Solution

1. B

Geometry Problems

It is clear that o
 Geometry ProblemsAT = AM and BR = BM
(Length of the tangents from an external point)
Hence, angle at the centre of the circle must be equal.
So We have to find

Geometry Problems= 360 – 140

[o, calculated earlier]

Geometry ProblemsGeometry Problems = 220/2 = 1100

2. C

Geometry Problems

As cube shown in the figure where to reach from A to B by the shortest route will be 2x (if x be the length of the side of the cube), and the longest route from B to A will be 6x.

Hence, 2x + 6x = 5040;  x = 5040/8 = 360m

Geometry Problems Area of a face = x2 = (630)2 = 396900 m2

3.  A

Geometry Problems

It is given that 3BE = 2DC or BE/DC = 2/3

Since Geometry ProblemsDCQ and Geometry ProblemsBQE are similar,

Geometry Problems

or Ar(Geometry ProblemsBQE) = 36 x 4/9 = 16

4.    B
     Geometry Problems

5. D

Here as given that PQ = R

Let us assume r be the radius of the inner circle.

Geometry Problems

6. B

Geometry Problems

Interior angle DCB = 3600 –b. Now, in quadrilateral ABCD, a + x + 3600 –b +c = 3600 => x = b – a - c.

7. E

Geometry Problems

 Angles drawn on the same arc and in the same segment are equal).

Geometry Problems 0 . Now in Geometry ProblemsBCF , 350 + (x+900) + y = 1800

=> x + y =1800 - 1250 = 550.

8. B

Geometry Problems

Geometry Problems

9. A

Geometry Problems

Similarly, Geometry Problems

Geometry Problems

10. B

We know that the diagonals of a parallelogram bisect each other. So, the coordinates of the mid-point of AC are same as the coordinates of the mid-point of BD.

Geometry Problems