Aptitude and Reasoning Questions

Q:

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.

What is the ratio of the volume of the sphere to that of cone?

A) 6√3:1 B) 7 : 2
C) 3√3:1   D) 5√3:1
 
Answer & Explanation Answer: A) 6√3:1

Explanation:
The top view of the given assembly will look like the figure above
Outermost is the sphere. Inside that there is a cube and within that there is a cone and cylinder with same radius.
Here side of cube = a
Diameter of Sphere = body diagnol = √3 a
Radius of sphere = √3 a/2 =r1
Height of Cylinder = Height of cone = side of cube = a =h
Radius of cylinder = Radius of cone = side of cube/2 = a/2 =r2(as shown in the figure)
Volume of sphere/volume of cone = 43πr1313πr22h = 6√3:1
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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

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Q:

ABCD is a quadrilateral in which BD and AC are diagonals then

A) AB + BC + CD + AD< AC + BD B) AB + BC + CD + DA>AC + BD
C) AB + BC + CD + DA=AC + BD D) AB + BC + CD + DA>2(AC + BD)
 
Answer & Explanation Answer: B) AB + BC + CD + DA>AC + BD

Explanation:
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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

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Q:

If x stands for addition, / stands for subtraction, + stands for multiplication and - stands for division, then what is the value of 20 x 8 / 8 - 4 + 2 ?

A) 24 B) 1
C) 20 D) 0
 
Answer & Explanation Answer: A) 24

Explanation:
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Q:

Three triangles are marked out of a bigger triangle at the three vertices such that each side of each of the smaller triangles is one-fourth as long as each corresponding side of the bigger triangle. The ratio of the area of the three small triangles taken together to that of the rest of the bigger triangle is

A) 4 : 15 B) 3 : 13
C) 3 : 16 D) 1 : 5
 
Answer & Explanation Answer: B) 3 : 13

Explanation:
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Filed Under: Ratios and Proportions
Exam Prep: Bank Exams

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Q:

 In the triangle ABC, the internal bisector of angle A meets the side BC at D. If BD=7.5 cm and BC=9 cm. Then calculate the value of AB:AC.

 

A) 2:1 B) 1:2
C) 3:1 D) 1:3
 
Answer & Explanation Answer: C) 3:1

Explanation:
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Filed Under: Ratios and Proportions
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Q:

If (7x -­ 13) ­ (12x + 3) = 14, then the value of x is ______ .

A) -6 B) 6
C) -2/5 D) 2/5
 
Answer & Explanation Answer: A) -6

Explanation:
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Filed Under: Simplification
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Q:

If 7/8th of 5/4th of a number is 315, then 5/9th of that number is _____

A) 123 B) 81
C) 140 D) 160
 
Answer & Explanation Answer: D) 160

Explanation:
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Filed Under: Percentage
Exam Prep: Bank Exams

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Q:

Select the odd word/letters/number/number pair from the given alternatives.

A) America B) India
C) Bangladesh D) Pakistan
 
Answer & Explanation Answer: A) America

Explanation:
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Filed Under: Odd Man Out
Exam Prep: Bank Exams

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