GATE General Aptitude & Logical Reasoning 5

Question 1

A sphere of radius r is inscribed in a cube. What is the ratio of the volume of the cube to the volume of the sphere?

Accepted Answer

6/π

Answer

Cube side = 2r; V_cube=(2r)³=8r³; V_sphere=4πr³/3; ratio=8r³/(4πr³/3)=6/π.

Question 2

P is taller than Q. R is taller than P. S is shorter than R but taller than Q. Who is the shortest?

Accepted Answer

Q

Answer

Order: R>P>S>Q (since S>Q and P>Q and R>P>Q); Q is shortest.

Question 3

A shopkeeper marks his goods at 25% above cost price and allows a 10% discount. What is his profit percentage?

Accepted Answer

12.5%

Answer

SP = CP×1.25×0.90 = 1.125×CP; profit = 12.5%.

Question 4

Read the passage: 'All employees who joined before 2010 are eligible for a pension. John joined in 2008.' Which conclusion is valid?

Accepted Answer

John is eligible for a pension

Answer

John joined in 2008, which is before 2010, so he meets the condition for pension eligibility.

Question 5

Which number replaces the question mark? 4 : 16 :: 7 : ?

Accepted Answer

49

Answer

The relationship is n : n²; 4→16=4², so 7→49=7².

(GATE) Graduate Aptitude Test in Engineering Practice Test