Both the numerator and the denominator of $${3 \over 4}$$ are increased by a positive $${15 \over 17}$$ integer, x, and those of _____ are decreased by the same integer. This operation results in the same value for both the fractions. What is the value of x?

Consider the following equations of straight lines :

Line L1 : 2x $$-$$ 3y = 5

Line L2 : 3x + 2y = 8

Line L3 : 4x $$-$$ 6y = 5

Line L4 : 6x $$-$$ 9y = 6

Which one of the following is the correct statement?

In the last few years, several new shopping malls were opened in the city. The total number of visitors in the malls is impressive. However, the total revenue generated through sales in the shops in these malls is generally low.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

Given below are two statements and four conclusions drawn based on the statements.

Statement 1 : Some soaps are clean.

Statement 2 : All clean objects are wet.

Conclusion I : Some clean objects are soaps.

Conclusion II : No clean object is a soap.

Conclusion III : Some wet objects are soaps.

Conclusion IV : All wet objects are soaps.

Which one of the following options can be logically inferred?