Linear and Quadratic Equations

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Modulus of a number cannot be negative. A simple idea that somehow escapes our mind every now and then.

Linear Equations - Integer Solutions

    2x + 5y = 103. Find the number of pairs of positive integers x and y that satisfy this equation.
    1. 9
    2. 10
    3. 12
    4. 20

 

  • Correct Answer
    Choice B. 10

Explanatory Answer

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Detailed Solution

Rearranging the equation, we get:
2x = 103 – 5y

This says that when you subtract a multiple of 5 from 103, you get an even number. You have to subtract an odd multiple of 5 from 103 in order to get an even number. There are 20 multiples of 5 till 100, ten of which are odd. (Note that you cannot subtract 105, or higher multiples as they result in a negative value for x.)

So, y can have ten integer values. x also has 10 integer values, each corresponding to a particular value of y.

y = 1, gives us a potential value for x, so do y = 3, 5, 7….19. y can take 10 values totally.

Correct Answer: 10 Pairs



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More Questions from Linear & Quad. Equations

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Solving equations well is an integral part to cracking any competitive exam. Get cartloads of practice on these two topics.