Linear and Quadratic Equations

You are here: Home  CAT Questionbank   CAT Quant  Linear & Quad. Eqns.  Question 7
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

Click to watch video solution
Click to view the explanation as a slide show

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

Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play

More Questions from Linear & Quad. Equations

  1. Integer Values; Modulus
  2. Integer Values; Modulus
  3. Integer Values; Modulus
  4. Quadratic Discriminant
  5. Quadratic Discriminant
  6. Quadratics - Counting
  7. Integer Solutions
  8. Linear Equations - Median
  9. Condition for Unique Soln.
Solving equations well is an integral part to cracking any competitive exam. Get cartloads of practice on these two topics.