If x and y are integers then the equation 5x + 19y = 64 has (CAT 2003) Options: A . &nbsp no solution for x < 300 and y < 0 B . &nbsp no solution for x > 250 and y > − 100 C . &nbsp a solution for 250 < x < 300 D . &nbsp a solution for − 59 < y < − 56 E . &nbsp 97 : 84

If x and y are integers then the equation 5x + 19y = 64 has (CAT 2003)

Question

If x and y are integers then the equation 5x + 19y = 64 has (CAT 2003)

Options:

A . no solution for

x < 300

and

y < 0

B . no solution for

x > 250

and

y > - 100

C . a solution for

250 < x < 300

D . a solution for

- 59 < y < - 56

E . 97 : 84

Answer: Option C
:
C

Soln:

We see that if y = 1, we get an integer solution for x = 9, now if y changes (increases or decreases) by 5, x will change (decrease or increase) by 19.

Looking at options, if x = 256 we get y = 64.

Using these values we see option 1, 2 and 4 are eliminated and also that these exists a solution for $250 < x < 300.$

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