Quantitative Aptitude – Equation – the number of pairs of integers


Slot – 1 – Quantitative Aptitude – Equation – the number of pairs of integers


Q. The number of pairs of integers (x,y) satisfying x≥y≥-20 and 2x+5y=99 is?
Answer: 17

Solution:
Given,
2x +5y = 99
2x = 99 -5y
x = (99 -5y )/2
x = 49 -2y + (1-y)/2
x is minimum when y is maximum and vice versa. Also for x to be integer y need to be odd integer .
Maximum value of x = 49 –2(-19) + 20/2 =97
Next value of x = 49 + 2*17 + 18/2 = 92
At least value of x , x =y
So 7x = 99
x = 99/7 = 14.14
As x is an integer so x can be 97, 92 , 87……..22 , 17
Number of possible pair = (97-17)/5 + 1 = 16+1 =17


Online Coaching Course for CAT 2021 + Test Series

a) 1000+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video