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27 Feb 2020, 00:32
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
39% (02:31) correct
61%
(02:47)
wrong
based on 164
sessions
History
Date
Time
Result
Not Attempted Yet
How many integer solutions exists for the equation 11x + 15y = -1 such that both x and y are less than 100?
A. 15
B. 16
C. 17
D. 18
E. 19
Are You Up For the Challenge: 700 Level Questions
A. 15
B. 16
C. 17
D. 18
E. 19
Are You Up For the Challenge: 700 Level Questions
27 Feb 2020, 00:45
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Quote:
We need to find all possible integer solutions (values less than 100) of the equation 11x + 15y = -1
To answer this we need to find one solution first which can be found either using hit and try or using other methodical method
Let/s try some hit and try,
11x + 15y = -1
x = 3 and y = -2, 11x + 15y = 11*3 +15*(-2) = 3 ≠ -1
[b]x = 4 and y = -3, 11x + 15y = 11*4 +15*(-3) = -1[/b]
i.e. (x, y) = (4, -3) is the first solution
RULE: To find the next solution, value of x differs by co-efficient of y and value of y differs by co-efficient of x
i.e. x will differ by 15 and y will differ by 11
i.e .Next solution will be x = 4+15 = 19 and y = -3-11 = -14
@ (x, y) = (19, -14), 11x + 15y = 11*19 +15*(-14) = 209-210 = -1
i.e. solutions can be listed down as per rule as follows
(x, y) = (-131, 96)
(x, y) = (-116, 85)
(x, y) = (-101, 74)
(x, y) = (-86, 63)
(x, y) = (-71, 52)
(x, y) = (-56, 41)
(x, y) = (-41, 30)
(x, y) = (-26, 19)
(x, y) = (-11, 8)
(x, y) = (4, -3)
(x, y) = (19, -14)
(x, y) = (34, -25)
(x, y) = (49, -36)
(x, y) = (64, -47)
(x, y) = (79, -58)
(x, y) = (94, -69)
16 solutions
Answer: Option B
27 Feb 2020, 01:17
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11x= 0 mod 11
-15y = 1 mod 11
y= -3 mod 11
Maximum value of y= 11*9-3=96
value of x when y is equal to 96= -131 (minm possible value of x, as slope of the line is negative)
-131+n*15<100
n<15.xyz
total possible solutions= 15+1=16
-15y = 1 mod 11
y= -3 mod 11
Maximum value of y= 11*9-3=96
value of x when y is equal to 96= -131 (minm possible value of x, as slope of the line is negative)
-131+n*15<100
n<15.xyz
total possible solutions= 15+1=16
Bunuel
