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27 Feb 2020, 00:32
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
56% (02:39) correct
44%
(02:42)
wrong
based on 191
sessions
History
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How many integer solutions exist for the equation 8x – 5y = 221 such that x*y < 0
A. 4
B. 5
C. 6
D. 7
E. 8
Are You Up For the Challenge: 700 Level Questions
A. 4
B. 5
C. 6
D. 7
E. 8
Are You Up For the Challenge: 700 Level Questions
27 Feb 2020, 00:51
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Bunuel
Integer solutions for 8x – 5y = 221
x*y < 0 i.e. one of x and y must be positive and other negative
5y = 8x - 221
for integer solution, 8x must have unit digit either 1 or 6 but 8x is Even so the unit digit must be 6 and not 1
for 8x to have unit digit 6, x must be {2, 7, 12, 17...}
But since we are taking x positive so y must be negative i.e. 8x < 221 i.e. x < 27.6
i.e. x maybe {2, 7, 12, 17, 22, 27} i.e. 6 solutions
FOr any negative value of x, y is never positive hence no solution this way
Total Solutions obtained = 6
Answer: Option C
shameekv1989
GMAT 3: 720 Q50 V38
Posts: 820
Updated on: 06 Mar 2023, 03:39
Originally posted by shameekv1989 on 27 Feb 2020, 17:24.
Last edited by Bunuel on 06 Mar 2023, 03:39, edited 2 times in total.
Last edited by Bunuel on 06 Mar 2023, 03:39, edited 2 times in total.
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Bunuel
This equation is of the form Linear Diophantine Equations - courtesy AnthonyRitz - https://www.youtube.com/watch?v=SCf-HrtYUMg
Find the first pair for the equation 8x – 5y = 221 such that xy < 0
x has to be such that 8x-221 is divisible by 5 for y to be integer => Let's try x=2 => Will give us y=-41
Now we just need to add a value to x and subtract from y or vice versa (In this case we subtract value to x, thus add 5 i.e. -(-5) and add in y - +8)
1) x=2; y=-41
2) x=2+5 =7 (Because of -5 in y); y=-41+8 = -33 (Because of 8 in x)
3) x=7+5 =12 (Because of -5 in y); y=-33+8 = -25 (Because of 8 in x)
4) x=12+5 =17 (Because of -5 in y); y=-25+8 = -17 (Because of 8 in x)
5) x=17+5 =22 (Because of -5 in y); y=-17+8 = -9 (Because of 8 in x)
6) x=22+5 =27 (Because of -5 in y); y=-9+8 = -1 (Because of 8 in x)
If we add any further value to y => y will become positive and xy > 0 which is a constraint in the question stem
Hence 6 integer solutions
Answer - C
