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02 Mar 2020, 03:37
Kudos
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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:
95%
(hard)
Question Stats:
40% (02:49) correct
60%
(02:50)
wrong
based on 126
sessions
History
Date
Time
Result
Not Attempted Yet
The number of ordered pairs of integers (x, y) satisfying the equation \(x^2 + 4y^2 < 100\) is:
A. 90
B. 95
C. 147
D. 180
E. 185
Are You Up For the Challenge: 700 Level Questions
A. 90
B. 95
C. 147
D. 180
E. 185
Are You Up For the Challenge: 700 Level Questions
02 Mar 2020, 03:53
Kudos
Bookmarks
y=0, x^2<100 or x can be from -9 to 9 (19 values)
y=1 or -1, x^2 <96 or x can be from -9 to 9 (19 values)
y=2 or -2, x^2<84 or x can be from -9 to 9 (19 values)
y=3 or -3, x^2<64 or x can be from -7 to 7 (15 values)
y=4 or -4, x^2<36 or x can be from -5 to 5 (11 values)
y=5 or -5, x^2<0 or x cab take 0 value
Total number of solutions= 19+(2*19)+(2*19)+(2*15)+(2*11)=147
y=1 or -1, x^2 <96 or x can be from -9 to 9 (19 values)
y=2 or -2, x^2<84 or x can be from -9 to 9 (19 values)
y=3 or -3, x^2<64 or x can be from -7 to 7 (15 values)
y=4 or -4, x^2<36 or x can be from -5 to 5 (11 values)
y=5 or -5, x^2<0 or x cab take 0 value
Total number of solutions= 19+(2*19)+(2*19)+(2*15)+(2*11)=147
Bunuel
General Discussion
02 Mar 2020, 03:59
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Bunuel
\(x^2 + 4y^2 < 100\)
SInce we have to take squares of values of x and y therefore the signs of x and y do not matter so
The solutions of \(x^2 + 4y^2 < 100\) at x= +1
\(1 + 4y^2 < 100\)
\(4y^2 < 99\)
\(y^2 < 24.75\)
\( -5 < y < 5\)
i.e. Available Values of x = 2 and for those values of x, values of y = 9 [Integers including -4 to +4]
i.e. Total Solutions = 2*9 = 18
The solutions of \(x^2 + 4y^2 < 100\) at x= +2
\(4 + 4y^2 < 100\)
\(4y^2 < 96\)
\(y^2 < 24\)
\( -5 < y < 5\)
i.e. Available Values of x = 2 and for those values of x, values of y = 9 [Integers including -4 to +4]
i.e. Total Solutions = 2*9 = 18
Similarly, at x= +3, \(-4.77 < y < 4.77\)
i.e. Available Values of x = 2 and for those values of x, values of y = 9 [Integers including -4 to +4]
i.e. Total Solutions = 2*9 = 18
Similarly, at x= +4, \(-4.58 < y < 4.58\)
i.e. Available Values of x = 2 and for those values of x, values of y = 9 [Integers including -4 to +4]
i.e. Total Solutions = 2*9 = 18
Similarly, at x= +5, \(-4.33 < y < 4.33\)
i.e. Available Values of x = 2 and for those values of x, values of y = 9 [Integers including -4 to +4]
i.e. Total Solutions = 2*9 = 18
Similarly, at x= +6, \(-4 < y < 4\)
i.e. Available Values of x = 2 and for those values of x, values of y = 7 [Integers including -3 to +3]
i.e. Total Solutions = 2*7 = 14
Similarly, at x= +7, \(-3.5 < y < 3.5\)
i.e. Available Values of x = 2 and for those values of x, values of y = 7 [Integers including -3 to +3]
i.e. Total Solutions = 2*7 = 14
Similarly, at x= +8, \(-3 < y < 3\)
i.e. Available Values of x = 2 and for those values of x, values of y = 5 [Integers including -2 to +2]
i.e. Total Solutions = 2*5 = 10
Similarly, at x= +9, \(-2.17 < y < 2.17\)
i.e. Available Values of x = 2 and for those values of x, values of y = 5 [Integers including -2 to +2]
i.e. Total Solutions = 2*5 = 10
Similarly, at x= 0, \(-5 < y < 5\)
i.e. Available Values of x = 1 and for those values of x, values of y = 9 [Integers including -4 to +4]
i.e. Total Solutions = 1*9 = 9
at x= +10, NO SOLUTION
Total Solutions = 18*5+14*2+10*2+9 = 90+28+20+9 = 147
Answer: Option C
