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For any numbers a and b, a#b = ab(3 − b). If a and a#b both represent
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31 Jul 2016, 04:19
31 Jul 2016, 04:19
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For any numbers a and b, a#b = ab(3 − b). If a and a#b both represent positive numbers, which of the following could be a value of b?
A. −5
B. −2
C. 2
D. 4
E. 7
A. −5
B. −2
C. 2
D. 4
E. 7
For any numbers a and b, a#b = ab(3 − b). If a and a#b both represent
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31 Jul 2016, 04:56
31 Jul 2016, 04:56
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Bunuel wrote:
For any numbers a and b, a#b = ab(3 − b). If a and a#b both represent positive numbers, which of the following could be a value of b?
A. −5
B. −2
C. 2
D. 4
E. 7
A. −5
B. −2
C. 2
D. 4
E. 7
if a#b is positive then there are 2 cases
either ab &(3-b) both are negatives or both positives
let both are positives then for (3-b) to be positive b has to less than 3 (3-b>0--->3>b)
from options b can be -5,-2,or2
but if we take negative value of b then ab will negative & hence a#b which is not possible.
also if we do both negative then (3-b) to be negative b has to be greater than 3 which from options are only 4&7
if we take any value then the term ab will positive leaving a#b negative.which is not possible
Hence b=2
Ans C
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Re: For any numbers a and b, a#b = ab(3 − b). If a and a#b both represent
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15 Nov 2020, 02:30
15 Nov 2020, 02:30
a>0, a#b > 0
b = ?, Simply plug in values,
b= -5, -5a(3-(-5)) = -5a(3+5) = -5a(8) = -40a
a>0, So -40a < 0.
b= -2, -2a(3-(-2)) = -2a(3+2) = -2a(5) = -10a
a>0, So -10a < 0.
b= 2, 2a(3-2) = 2a
a>0, So 2a > 0. CAN BE TRUE,
b= 4, 4a(3-4) = 4a(-1) = -4a
a>0, So -4a < 0.
b= 7, 7a(3-7) = 7a(-4) = -28a
a>0, So -28a < 0.
b = ?, Simply plug in values,
b= -5, -5a(3-(-5)) = -5a(3+5) = -5a(8) = -40a
a>0, So -40a < 0.
b= -2, -2a(3-(-2)) = -2a(3+2) = -2a(5) = -10a
a>0, So -10a < 0.
b= 2, 2a(3-2) = 2a
a>0, So 2a > 0. CAN BE TRUE,
b= 4, 4a(3-4) = 4a(-1) = -4a
a>0, So -4a < 0.
b= 7, 7a(3-7) = 7a(-4) = -28a
a>0, So -28a < 0.
