Can you Find x.?
If we denote the distance of B from the center of the circle as y, y=1.5; y² + x² = 2.5²; x² = 6.25 - 2.25 = 4; x = 2
3. A maths professor asked one of his students to visit his house regarding some work. The student asked the professor his house number. The professor replied in a strange way:
1. If my house number is a multiple of 3, then it is a number from 50 to 59.
2. If my house number is not a multiple of 4, then it is a number from 60 to 69.
3. If my house number is not a multiple of 6, then it is a number from 70 to 79.
Can you determine the professor's house number?
Sol://
#1: divisible by 3: then in 50 - 59
#2: not divisible by 4: then in 60 - 69
#3: not divisible by 6: then in 70 - 79
let h be house #
50-59
rule 1: div 3 : h must be 51, 54, 57
rule 2: div 4 : h must be 52, 56
rule 3: div 6 : h must be 54
common: none >> exclude range
60-69
rule 1: ! div 3 : h must be 61, 62, 64, 65, 67, 68
rule 2: ! div 4 : h must be 61, 62, 63, 65, 66, 67, 69
rule 3: div 6 : h must be 60, 66
common: none >> exclude range
70-79
rule 1: !div 3 : h must be 70, 71, 73, 74, 76, 77, 79
rule 2: div 4 : h must be 72, 76
rule 3: !div 6 : h must be 70, 71, 73, 74, 75, 76, 77, 79
common: 76
house # is 76
2: 4$2 = 0
3$2 = 1
1$4 = -3
2$5 = 7
then
What is 6$2?
Sol: Think Logically 4$2 = 4^2 - 2^4 = 0
3$2 = 3^2 - 2^3 = 1
1$4 = 1^4 - 4^1 = -3
2$5 = 2^5 - 5^2 = 7
6$2 = 6^2 - 2^6 = 36 - 64 = -28
1: In January, Bart's electricity bill was $35.00. In February, his bill was $42.00. By what percent did his electricity bill increase?
a. 7%
b. 12%
c. 16%
d. 20%
Sol: amount of bill increased = $42 - $35 = $7
so total % increased by January's bill = (7/35)x100 = 20%
So Ans will be option d. 20%
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