45. In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
A) 5
B) 10
C) 15
D) 20
E) 25
Soln: n(1U2U3) = n(1) + n(2) + n(3) - n(1n2) - n(2n3) - n(1n3) + n (1n2n3)
85=50+30+20- [n(1n2) - n(2n3) - n(1n3)] +5
[n(1n2) - n(2n3) - n(1n3)] = 20
The solution says it's 20, but I recall the answer from another test that I took previously that says it should be 10. This is how it's done: I draw three circles, and call 1 repeats X, Y and X, the 2 repeat =N
50+30+20 - (X + Y + Z) -2N = 85
100-(X+Y+Z) -10=85, X+Y+Z = 5
X+Y+Z+N=5+5 = 10.
51. How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?
A.14 B.15. C.16 D.17 E.18
Soln: if we arrange this in AP, we get
4+7+10+.......+49
so 4+(n-1)3=49: n=16
C is my pick
The answer states that it's C. 16, but does the calculation consider 0 also? Because 0 divided by 3 also has a remainder of 1 doesn't it? So the answer should be D. 17 right???
A) 5
B) 10
C) 15
D) 20
E) 25
Soln: n(1U2U3) = n(1) + n(2) + n(3) - n(1n2) - n(2n3) - n(1n3) + n (1n2n3)
85=50+30+20- [n(1n2) - n(2n3) - n(1n3)] +5
[n(1n2) - n(2n3) - n(1n3)] = 20
The solution says it's 20, but I recall the answer from another test that I took previously that says it should be 10. This is how it's done: I draw three circles, and call 1 repeats X, Y and X, the 2 repeat =N
50+30+20 - (X + Y + Z) -2N = 85
100-(X+Y+Z) -10=85, X+Y+Z = 5
X+Y+Z+N=5+5 = 10.
51. How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?
A.14 B.15. C.16 D.17 E.18
Soln: if we arrange this in AP, we get
4+7+10+.......+49
so 4+(n-1)3=49: n=16
C is my pick
The answer states that it's C. 16, but does the calculation consider 0 also? Because 0 divided by 3 also has a remainder of 1 doesn't it? So the answer should be D. 17 right???
