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16 Sep 2019, 09:08
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C
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\(a=\frac{x}{y}\), such that "a' is a fraction written in lowest terms and \(0<a<1\). Also, x+y=100. How many values of 'a' are possible.
A. 15
B. 18
C. 20
D. 25
E. 30
A. 15
B. 18
C. 20
D. 25
E. 30
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16 Sep 2019, 10:15
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since 0<a<1 we learn that x<y ==> combined with x+y=100 we get x=1,...,49 and y=99,...,50
there are 50 fractions we can create.
there are 25 pairs of (x,y) which are both even, therefore not at their lowest term form
there are 5 more pairs where x=10*k+5, such that we count all multiples of 5 but not the multiple of 10.
multiples of 3 are out of sync, so does the rest of the multiples of primes.
so we get 50-25-5=20.
please let me know if you agree with my solution.
there are 50 fractions we can create.
there are 25 pairs of (x,y) which are both even, therefore not at their lowest term form
there are 5 more pairs where x=10*k+5, such that we count all multiples of 5 but not the multiple of 10.
multiples of 3 are out of sync, so does the rest of the multiples of primes.
so we get 50-25-5=20.
please let me know if you agree with my solution.
16 Sep 2019, 14:41
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a=x/y where 0<a<1 and a is a fraction written in lowest terms. Since x+y=100 and logically x<y, there are max. 50 combinations of x and y:
x=1,2,...,50
y=51,52,...,100
If both x and y are even (there are 25 combinations of x and y that are both even), x/y can NOT be written in lowest term, e.g. x/y=2/98, 4/94,..., 48/52, 50/50.
If both x and y are multiples of 5 (there are 5 combinations of x and y that are multiples of 5), x/y can NOT be written in lowest term, e.g. x/y=5/95, 15/85,..., 45/55.
Rest of the (x, y) combinations can be written in the lowest term. No of possible values of 'a' = 50 - 25 - 5 = 20.
Answer is (C)
Posted from my mobile device
x=1,2,...,50
y=51,52,...,100
If both x and y are even (there are 25 combinations of x and y that are both even), x/y can NOT be written in lowest term, e.g. x/y=2/98, 4/94,..., 48/52, 50/50.
If both x and y are multiples of 5 (there are 5 combinations of x and y that are multiples of 5), x/y can NOT be written in lowest term, e.g. x/y=5/95, 15/85,..., 45/55.
Rest of the (x, y) combinations can be written in the lowest term. No of possible values of 'a' = 50 - 25 - 5 = 20.
Answer is (C)
Posted from my mobile device
