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In a certain list of positive integers, the ratio of the number of odd

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In a certain list of positive integers, the ratio of the number of odd  [#permalink]

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New post 25 Nov 2018, 23:33
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In a certain list of positive integers, the ratio of the number of odd integers to the number of even integers is 7 to 4. One-fourth of the number of odd integers is what fraction of the total number of integers in the list?

A. 7/44
B. 3/16
C. 11/28
D. 7/16
E. 9/16

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Re: In a certain list of positive integers, the ratio of the number of odd  [#permalink]

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New post 26 Nov 2018, 06:51
Bunuel wrote:
In a certain list of positive integers, the ratio of the number of odd integers to the number of even integers is 7 to 4. One-fourth of the number of odd integers is what fraction of the total number of integers in the list?

A. 7/44
B. 3/16
C. 11/28
D. 7/16
E. 9/16


No of odd integers/no of even integers=7k/4k

1/4of 7k/11k as 7k has to be integer so k should be 4

Total odd integers=7k=7*4=28
Total even integers=11k=11* 4=44

So ratio of 1/4th of odd/total integers=7/44
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In a certain list of positive integers, the ratio of the number of odd  [#permalink]

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New post 26 Nov 2018, 07:03
let \(x\) be number of ODD integers

let \(y\) be number of EVEN integers

ratio X to Y \(\frac{7x}{4y}\)

\(\frac{1}{4} *7x\) = \(\frac{7x}{4}\)

\(\frac{\frac{7x}{4}}{\frac{11}{1}}\) = \(\frac{7x}{4}*\frac{1}{11}\) = \(\frac{7x}{44}\)


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Re: In a certain list of positive integers, the ratio of the number of odd  [#permalink]

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New post 26 Nov 2018, 09:50
Top Contributor
Bunuel wrote:
In a certain list of positive integers, the ratio of the number of odd integers to the number of even integers is 7 to 4. One-fourth of the number of odd integers is what fraction of the total number of integers in the list?

A. 7/44
B. 3/16
C. 11/28
D. 7/16
E. 9/16


Another approach is to work with numbers that satisfy the given information.

The ratio of the number of odd integers to the number of even integers is 7 to 4
So. let's say there are 7 odd integers and 4 even integers

One-fourth of the number of odd integers is what fraction of the total number of integers in the list?
1/4 of 7 = (1/4)(7) = 7/4
TOTAL number of integers = 7 + 4 = 11

(7/4)/11 = (7/4)/(11/1)
= (7/4)(1/11)
= 7/44

Answer: A

ASIDE: Yes, 7/4 is not an integer. That's fine, since we're talking about proportions and not actual values.

Cheers,
Brent
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Re: In a certain list of positive integers, the ratio of the number of odd  [#permalink]

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New post 26 Nov 2018, 10:10
(1/4)*(7/11)=7/44

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Re: In a certain list of positive integers, the ratio of the number of odd &nbs [#permalink] 26 Nov 2018, 10:10
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