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a,b,c and d are all positive integers.....

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NeophyteNitol
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a,b,c and d are all positive integers..... [#permalink] New post   Updated on: 07 Oct 2022, 05:24
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If a, b, c, and d are all positive integers. \(\frac{ab}{c+d}=3.7\), which of the following statements must be true ?

Indicate all such statement

A. ab is divisible by 5
B. c+d is divisible by 5
C. If c is even, then d must be even
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B,C

Originally posted by NeophyteNitol on 07 Jun 2017, 06:38.
Last edited by Carcass on 07 Oct 2022, 05:24, edited 2 times in total.
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sandy
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Re: a,b,c and d are all positive integers..... [#permalink] New post   07 Jun 2017, 11:01
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Please follow the community guidelines for posting. It helps other students as well!




Now a, b, c and d are all positive integers and given that

\(ab = 3.7 \times (c+d)\). Now \(ab\) also must be an integer as as product of two integers is an integer.

\(3.7=\frac{37}{10}\). This is lowest reducable form as 37 and 10 have no common factors.

So \(c+d\) must have a factor of 10. So \(c+d\) is an even number with a factor of 10.

Hence option B and C are correct!

Now option A is not correct because if \(c+d\) is 10 then \(ab=37\), which is not divisible by 5.
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Re: a,b,c and d are all positive integers..... [#permalink] New post   24 Jun 2022, 17:06
sandy, why do we need to look for the lowest reducible form of 3.7?
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Re: a,b,c and d are all positive integers..... [#permalink] New post   24 Jun 2022, 23:06
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ab/c+d=3.7

The only way we do have this is 37/10

Now 37 is prime so cannot be divisible by 5 A is not true

c+d=10 is divisible by five. yes must be true

c+d and c is even also d must be even

the only combinations are : 2+8;4+6;6+4;8+2

C option must be also true

B and C are the answers
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Re: a,b,c and d are all positive integers..... [#permalink] New post   25 Sep 2023, 09:54
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: a,b,c and d are all positive integers..... [#permalink]
25 Sep 2023, 09:54
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