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# a, b, s, k are different non-zero integers...

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Intern
Joined: 25 Jun 2017
Posts: 13
a, b, s, k are different non-zero integers...  [#permalink]

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02 Aug 2017, 16:28
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24% (02:00) correct 76% (01:52) wrong based on 27 sessions

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a, b, k, s are different non-zero integers, $$\frac{2}{a}$$ +$$\frac{4}{b}$$ = $$\frac{k}{s}$$ and $$\frac{k}{s}$$ is maximally reduced. Does s = ab?

1) a and b are primes

2) a and b have gcd = 1
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Joined: 02 Aug 2009
Posts: 7989
Re: a, b, s, k are different non-zero integers...  [#permalink]

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03 Aug 2017, 09:21
Limara1 wrote:
a, b, k, s are different non-zero integers, $$\frac{2}{a}$$ +$$\frac{4}{b}$$ = $$\frac{k}{s}$$ and $$\frac{k}{s}$$ is maximally reduced. Does s = ab?

1) a and b are primes

2) a and b have gcd = 1

Sorry don't have the OA.

Hi...

It's all about what values can a and b take....

$$\frac{2}{a}$$ +$$\frac{4}{b}$$ = $$\frac{k}{s}$$...
$$\frac{2b+4a}{ab}=\frac{k}{s}$$..
I tells us a and b are prime..
If any of a or b is 2, it will cancel out from NUMERATOR, so k =ab/2... No
If they are prime other than 2, k=ab. Yes..
Insufficient..
SAME will stand for II, where they are coprimes.
Ans E
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Re: a, b, s, k are different non-zero integers...  [#permalink]

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03 Aug 2017, 11:24
chetan2u wrote:
Limara1 wrote:
a, b, k, s are different non-zero integers, $$\frac{2}{a}$$ +$$\frac{4}{b}$$ = $$\frac{k}{s}$$ and $$\frac{k}{s}$$ is maximally reduced. Does s = ab?

1) a and b are primes

2) a and b have gcd = 1

Sorry don't have the OA.

Hi...

It's all about what values can a and b take....

$$\frac{2}{a}$$ +$$\frac{4}{b}$$ = $$\frac{k}{s}$$...
$$\frac{2b+4a}{ab}=\frac{k}{s}$$..
I tells us a and b are prime..
If any of a or b is 2, it will cancel out from NUMERATOR, so s =ab/2... No
If they are prime other than 2, s=ab. Yes..
Insufficient..
SAME will stand for II, where they are coprimes.
Ans E

You say that if a and b are primes other than 2 then s=ab, but is this always true? Can you prove this (i.e. prove that neither of primes a or b is a factor in b+2a)?

Anyway, for the purposes of this DS question it's enough to show that primes a and b CAN also be such that s=ab (which is pretty obvious, e.g. take a=3, b=5).
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Joined: 23 May 2017
Posts: 234
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: a, b, s, k are different non-zero integers...  [#permalink]

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03 Aug 2017, 11:54
$$\frac{2}{a}$$ + $$\frac{4}{b}$$ = $$\frac{k}{s}$$

$$\frac{2b + 4a}{ab}$$ = $$\frac{k}{s}$$

given : {2b + 4a} is not divisible by ab or there is no common factor of {2b + 4a} and ab

I have a question here ; Isn't the even value of a or b is out of scope(already discarded) due to the given statement that $$\frac{k}{s}$$ is maximally reduced.

In that case we can pick only odd primes from statement 1 which will give us answer yes to the given question
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Intern
Joined: 25 Jun 2017
Posts: 13
Re: a, b, s, k are different non-zero integers...  [#permalink]

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03 Aug 2017, 17:57
Leo8 wrote:

given : {2b + 4a} is not divisible by ab or there is no common factor of {2b + 4a} and ab

I think you're mistaken here. The prompt says $$\frac{s}{k}$$ is maximally reduced, NOT that $$\frac{2}{a}$$ + $$\frac{4}{b}$$ = $$\frac{2b+4a}{ab}$$ is maximally reduced too.

In fact, the whole point of the question is to prove / disprove whether the latter is always true in this situation.
Re: a, b, s, k are different non-zero integers...   [#permalink] 03 Aug 2017, 17:57
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