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GRE Math Challenge #14 - 72.42= k(24 + n/100) : Numeric Entry Question

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Re: GRE Math Challenge #14 - 72.42= k(24 + n/100) [#permalink]
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amorphous wrote:
if \(K = 100\) and \(n = - 2327.58\)

This satisfies the eqn and condition and their sum is \(-2227.58\)


Good point!
I have added a restriction to n to prevent more than 1 correct answer.

Cheers,
Brent
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Re: GRE Math Challenge #14 - 72.42= k(24 + n/100) [#permalink]
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Interesting solution. I don't think I would have ever guessed. It makes sense when you write it all out, but it's like you saw a path that was completely hidden, at least from non-math people.
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Re: GRE Math Challenge #14 - 72.42= k(24 + n/100) [#permalink]
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sandy wrote:
If 0 < n < 100 and 72.42 = k(24 + n/100), then k + n =


Here's another approach:

GIVEN: \(72.42 = k(24 + \frac{n}{100})\)

Expand right side: \(72.42 = 24k+\frac{kn}{100}\)

Multiply both sides by 100 to get: \(7242 = 2400k+kn\)

Factor out the k to get: \(7242 = k(2400+n)\)

ASIDE: Since n is POSITIVE, we know that k is positive.
Since \((3)(2400)=7200\), and since 7200 is pretty close to 7242, let's see how things look if we try factoring a 3 from the left side of the equation.

We get: \(3(2414)= k(2400+n)\)

We can rewrite 2414 as follows: \(3(2400+14)= k(2400+n)\)

At this point, we can see that \(k=3\) and \(n=14\)

So, \(k+n=3+14=17\)

Answer: 17

Cheers,
Brent
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Re: GRE Math Challenge #14 - 72.42= k(24 + n/100) [#permalink]
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this type of problem is beyond complicated and it definitely takes more than 2 min to solve.
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Re: GRE Math Challenge #14 - 72.42= k(24 + n/100) [#permalink]
I do not understand how you are able to conclude that 24k = 72 and kn/100 = 42/100 if we do not know the value of k?
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Re: GRE Math Challenge #14 - 72.42= k(24 + n/100) [#permalink]
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Quote:
If 0 < n < 100 and 72.42 = k(24 + n/100), then k + n =

Step 1: Understanding the question
Here value of n lies between 0 to 100 and respective value of k can be calculated

Step 2: Calculation
When n = 10,
72.42 = k(24 + 10/100)
k = \(\frac{72.42 }{ 24.1}\) = 3.004, hence n + k = 10 + 3 = 13 (approx)

When n = 20
72.42 = k(24 + 20/100)
k = \(\frac{72.42 }{ 24.2}\) = 3 (approx), here value of n + k = 20 + 3 = 23 (approx)

As n lies between 0 to 100, there will be multiple values of k and hence of n+k.
Therefore, there is no specific value for n + k.
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Re: GRE Math Challenge #14 - 72.42= k(24 + n/100) [#permalink]
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Re: GRE Math Challenge #14 - 72.42= k(24 + n/100) [#permalink]
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