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What is the largest possible value of c if 5c + (d-12)^2 = 235?

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noTh1ng
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What is the largest possible value of c if 5c + (d-12)^2 = 235? [#permalink] New post   Updated on: 28 Jul 2015, 00:36
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What is the largest possible value of \(c\) if \(5c + (d-12)^2 = 235\) ?

A) 17
B) 25
C) 35
D) 42
E) 47
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E

Originally posted by noTh1ng on 24 Jul 2015, 05:11.
Last edited by noTh1ng on 28 Jul 2015, 00:36, edited 1 time in total.
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Re: What is the largest possible value of c if 5c + (d-12)^2 = 235? [#permalink] New post   24 Jul 2015, 05:15
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noTh1ng wrote:
What is the largest possible value of \(c\) if \(5c + (d-12)^2 = 235\) ?

A) 17
B) 25
C) 35
D) 42
E) 47


I was not able to solve this algebraically...


To maximize c, we should minimize (d-12)^2. (d-12)^2 is a square of a number, thus its smallest possible value is 0 (for d = 12).

In this case we'd have 5c + 0 = 235 --> c = 47.

Answer: E.
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Re: What is the largest possible value of c if 5c + (d-12)^2 = 235? [#permalink] New post   24 Jul 2015, 05:21
noTh1ng wrote:
What is the largest possible value of \(c\) if \(5c + (d-12)^2 = 235\) ?

A) 17
B) 25
C) 35
D) 42
E) 47


I was not able to solve this algebraically...


You need to remember that the minimum value of a square term is 0. Any square \(\geq\) 0

Thus, the given equation is : \(5c + (d-12)^2 = 235\) ---> \(5c = 235 - (d-12)^2\)

Now, based on the above manipulation, we can see that 235- a positive quantity = will only decrease the value of c.

Thus the maximum value of c will be obtained when (d-12)^2 = 0 ---> d =12

Thus the maximum value of c = (235-0 )/5 = 47. E is the correct answer.
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Re: What is the largest possible value of c if 5c + (d-12)^2 = 235? [#permalink] New post   24 Jul 2015, 06:26
Expert Reply
noTh1ng wrote:
What is the largest possible value of \(c\) if \(5c + (d-12)^2 = 235\) ?

A) 17
B) 25
C) 35
D) 42
E) 47


I was not able to solve this algebraically...


Clearly d needs to be minimized to find the maximum value of c
i.e. d-12 must be a minimum perfect square and 235 - (d-12)^2 must be a multiple of 5
which is possible when d=12 i.e. d-12 = 0
i.e. 5c = 235 - 0 = 235
i.e. c = 47

Answer: option E
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Re: What is the largest possible value of c if 5c + (d-12)^2 = 235? [#permalink] New post   24 Jul 2015, 06:42
5c + (d-12)^2 = 235.

to maximise the value of c the value of (d-12)^2 must be minimised.

(d-12)^2 is minimum when d = 12: (12-12)^2 = 0.

So, 5c = 235, c = 235/5 = 47. Ans (E).
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Re: What is the largest possible value of c if 5c + (d-12)^2 = 235? [#permalink] New post   25 Feb 2016, 17:50
Engr2012 wrote:
You need to remember that the minimum value of a square term is 0. Any square \(\geq\) 0


Well, only if you exclude imaginary numbers, which my brain didn't automatically do.

I had to re-read this question a few times and look at the answer choices until I realized that we're excluding imaginary numbers.

Is it safe to assume that the GMAT will always disregard imaginary numbers? Or do you have to infer whether imaginary numbers are valid based on the question and answer choices?

This is another way of asking: Can we safely assume, 100% of the time, that if we see a squared number, it is greater than 0? Because \(i^2\) is -1--which is less than 0.

Thanks for helping me get this clarified!

-Josh
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Re: What is the largest possible value of c if 5c + (d-12)^2 = 235? [#permalink] New post   25 Feb 2016, 22:34
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joshbeall wrote:
Engr2012 wrote:
You need to remember that the minimum value of a square term is 0. Any square \(\geq\) 0


Well, only if you exclude imaginary numbers, which my brain didn't automatically do.

I had to re-read this question a few times and look at the answer choices until I realized that we're excluding imaginary numbers.

Is it safe to assume that the GMAT will always disregard imaginary numbers? Or do you have to infer whether imaginary numbers are valid based on the question and answer choices?

This is another way of asking: Can we safely assume, 100% of the time, that if we see a squared number, it is greater than 0? Because \(i^2\) is -1--which is less than 0.

Thanks for helping me get this clarified!

-Josh


All numbers on the GMAT are by default real numbers. So, we do not consider complex/imaginary numbers on the GMAT.
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Re: What is the largest possible value of c if 5c + (d-12)^2 = 235? [#permalink] New post   04 Mar 2017, 23:30
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noTh1ng wrote:
What is the largest possible value of \(c\) if \(5c + (d-12)^2 = 235\) ?

A) 17
B) 25
C) 35
D) 42
E) 47


Check using the options , I will try with the largest value of c ( As given in the option )

\(5c + (d-12)^2 = 235\)

Or, \(5*47 + (d-12)^2 = 235\)

Or, \(235 + (d-12)^2 = 235\)

Or, \((d-12)^2 = 0\)

Thus, if d = 12 ; \((d-12)^2 = 0\)

So, the greatest possible value of c will be (E) 47...
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Re: What is the largest possible value of c if 5c + (d-12)^2 = 235? [#permalink] New post   07 Jun 2022, 12:07
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Re: What is the largest possible value of c if 5c + (d-12)^2 = 235? [#permalink]
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