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# If C + D = 11 and C and D are positive integers, which of

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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]
sugu86 wrote:
If C + D = 11 and C and D are positive integers, which of the following is a possible value for 5C + 8D?

A. 55
B. 61
C. 69
D. 83
E. 88

You can also use simple brute force here if nothing works.
Since C+D = 11,
C and D would take values from one of the pairs {1, 10}, {2, 9}, {3, 8}, {4, 7}, {5, 6}

5C + 8D could be 5*1 + 8*10 = 85 or 5*10 + 8*1 = 58
5C + 8D could be 5*2 + 8*9 = 82 or 5*9 + 8*2 = 61 (that's one of the options)

Mind you, brute force works only for some low level questions (but it is an option).
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Abhii46 wrote:
c + d = 11
5c + 8d = 5c + 5d + 3d = 5(c+d) + 3d = 55 + 3d.
Now 3d is a multiple of 3, so the right answer should be 55 + multiple of 3. Or we can subtract 55 from the options and see which one results in a multiple of 3.
61 - 55 = 2*3
Hence B is the right answer.

Please give a kudo if you like my explanation.

Hi Abhii46, your explanation makes sense, but it still leaves open the possibility of 88, since that is 55 + 33. However, 88 cannot be an answer to this question, so the answer is indeed B. Can anyone explain why E isn't a valid option?

Thanks!
-Ron
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88 cannot be the option because then for that d has to be 11, which makes c = 0.
Sorry, I missed that.
85 can be the answer, which makes d = 10 and c = 1.
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marcovg4 wrote:
This problem is presented in one of the MGMAT strategy books (Algebra):

If c+d=11 and c and d are positive integers, wich of the followings is a possible value for 5c+8d?

A) 55
B) 61
C) 69
D) 83
E) 88

SO c+d = 11. Now 5c+8d = 5(c+d)+3d = 55+3d. Thus as d is an integer, when 55 is subtracted from the given options should be divisible by 3. Taking the options, we see that A=55 gives d=0. Not possible as it states d is a positive integer.Again E=88 gives d=11, but this will make c=0 which is again not possible. Thus the only answer is B=61.

B.
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Thanks for the explanation.

I though A was the answer, considering d = 0, since I read (dont remeber where) 0 as a positive integer. Correct me if Im wrong.

Thanks
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Ok, so 0 must be considered an Even number, not a positive nor negative integer. Sorry, I confuse those unique properties of the zero.

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marcovg4 wrote:
Ok, so 0 must be considered an Even number, not a positive nor negative integer. Sorry, I confuse those unique properties of the zero.

Hi marcovg4, you're completely right, zero is even and neither positive nor negative (the only number with this property.

Zero is one of those numbers that comes up over and over on the GMAT (I may have to write a ROn Point blog about that soon!). Aside from being even even, and neither positive nor negative, it also has the properties of not being a prime number, being a multiple of every number, 0!=1, x^0 = 1, and being neither red nor black (this applies to the roulette wheel only ).

Thanks!
-Ron
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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]
VeritasPrepKarishma wrote:
C and D would take values from one of the pairs {1, 10}, {2, 9}, {3, 8}, {4, 7}, {5, 6}.

Actually we don't know if C>D or C<D , hence there will be more pairs to consider : {10,1} , {9,2} , {8,3} and so on ...

Correct if i am wrong but i think that the brutal force here would take more time to be attempted
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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]
Rock750 wrote:
VeritasPrepKarishma wrote:
C and D would take values from one of the pairs {1, 10}, {2, 9}, {3, 8}, {4, 7}, {5, 6}.

Actually we don't know if C>D or C<D , hence there will be more pairs to consider : {10,1} , {9,2} , {8,3} and so on ...

Correct if i am wrong but i think that the brutal force here would take more time to be attempted

If you read the explanation further, you will notice that I have considered both possibilities for each pair

Quote from my post above:
"5C + 8D could be 5*1 + 8*10 = 85 or 5*10 + 8*1 = 58
5C + 8D could be 5*2 + 8*9 = 82 or 5*9 + 8*2 = 61 (that's one of the options)"

C can be 1 and D can be 10 or C can be 10 or D can be 1 etc.

And also, as I mentioned before - brute force works only for some low level questions. I don't particularly endorse it but it is an option and if nothing else comes to mind, just try some values - things might fall in place. Point is, it's better than staring at the question wondering what to do.
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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]
You are right Karishma

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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]
5C+8D can't be 55 or 88. So, eliminate options A and E.

5C + 8D = 5 * (C + D) + 3D
= 5 * 11 + 3D
= 55 + 3D

Subtracting 55 from options B,C and D,we get 6,14 and 28 respectively.
Here only 6 is divisible by 3.
Hence, Option B is the answer.
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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]
Thank you Bunuel, I dont think a question exists in GMAT which you and Karishma cant solve.
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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]
Excellent Question
Here just by replacing 5c+8d => 5c-3c+88=Value in the option (say V)
hence c=88-V/3
as we can see only B satisfies it.
remember E is not sufficient as it will make c=0 which is not possible.
Hence B
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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]
C+D=11
what is 5C+8D
Lets us find pairs in which C and D add up to 11
If C=10,9,8,7,6,5,4,3,2,1
Than D=1,2,3,4,5,6,7,8,9,10
plug in value of C and as per the above pair only

If C=10 than D=1
5X10+8X1=55+8=63 not correct as none of the answer choice has 63 as an option
Next pair
C=9 and D=2
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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]
If you multiply c+d = 11 by 5 you get 5c+5d=55

5c+8d = ?
5c+5d = 55
-_________
3d = ? - 55

Now test the values
A) immediately out
B) 61-55 = 6, 3d = 6 so d = 2
c + 2 = 11, so c = 9
5(9) + 8(2) --> 45 + 16 = 61, this matches so it's B
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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]
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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]
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