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

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

\(C+D=11\) --> \(C=11-D\) --> \(5C + 8D=5(11-D)+8D=55+3D\), so the answer must be 55 plus some multiple of 3.

Only B and E satisfy this: 61=55+3*2 and 88=55+3*11, but the second case is not possible because in this case D=11 and C=0, and we are told that C is a positive integers.

Answer: B.

P.S. Do not shorten or reword the questions you post.
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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
88 - 55 = 33 = 3*11.
But if d = 11 then c = 0.
So, 88 cannot be the option.
Hence, B is the right answer.

Please give a kudo if you like my explanation.

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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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?

(Hint: Think of what would have happened had the answer choice been 85 instead.)

Thanks!
-Ron

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.

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

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

Thanks everyone, very helpful explanations

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

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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You are right Karishma

Thanks for your quick reply

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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Please press KUDOS if you like my post.

Thank you Bunuel, I dont think a question exists in GMAT which you and Karishma cant solve.

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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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
5X9+8X2=45+16=61= answer B

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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