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

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If C + D = 11 and C and D are positive integers, which of [#permalink]  25 Apr 2012, 23:45
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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
[Reveal] Spoiler: OA
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Re: If C+D=11 and C & D are positive integers, which of the foll [#permalink]  26 Apr 2012, 00:10
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sugu86 wrote:
Hi guys,

Way to solve the below problem ?

If C+D=11 and C & D are positive integers, which of the following is a possible value of 5C+8D ?

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

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.

P.S. Do not shorten or reword the questions you post.
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Re: Extra Equation Strategie [#permalink]  20 Mar 2013, 19:58
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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.

Last edited by Abhii46 on 20 Mar 2013, 20:58, edited 1 time in total.
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Re: Extra Equation Strategie [#permalink]  20 Mar 2013, 21:28
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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]  28 Mar 2013, 03:23
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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: Extra Equation Strategie [#permalink]  20 Mar 2013, 20:29
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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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Re: Extra Equation Strategie [#permalink]  20 Mar 2013, 20:55
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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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Re: Extra Equation Strategie [#permalink]  20 Mar 2013, 21:08
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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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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]  26 Apr 2012, 22:37
Expert's post
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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Current Student Joined: 15 Mar 2012 Posts: 60 Location: United States Concentration: Marketing, Strategy Followers: 0 Kudos [?]: 14 [0], given: 19 Re: Extra Equation Strategie [#permalink] 20 Mar 2013, 21:10 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 _________________ MV "Better to fight for something than live for nothing.” ― George S. Patton Jr Current Student Joined: 15 Mar 2012 Posts: 60 Location: United States Concentration: Marketing, Strategy Followers: 0 Kudos [?]: 14 [0], given: 19 Re: Extra Equation Strategie [#permalink] 20 Mar 2013, 21:16 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 _________________ MV "Better to fight for something than live for nothing.” ― George S. Patton Jr Senior Manager Status: Final Lap Joined: 25 Oct 2012 Posts: 287 Concentration: General Management, Entrepreneurship GPA: 3.54 WE: Project Management (Retail Banking) Followers: 3 Kudos [?]: 206 [0], given: 85 Re: If C + D = 11 and C and D are positive integers, which of [#permalink] 21 Mar 2013, 03:02 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 _________________ KUDOS is the good manner to help the entire community. "If you don't change your life, your life will change you" Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6238 Location: Pune, India Followers: 1683 Kudos [?]: 9652 [0], given: 198 Re: If C + D = 11 and C and D are positive integers, which of [#permalink] 21 Mar 2013, 09:44 Expert's post 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]  21 Mar 2013, 10:01
You are right Karishma

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Re: If C + D = 11 and C and D are positive integers, which of [#permalink]  09 Sep 2013, 07:13
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]  10 Dec 2014, 09:00
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Re: If C + D = 11 and C and D are positive integers, which of   [#permalink] 10 Dec 2014, 09:00
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