GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 16:04

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 27 Mar 2012
Posts: 14
If C + D = 11 and C and D are positive integers, which of  [#permalink]

### Show Tags

26 Apr 2012, 00:45
21
00:00

Difficulty:

35% (medium)

Question Stats:

74% (02:01) correct 26% (02:08) wrong based on 408 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 58320
Re: If C+D=11 and C & D are positive integers, which of the foll  [#permalink]

### Show Tags

26 Apr 2012, 01:10
10
7
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.
_________________
Manager
Joined: 12 Mar 2012
Posts: 79
Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q49 V36
GPA: 3.2
WE: Information Technology (Computer Software)
Re: Extra Equation Strategie  [#permalink]

### Show Tags

Updated on: 20 Mar 2013, 21:58
6
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.

Originally posted by Abhii46 on 20 Mar 2013, 20:58.
Last edited by Abhii46 on 20 Mar 2013, 21:58, edited 1 time in total.
##### General Discussion
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9699
Location: Pune, India
Re: If C + D = 11 and C and D are positive integers, which of  [#permalink]

### Show Tags

26 Apr 2012, 23:37
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).
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 312
Re: Extra Equation Strategie  [#permalink]

### Show Tags

20 Mar 2013, 21:29
1
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?

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

Thanks!
-Ron
_________________
Manager
Joined: 12 Mar 2012
Posts: 79
Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q49 V36
GPA: 3.2
WE: Information Technology (Computer Software)
Re: Extra Equation Strategie  [#permalink]

### Show Tags

20 Mar 2013, 21:55
2
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.
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 591
Re: Extra Equation Strategie  [#permalink]

### Show Tags

20 Mar 2013, 22:08
2
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.
_________________
Intern
Joined: 15 Mar 2012
Posts: 47
Location: United States
Concentration: Marketing, Strategy
Re: Extra Equation Strategie  [#permalink]

### Show Tags

20 Mar 2013, 22:10
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
Intern
Joined: 15 Mar 2012
Posts: 47
Location: United States
Concentration: Marketing, Strategy
Re: Extra Equation Strategie  [#permalink]

### Show Tags

20 Mar 2013, 22:16
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
Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 312
Re: Extra Equation Strategie  [#permalink]

### Show Tags

20 Mar 2013, 22:28
2
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.

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
_________________
Manager
Status: Final Lap
Joined: 25 Oct 2012
Posts: 227
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)
Re: If C + D = 11 and C and D are positive integers, which of  [#permalink]

### Show Tags

21 Mar 2013, 04:02
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: 9699
Location: Pune, India
Re: If C + D = 11 and C and D are positive integers, which of  [#permalink]

### Show Tags

21 Mar 2013, 10:44
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Status: Final Lap
Joined: 25 Oct 2012
Posts: 227
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)
Re: If C + D = 11 and C and D are positive integers, which of  [#permalink]

### Show Tags

21 Mar 2013, 11:01
You are right Karishma

_________________
KUDOS is the good manner to help the entire community.

"If you don't change your life, your life will change you"
Intern
Joined: 22 Jan 2010
Posts: 24
Location: India
Concentration: Finance, Technology
GPA: 3.5
WE: Programming (Telecommunications)
Re: If C + D = 11 and C and D are positive integers, which of  [#permalink]

### Show Tags

28 Mar 2013, 04:23
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.
------------------------------------------------
Please press KUDOS if you like my post.
_________________
Please press +1 KUDOS if you like my post.
Manager
Joined: 13 Jul 2013
Posts: 61
GMAT 1: 570 Q46 V24
Re: If C + D = 11 and C and D are positive integers, which of  [#permalink]

### Show Tags

09 Sep 2013, 08:13
Thank you Bunuel, I dont think a question exists in GMAT which you and Karishma cant solve.
Current Student
Joined: 12 Aug 2015
Posts: 2572
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If C + D = 11 and C and D are positive integers, which of  [#permalink]

### Show Tags

14 Mar 2016, 05:15
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
_________________
Manager
Joined: 04 May 2014
Posts: 152
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: If C + D = 11 and C and D are positive integers, which of  [#permalink]

### Show Tags

22 Aug 2017, 21:09
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
Senior Manager
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 433
Re: If C + D = 11 and C and D are positive integers, which of  [#permalink]

### Show Tags

20 Apr 2019, 08:11
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
Re: If C + D = 11 and C and D are positive integers, which of   [#permalink] 20 Apr 2019, 08:11
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne