AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
(A) 1
(B) 3
(C) 7
(D) 9
(E) Cannot be determined
Unknown Digits
This topic has expert replies
-
- Junior | Next Rank: 30 Posts
- Posts: 11
- Joined: Sat Aug 11, 2012 1:59 pm
GMAT/MBA Expert
- Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
Maximum possible value of the sum of 2 two-digit number is (99 + 99) = 198damilolaamele wrote:AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
In this case the sum is of the form AAA, i.e. a three-digit number whose all the three digits are same. Only possible sum is 111. This means A = 1
Now we can approach for finding C in two ways,
Method #1
- As A = 1, AB < 20
Hence, CD > (111 - 20) ---> CD > 91
Hence, C = 9
- (1B + CD) = 111
As B and D are distinct positive integers less than 9 and their sum has unit's digit 1, we must have a carry of 1 if we add them.
Hence, (1 + 1 + C) = 11 --> C = 9
Last edited by Anurag@Gurome on Mon Mar 04, 2013 12:16 am, edited 2 times in total.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT/MBA Expert
- Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
Algebraic Solution:
AB = (10A + B)
CD = (10C + D)
AAA = (100A + 10A + A)
So, (10A + B) + (10C + D) = (100A + 10A + A)
--> 10C + B + D = 100A + A
--> C = [101A - (B + D)]/10
Form my above post, only possible value of A is 1.
Now, maximum value of (B + D) is (9 + 8) = 17
Hence, C ≥ [101 - 17]/10 = 84/10 = 8.4
As C must be an integer, only possible value of C is 9.
The correct answer is D.
AB = (10A + B)
CD = (10C + D)
AAA = (100A + 10A + A)
So, (10A + B) + (10C + D) = (100A + 10A + A)
--> 10C + B + D = 100A + A
--> C = [101A - (B + D)]/10
Form my above post, only possible value of A is 1.
Now, maximum value of (B + D) is (9 + 8) = 17
Hence, C ≥ [101 - 17]/10 = 84/10 = 8.4
As C must be an integer, only possible value of C is 9.
The correct answer is D.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Since 99 + 99 < 200, AB + CD < 200.damilolaamele wrote:AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
(A) 1
(B) 3
(C) 7
(D) 9
(E) Cannot be determined
Thus, AAA = 111.
Since AB = 1B, AB≤19.
Since 111 = 19 + 92, CD≥92.
Thus, C=9.
The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
- Junior | Next Rank: 30 Posts
- Posts: 11
- Joined: Sat Aug 11, 2012 1:59 pm