It is currently 18 Oct 2017, 04:20

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

AB + CD = AAA, where AB and CD are 2 digit numbers and AAA

Author Message
TAGS:

Hide Tags

Manager
Joined: 28 Jun 2004
Posts: 90

Kudos [?]: 104 [0], given: 0

AB + CD = AAA, where AB and CD are 2 digit numbers and AAA [#permalink]

Show Tags

08 Jun 2005, 11:32
7
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:24) correct 33% (01:21) wrong based on 282 sessions

HideShow timer Statistics

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: ab-cd-aaa-where-ab-and-cd-are-two-digit-numbers-and-aa-136903.html
[Reveal] Spoiler: OA

Kudos [?]: 104 [0], given: 0

Manager
Joined: 28 Jun 2004
Posts: 90

Kudos [?]: 104 [0], given: 0

Show Tags

08 Jun 2005, 12:57
Yep, thats right. Can you please explain how you got that? These kinda questions always stumps me.

Kudos [?]: 104 [0], given: 0

Director
Joined: 18 Apr 2005
Posts: 543

Kudos [?]: 37 [0], given: 0

Location: Canuckland

Show Tags

08 Jun 2005, 13:04
smcgrath12 wrote:
Yep, thats right. Can you please explain how you got that? These kinda questions always stumps me.

AB +
CD =
AAA

We know that A must be 1 since A + C (+1 maybe)= AA
(+1 maybe) means that an extra unit can be carried over from summing B and D.
The largest number AA can be cannot exceed 19.

Now since A=1 1+C = 11, C cannot be 10, so we need one unit to be carried over from B+D so C equals 9.

p.s. there are multiple combinations for B and D as long as B+D = 11

Kudos [?]: 37 [0], given: 0

Manager
Joined: 28 Jun 2004
Posts: 90

Kudos [?]: 104 [1], given: 0

Show Tags

08 Jun 2005, 13:08
1
KUDOS
Think I got it one way.

From AB + CD = AAA, we get 10A + B + 10C + D = 111A

Meaning, 101A = 10C + (B + D) ------------- (A)

Now, there are 2 possibilities,

1) B + D = A. Putting B+D=A in A, we get C = 10A. But that would violate the data given. Even if A=1 (minimum), C=10. So this condition is false.

2) B + D = 10 + A. Putting B+D=10+A in A, we get C = 10A - 1. Now, the only way C < 10, is when A=1.

Thus, we get A=1, C=9.

Any other ways to approach this??

Kudos [?]: 104 [1], given: 0

Current Student
Joined: 28 Dec 2004
Posts: 3351

Kudos [?]: 319 [0], given: 2

Location: New York City
Schools: Wharton'11 HBS'12

Show Tags

08 Jun 2005, 17:37
9 for me...

I just picked AAA=111

then worked my way back, knowing A was 1!

Kudos [?]: 319 [0], given: 2

Senior Manager
Joined: 17 May 2005
Posts: 270

Kudos [?]: 17 [0], given: 0

Location: Auckland, New Zealand
Re: Number properties - PS [#permalink]

Show Tags

09 Jun 2005, 03:28
smcgrath12 wrote:
AB + CD = AAA, where AB and CD are 2 digit numbers and AAA is a 3 digit number. A,B,C and D are distinct positive numbers. In the above addition problem, what is the value of C?

from AB+CD=AAA:
B+D=10+A
A+C+1=10A+A -> C+1=10A
A has to be 1 as if the sum of two 2-digit numbers equals a 3-digit number, the max that the 3-digit number can be is 198...
if A=1, C=9

Kudos [?]: 17 [0], given: 0

Senior Manager
Joined: 17 Apr 2005
Posts: 372

Kudos [?]: 30 [3], given: 0

Location: India
Re: Number properties - PS [#permalink]

Show Tags

09 Jun 2005, 08:57
3
KUDOS
1
This post was
BOOKMARKED
smcgrath12 wrote:
AB + CD = AAA, where AB and CD are 2 digit numbers and AAA is a 3 digit number. A,B,C and D are distinct positive numbers. In the above addition problem, what is the value of C?

The sum of two 2 digit numbers cannot be more than 200. Hence A had to be 1.

Since AB < 20 ( a=1) , CD > 90 , hence C = 9.

HMTG.

Kudos [?]: 30 [3], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16715

Kudos [?]: 273 [0], given: 0

Re: AB + CD = AAA, where AB and CD are 2 digit numbers and AAA [#permalink]

Show Tags

24 Feb 2014, 09:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128685 [1], given: 12182

Re: AB + CD = AAA, where AB and CD are 2 digit numbers and AAA [#permalink]

Show Tags

24 Feb 2014, 11:48
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
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

Since AB and CD are two-digit integers, their sum can give us only one three digit integer of a kind of AAA: 111.

So, A=1 and we have 1B+CD=111

Now, C can not be less than 9, because no two-digit integer with first digit 1 (1B<20) can be added to two-digit integer less than 90, so that to have the sum 111 (if CD<90, so if C<9, CD+1B<111).

Hence C=9.

OPEN DISCUSSION OF THIS QUESTION IS HERE: ab-cd-aaa-where-ab-and-cd-are-two-digit-numbers-and-aa-136903.html
_________________

Kudos [?]: 128685 [1], given: 12182

Re: AB + CD = AAA, where AB and CD are 2 digit numbers and AAA   [#permalink] 24 Feb 2014, 11:48
Display posts from previous: Sort by