NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 10:18 It is currently 23 Apr 2024, 10:18
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Given that a, b, c, and d are different nonzero digits and that 10d +

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
enigma123
Senior Manager
Senior Manager
Joined: 25 Jun 2011
Status:Finally Done. Admitted in Kellogg for 2015 intake
Posts: 396
Own Kudos [?]: 16642 [115]
Given Kudos: 217
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE:Information Technology (Consulting)
Send PM
Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   31 Jan 2012, 17:51
11
Kudos
104
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

34% (02:34) correct 66% (02:51) wrong based on 515 sessions
Hide Show timer Statistics
Given that a, b, c, and d are different nonzero digits and that 10d + 11c < 100 – a, which of the following could not be a solution to the addition problem below?

abdc
+ dbca

(A) 3689
(B) 6887
(C) 8581
(D) 9459
(E) 16091

Show Spoiler
This is the original question and its beyond my head to solve this. can someone please help and try to explain the concept of this?

Also , can you please tell how to solve if the question says COULD BE a solution to the addition problem?
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92875
Own Kudos [?]: 618548 [63]
Given Kudos: 81561
Send PM
CAT Tests Forum Quiz Mode
Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   31 Jan 2012, 18:14
39
Kudos
24
Bookmarks
Expert Reply
enigma123 wrote:
Given that a, b, c, and d are different nonzero digits and that 10d + 11c < 100 – a, which of the following could not be a solution to the addition problem below?
abdc
+ dbca
(A) 3689
(B) 6887
(C) 8581
(D) 9459
(E) 16091

This is the original question and its beyond my head to solve this. can someone please help and try to explain the concept of this?

Also , can you please tell how to solve if the question says COULD BE a solution to the addition problem?


\(10d + 11c < 100 – a\);
\(10d+11c+a<100\);
\((10d+c)+(10c+a)<100\).

(10d+c) is the way of writing two-digit integer dc and (10c+a) is the way of writing two-digit integer ca. Look at the sum:

abdc
+dbca
-----

Now, as two-digit integer dc + two-digit integer ca is less than 100, then there won't be carried over 1 to the hundreds place and as b+b=2b=even then the hundreds digit of the given sum must be even too. Thus 8581 could not be the sum of abdc+dbca (for any valid digits of a, b, c, and d).

Answer: C.

As for "could be true" questions: try our new "Must or Could be True Questions" tag - https://gmatclub.com/forum/search.php?se ... tag_id=193 to learn more about this type of questions.

Hope it helps.
General Discussion
User avatar
enigma123
Senior Manager
Senior Manager
Joined: 25 Jun 2011
Status:Finally Done. Admitted in Kellogg for 2015 intake
Posts: 396
Own Kudos [?]: 16642 [1]
Given Kudos: 217
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE:Information Technology (Consulting)
Send PM
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   31 Jan 2012, 18:21
1
Kudos
Bunuel - thanks for this buddy. Its almost clear apart from how did you get

Now, as two-digit integer dc + two-digit integer ca is less than 100 then there won't be carried over 1 to the hundreds place and as b+b must be ecen then the hundreds digit of the given sum must be even too
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92875
Own Kudos [?]: 618548 [2]
Given Kudos: 81561
Send PM
CAT Tests Forum Quiz Mode
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   31 Jan 2012, 18:27
2
Kudos
Expert Reply
enigma123 wrote:
Bunuel - thanks for this buddy. Its almost clear apart from how did you get

Now, as two-digit integer dc + two-digit integer ca is less than 100 then there won't be carried over 1 to the hundreds place and as b+b must be ecen then the hundreds digit of the given sum must be even too


Two-digit integer dc + two-digit integer ca is less than 100: suppose they are 12 and 23:
ab12
+db23
-----
XY35

So, there is no carried over 1 to hundreds place or to b+b. Next, b+b=2b=even so the hundreds digit of the given sum, Y in our example, must be even too.

Hope it's clear.
User avatar
enigma123
Senior Manager
Senior Manager
Joined: 25 Jun 2011
Status:Finally Done. Admitted in Kellogg for 2015 intake
Posts: 396
Own Kudos [?]: 16642 [0]
Given Kudos: 217
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE:Information Technology (Consulting)
Send PM
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   31 Jan 2012, 18:29
Perfect!!!! What an explanation. Thanks a ton.
avatar
subhajeet
Manager
Manager
Joined: 12 Jun 2010
Status:MBA Aspirant
Posts: 79
Own Kudos [?]: 247 [2]
Given Kudos: 1
Location: India
Concentration: Finance, International Business
WE:Information Technology (Investment Banking)
Send PM
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   31 Jan 2012, 21:08
1
Kudos
1
Bookmarks
enigma123 wrote:
Given that a, b, c, and d are different nonzero digits and that 10d + 11c < 100 – a, which of the following could not be a solution to the addition problem below?
abdc
+ dbca
(A) 3689
(B) 6887
(C) 8581
(D) 9459
(E) 16091

This is the original question and its beyond my head to solve this. can someone please help and try to explain the concept of this?

Also , can you please tell how to solve if the question says COULD BE a solution to the addition problem?


Given 10d+11c+a<100

now we have to find the sum of -> 1000a+100b+10d+c+1000d+100b+10c+a

we simplify it further to get -> 1000a+1000d+200b+(11c+10d+a)
we know that the value in bracket has to be less than 100
now take the options - let us take C which is 8581
we can break it to 8000+500+81 -> since each of a,b,c and d is an integer so we cannot find a value of b to get the sum of 500
Thus C is the answer
avatar
M3tm4n
Intern
Intern
Joined: 06 Nov 2011
Posts: 28
Own Kudos [?]: 15 [2]
Given Kudos: 50
Location: Germany
Concentration: Entrepreneurship, General Management
GMAT Date: 03-10-2012
GPA: 3
Send PM
GMAT ToolKit User
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   Updated on: 20 Feb 2012, 04:16
1
Kudos
Isn't it be easier just to look for b? The hundreds digit of the sum must be even. There is only one answer choice where the hundreds digit is odd.

Posted from GMAT ToolKit

Originally posted by M3tm4n on 19 Feb 2012, 15:55.
Last edited by M3tm4n on 20 Feb 2012, 04:16, edited 1 time in total.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92875
Own Kudos [?]: 618548 [1]
Given Kudos: 81561
Send PM
CAT Tests Forum Quiz Mode
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   19 Feb 2012, 22:36
1
Kudos
Expert Reply
M3tm4n wrote:
Isn't it be easier just to look for b? The hundreds digit of the sum must be even. There is online one answer choice where the hundreds digit is odd.

Posted from GMAT ToolKit


No that's not correct. The hundreds digit will be even if there is no carried over 1 from the sum of the tens digits. So you should check this first. Please refer to the complete solution above.

Hope it helps.
avatar
wfmd
Intern
Intern
Joined: 19 Aug 2013
Posts: 15
Own Kudos [?]: 19 [0]
Given Kudos: 0
Location: Germany
Concentration: International Business, Technology
Schools: HKU '15 (A)
GMAT 1: 580 Q35 V35
GMAT 2: 690 Q44 V40
GPA: 3.85
WE:Information Technology (Consulting)
Send PM
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   21 Nov 2013, 07:42
Hey Bunuel,

most is clear, except for the starting point:

Quote:
10d + 11c < 100 – a --> 10d+11c+a<100 --> (10d+c)+(10c+a)<100


Why is 10d + 11c < 100 – a the same as (10d+c)+(10c+a)<100 ???
That's not clear for me... :-/
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92875
Own Kudos [?]: 618548 [0]
Given Kudos: 81561
Send PM
CAT Tests Forum Quiz Mode
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   21 Nov 2013, 08:11
Expert Reply
wfmd wrote:
Hey Bunuel,

most is clear, except for the starting point:

Quote:
10d + 11c < 100 – a --> 10d+11c+a<100 --> (10d+c)+(10c+a)<100


Why is 10d + 11c < 100 – a the same as (10d+c)+(10c+a)<100 ???
That's not clear for me... :-/


10d + 11c < 100 – a

Add a to both sides: 10d + 11c + a< 100;
10d + (10c + c) + a< 100;
(10d+c)+(10c+a)<100.

Hope it's clear.
User avatar
S
Nixondutta
Intern
Intern
Joined: 24 Apr 2017
Status:The journey is always more beautiful than the destination
Affiliations: Computer Science
Posts: 43
Own Kudos [?]: 72 [1]
Given Kudos: 83
Location: India
Concentration: Statistics, Strategy
Schools: Columbia EMBA"19 Simon '19 Mason '19
GMAT 1: 570 Q40 V28
GPA: 3.14
Send PM
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   23 Apr 2018, 00:10
Bunuel wrote:
enigma123 wrote:
Given that a, b, c, and d are different nonzero digits and that 10d + 11c < 100 – a, which of the following could not be a solution to the addition problem below?
abdc
+ dbca
(A) 3689
(B) 6887
(C) 8581
(D) 9459
(E) 16091

This is the original question and its beyond my head to solve this. can someone please help and try to explain the concept of this?

Also , can you please tell how to solve if the question says COULD BE a solution to the addition problem?


10d + 11c < 100 – a --> 10d+11c+a<100 --> (10d+c)+(10c+a)<100. (10d+c) is the way of writing two-digit integer dc and (10c+a) is the way of writing two-digit integer ca. Look at the sum:

abdc
+dbca
-----

Now, as two-digit integer dc + two-digit integer ca is less than 100, then there won't be carried over 1 to the hundreds place and as b+b=2b=even then the hundreds digit of the given sum must be even too. Thus 8581 could not be the sum of abdc+dbca (for any valid digits of a, b, c, and d).

Answer: C.

As for "could be true" questions: try our new "Must or Could be True Questions" tag - https://gmatclub.com/forum/search.php?se ... tag_id=193 to learn more about this type of questions.

Hope it helps.

Best explanation ever. couldn't be more clear.
avatar
B
htieuan
Intern
Intern
Joined: 02 Oct 2019
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 9
Send PM
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   15 Apr 2020, 22:52
My question is b is nonzero digit, how can 2b=0 in option E?

Posted from my mobile device
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92875
Own Kudos [?]: 618548 [1]
Given Kudos: 81561
Send PM
CAT Tests Forum Quiz Mode
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   16 Apr 2020, 00:03
1
Kudos
Expert Reply
htieuan wrote:
My question is b is nonzero digit, how can 2b=0 in option E?

Posted from my mobile device

______________________
What if b = 5?
User avatar
D
udaypratapsingh99
Senior Manager
Senior Manager
Joined: 12 Jan 2019
Posts: 404
Own Kudos [?]: 216 [1]
Given Kudos: 372
Location: India
Concentration: Strategy, Leadership
Schools: Fuqua '24 Harvard '24 LBS '24 NTU NUS Said '23 Ross '24 Sloan '24 Stanford '24 Tepper '24 Tuck '24 Wharton '24 Yale '24
GMAT 1: 660 Q47 V34
Send PM
Reviews Badge CAT Tests
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   09 Oct 2022, 05:28
1
Kudos
enigma123 wrote:
Given that a, b, c, and d are different nonzero digits and that 10d + 11c < 100 – a, which of the following could not be a solution to the addition problem below?

abdc
+ dbca

(A) 3689
(B) 6887
(C) 8581
(D) 9459
(E) 16091

Show Spoiler
This is the original question and its beyond my head to solve this. can someone please help and try to explain the concept of this?

Also , can you please tell how to solve if the question says COULD BE a solution to the addition problem?



Given: 10d + 11c < 100 – a,
Inference: Neither of 'd' and 'c' can be 9

Now,
abdc
+dbca

1) As above addition operation has unit b on hundreds place, b+b must give an even number unless a 1 is carried from the addition at the tens place.
2) As neither of 'd' and 'c' can be 9, both (i) digit of sum at tens place to be 8 and (ii) carry over of 1 to hundreds place, cannot happen together.

Thus, option (C) 8581 is not possible.

C is the Correct Answer
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5342
Own Kudos [?]: 3962 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   09 Oct 2022, 07:21
Asked: Given that a, b, c, and d are different nonzero digits and that 10d + 11c < 100 – a, which of the following could not be a solution to the addition problem below?

abdc
+ dbca

abdc = 1000a + 100b + 10d + c
dbca = 1000d + 100b + 10c + a

Sum of last 2 digits = 10d + 11c + a < 100; There is no carry over to hundredth digit

Hundredth digit = 200b is even; therefore, abdc + dbca can not be 8581.

IMO C
avatar
B
DeepanshuGupta
Intern
Intern
Joined: 10 Jul 2022
Posts: 20
Own Kudos [?]: 1 [0]
Given Kudos: 7
Send PM
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   12 Jan 2023, 01:18
I am all clear with the question only if I take a simple assumption that the no. are positive. But my point is that where is it written that they are positive? It is written that the numbers are non-zero. Now non-zero could be either positive or negative. Is it so that we have eliminated the possibility of numbers being negative by looking at the answer options. Kindly explain.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32624
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink] New post   19 Feb 2024, 06:32
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.
GMAT Club Bot
gmatclubot
Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
19 Feb 2024, 06:32
Moderators:
Bunuel
Math Expert
92875 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions