Author 
Message 
TAGS:

Hide Tags

Director
Joined: 03 Sep 2006
Posts: 608

Both a, b, and c are 3digits integers, where a=b+c. Is the
[#permalink]
Show Tags
26 Jan 2012, 06:34
Question Stats:
61% (01:44) correct 39% (02:15) wrong based on 181 sessions
HideShow timer Statistics
Both a, b, and c are 3digits integers, where a=b+c. Is the hundreds' digit of number a equal to sum of that of b and c? (1) Tens' digit of a=tens' digit of b+tens' digit of c (2) Units' digit of a=units' digit of b+units' digit of c
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 59685

Re: Hundred's digit of sum of numbers
[#permalink]
Show Tags
26 Jan 2012, 12:05
Both a, b, and c are 3digits integers, where a=b+c. Is the hundreds' digit of number a equal to sum of that of b and c?Hundreds digit of \(a\) will equal to the sum of hundreds digits of \(b\) and \(c\) if there is no carried over 1 from the sum of the tens digits of \(b\) and \(c\). To illustrate: 149=b 249=b  398=a As you can see there is no carried over 1 from the sum of 4+4+1=9 (1 is carried over from the sum of units digits) and thus hundreds digit of \(a\) equal to the sum of hundreds digits of \(b\) and \(c\): 3=1+2; But if: 170=b 240=b  410=a As you can see there is a carried over 1 from the sum of 7+4=11 and thus hundreds digit of \(a\) doesn't equal to the sum of hundreds digits of \(b\) and \(c\): \(4\neq{1+2}.\) (1) Tens' digit of a=tens' digit of b+tens' digit of c > there can not be carried over 1 from this sum as it must be less than 10 to equal to tens' digit of \(a\). Sufficient. (2) Units' digit of a=units' digit of b+units' digit of c. Clearly insufficient as no info about tens digits. Answer: A.
_________________



Manager
Joined: 20 Jun 2012
Posts: 73
Location: United States
Concentration: Finance, Operations

If a, b, and c are 3digit positive integers, where a=b+c,
[#permalink]
Show Tags
Updated on: 25 Jun 2013, 05:09
If a, b, and c are 3digit positive integers, where a=b+c, is the hundreds' digit of a equal to the hundreds' digit of b plus the hundreds' digit of c? (1) The tens' digit of a is equal to the tens digit of b plus the tens' digit of c. (2) The units' digit of a is equal to the units' digit of b plus the units' digit of c. I am not okay with the OA provided. I think its C.
Originally posted by stunn3r on 25 Jun 2013, 05:06.
Last edited by Bunuel on 25 Jun 2013, 05:09, edited 1 time in total.
Edited the question.



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4472

Re: If a, b, and c are 3digit positive integers, where a=b+c,
[#permalink]
Show Tags
25 Jun 2013, 17:26
stunn3r wrote: If a, b, and c are 3digit positive integers, where a=b+c, is the hundreds' digit of a equal to the hundreds' digit of b plus the hundreds' digit of c? (1) The tens' digit of a is equal to the tens digit of b plus the tens' digit of c. (2) The units' digit of a is equal to the units' digit of b plus the units' digit of c.
What is the source of this question? The sum of the hundred's digits of a & b will equal the hundred's digit of c if nothing "carries" from the tens column. 123 + 351 = 474 123 + 358 = 481 Both of those lead to "yes" answer to the prompt question. In order for statement #1 to be true, it must be true that nothing carries from the ones column to the tens column (only the first of the two example addition statements satisfies this)  thus, statement #1 automatically implies statement #2. That's why statement #1, by itself, is sufficient  it already completely contains the information in statement #2. That's why (A) has to be the answer. In other words, I am claiming that it is utterly impossible to find numbers that satisfy both the prompt condition and statement #1 but not statement #2. In order for (C) to be the answer, there would have to be a case in which you could add two three digit numbers which met statement #1, did not meet statement #2, and the threedigit sum did not work out neatly in the hundreds column. You would have to able to find such a case, and I claim that finding such a case is impossible. That's why (C) can't be the answer. Does all this make sense? Mike
_________________
Mike McGarry Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)



Manager
Joined: 20 Jun 2012
Posts: 73
Location: United States
Concentration: Finance, Operations

Re: If a, b, and c are 3digit positive integers, where a=b+c,
[#permalink]
Show Tags
26 Jun 2013, 02:00
mikemcgarry wrote: stunn3r wrote: If a, b, and c are 3digit positive integers, where a=b+c, is the hundreds' digit of a equal to the hundreds' digit of b plus the hundreds' digit of c? (1) The tens' digit of a is equal to the tens digit of b plus the tens' digit of c. (2) The units' digit of a is equal to the units' digit of b plus the units' digit of c.
What is the source of this question? The sum of the hundred's digits of a & b will equal the hundred's digit of c if nothing "carries" from the tens column. 123 + 351 = 474 123 + 358 = 481 Both of those lead to "yes" answer to the prompt question. In order for statement #1 to be true, it must be true that nothing carries from the ones column to the tens column (only the first of the two example addition statements satisfies this)  thus, statement #1 automatically implies statement #2. That's why statement #1, by itself, is sufficient  it already completely contains the information in statement #2. That's why (A) has to be the answer. In other words, I am claiming that it is utterly impossible to find numbers that satisfy both the prompt condition and statement #1 but not statement #2. In order for (C) to be the answer, there would have to be a case in which you could add two three digit numbers which met statement #1, did not meet statement #2, and the threedigit sum did not work out neatly in the hundreds column. You would have to able to find such a case, and I claim that finding such a case is impossible. That's why (C) can't be the answer. Does all this make sense? Mike hmm .. true .. Thanks mike .. I figured it out when I retried the question but your explanation made it more clear. I've this hard copy of 200 mixed bag questions .. these are good concept building and "makes you scratch your head a little" type questions. I am posting all which I think would give something to learn to forum members and the questions which I get wrong I did first 40 of this set yesterday and posted around 78 questions. will post more, keep answering.



Math Expert
Joined: 02 Sep 2009
Posts: 59685

Re: If a, b, and c are 3digit positive integers, where a=b+c,
[#permalink]
Show Tags
01 Jul 2013, 13:06
stunn3r wrote: If a, b, and c are 3digit positive integers, where a=b+c, is the hundreds' digit of a equal to the hundreds' digit of b plus the hundreds' digit of c? (1) The tens' digit of a is equal to the tens digit of b plus the tens' digit of c. (2) The units' digit of a is equal to the units' digit of b plus the units' digit of c. I am not okay with the OA provided. I think its C. ______ Merging topics.
_________________



NonHuman User
Joined: 09 Sep 2013
Posts: 13744

Re: Both a, b, and c are 3digits integers, where a=b+c. Is the
[#permalink]
Show Tags
17 Mar 2019, 07:42
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.
_________________




Re: Both a, b, and c are 3digits integers, where a=b+c. Is the
[#permalink]
17 Mar 2019, 07:42






