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Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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31 Jan 2012, 16:51
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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?
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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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31 Jan 2012, 17:14
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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 twodigit integer dc and (10c+a) is the way of writing twodigit integer ca. Look at the sum: ab dc+db ca Now, as twodigit integer dc + twodigit 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 8 581 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  search.php?search_id=tag&tag_id=193 to learn more about this type of questions. Hope it helps.
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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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31 Jan 2012, 17:21
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Bunuel  thanks for this buddy. Its almost clear apart from how did you get Now, as twodigit integer dc + twodigit 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
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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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31 Jan 2012, 17:27



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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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31 Jan 2012, 17:29
Perfect!!!! What an explanation. Thanks a ton.
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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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31 Jan 2012, 20:08
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



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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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19 Feb 2012, 14:55
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
Last edited by M3tm4n on 20 Feb 2012, 03:16, edited 1 time in total.



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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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19 Feb 2012, 21:36



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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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20 Feb 2012, 03:22
Bunuel wrote: 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 ToolKitNo 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. Okay, got it. Thank you.



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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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03 Jun 2013, 07:16
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? Bunuel's solution is always the perfect one, but I just wanted to share what I did. Pretty much the same as above, though... 10d + 11c + a = 10d + 10c + c + a < 100 this means, 10d + 10c <= 90 (since it cannot be equal to hundred) then, 10(d+c) <= 90 thus, d + c < 10 and also, c + a < 10 This concludes that hundreds digit needs to be even because there is no carry over.



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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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21 Nov 2013, 06:42
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... :/



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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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21 Nov 2013, 07:11



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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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21 Nov 2013, 07:13
Ok, got it now...I think I worked on too many problems today, so I oversaw that... Anyway, thanks!



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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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03 Mar 2017, 09:08
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 twodigit integer dc and (10c+a) is the way of writing twodigit integer ca. Look at the sum: ab dc+db ca Now, as twodigit integer dc + twodigit 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 8 581 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: [b]try our new "Must or Could be True Questions" to learn more about this type of questions. Hope it helps. I adopted a different approach and was able to eliminate a different option. The numeric form of abdc + dbca, lets call it sum S, is (1001a + 1010d + 200b + 11c). From the the other given condition 10d+11c<100a implies 11c <100a10d. When we substitute for 11c in S, we get 1001a + 1010d + 200b + 11c < 1001a + 1010d + 200b + (100a10d) => S < 1000a + 1000d + 200b + 100 The minumum value of S (given that a,b,c,d are digits i.e. positive DIFFERENT integers) will be 3700. So, option A (3689) can never be a value of S.



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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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18 Mar 2017, 12:29
if we take b digit for a quick analysis, 2b in the sum is supposed to b even. C is the only answer that stands out



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Re: Given that a, b, c, and d are different nonzero digits and that 10d + [#permalink]
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19 Aug 2017, 06:11
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? This is one of the easiest methods; abdc + dbca Clearly unit digit of sum will depend upon (c+a) and tenth digit will depend upon (d+c); We have 10d + 11c < 100 – a or we can say 10d+11c+a< 100 or 10d+10c+c+a< 100 or 10(d+c)+ (c+a)< 100Now just go through the options; 1. 3689 so (c+a)=9 and we have 10(d+c)+ (c+a)< 100..so (d+c)< 9...here it is 8 (tenth digit) ..so possible 2. 6887 so (c+a)=7 or 17 and we have 10(d+c)+ (c+a)< 100..so (d+c)<9 or 8...here it is 8 (tenth digit) ..so possible 3. 8581 so (c+a)=11..it cant be 1 as a, b, c, and d are different nonzero digits and we have 10(d+c)+ (c+a)< 100..so (d+c)< 8...here it is 8 (tenth digit) ..which can not be possible....So option C..Give kudos if you find this solution useful. :)
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Re: Given that a, b, c, and d are different nonzero digits and that 10d +
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