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# Which of the following cannot be the sum of a 6-digit number

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Manager
Joined: 20 Feb 2018
Posts: 53
Location: India
Schools: ISB '20
Which of the following cannot be the sum of a 6-digit number  [#permalink]

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08 Jul 2019, 08:23
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Difficulty:

75% (hard)

Question Stats:

39% (02:08) correct 61% (01:55) wrong based on 44 sessions

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Which of the following cannot be the sum of a 6-digit number and the number formed by reversing its digits?

A. 777777
B. 1234442
C. 424523
D. 951467
E. 999999
Manager
Joined: 20 Feb 2018
Posts: 53
Location: India
Schools: ISB '20
Re: Which of the following cannot be the sum of a 6-digit number  [#permalink]

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08 Jul 2019, 13:15

Can you please provide solution to the above problem?
Sum of the number and its reverse is a multiple of 11 but here all the numbers are divisible by 11. So I believe this concept doesn't apply here. How can we solve it?
Director
Joined: 19 Oct 2018
Posts: 989
Location: India
Which of the following cannot be the sum of a 6-digit number  [#permalink]

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08 Jul 2019, 13:43
1
Let 'abcdef' is a 6-digit number.
sum of a 6-digit number and the number formed by reversing its digits= 100000(a+f)+10000(b+e)+1000(c+d)+100(c+d)+10(b+e)+(a+f)

Hence we can notice that difference between Hundred-thousands digit and unit digit can be 0 (if b+e<10), or 1 (if b+e>9).

In option D difference between Hundred-thousands digit and unit digit is 9-7=2
hence 951467 can never be the sum of a 6-digit number and the number formed by reversing its digits.

shobhitkh wrote:
Which of the following cannot be the sum of a 6-digit number and the number formed by reversing its digits?

A. 777777
B. 1234442
C. 424523
D. 951467
E. 999999
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: Which of the following cannot be the sum of a 6-digit number  [#permalink]

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08 Jul 2019, 22:49
3
shobhitkh wrote:
Which of the following cannot be the sum of a 6-digit number and the number formed by reversing its digits?

A. 777777
B. 1234442
C. 424523
D. 951467
E. 999999

Let the numbers be abcdef and fedcba. When we add them we get

100000(a+f) + 10000(b+e) + 1000(c+d) + 100(d+c) +10(b+e) + (f+a)
= 100001(a+f) + 10010(b+e) + 1100(c+d)

Whatever (a+f) is, that will be the first digit and the last digit. (a+f) can be anything from 2 (=1+1) to 18 (=9+9). Option (A) works if (a+f) = 7, option (B) works if (a+f) = 12, option (C) works if (a+f) = 3 (and there is a carry over of 1 from b+e). Option (E) works if (a+f) = 9.
Option (D) does not work since if (a+f) = 7, the first digit cannot be 9. Even with a carry over, it can only be 8. Two single digits can never add up to give a carry over of 2.

_________________
Karishma
Veritas Prep GMAT Instructor

Re: Which of the following cannot be the sum of a 6-digit number   [#permalink] 08 Jul 2019, 22:49
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