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.
Answer (D)
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Karishma
Veritas Prep GMAT Instructor
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