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by shankar.ashwin » Thu Oct 06, 2011 10:19 am
A letter stands for each digit between 0 and 9 (including both the digits). No two letters stand for the same digit. If (AB)^2 = CBB, (DE)^2 = GDE. Find A + B + C.


A) 6
B) 9
C) 12
D) 15
E) Cannot be determined
Last edited by shankar.ashwin on Thu Oct 06, 2011 10:30 am, edited 1 time in total.
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by GmatKiss » Thu Oct 06, 2011 10:24 am
I dont think this is a valid GMAT question!!
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by GmatMathPro » Thu Oct 06, 2011 10:50 am
(AB)^2=CBB would be true for B=0 and A=2 or A=3

20^2=400: A=2, B=0, C=4

30^2=900: A=3, B=0, C=9

(DE)^2=GDE implies that a two digit number squared produces a three digit number that ends in the same two digits as the number that was squared. 25^2=625 jumps to mind as a possibility, but let's see if there are others. This could only work if E=1,5, or 6, and if the number DE<32. 11^2=121, 15^2=225, 16^2=256, 21^2=441, 25^2=625, 26^2=676, 31^2=961. Only 25^2 fits the pattern. therefore, D=2, E=5, G=6

This conflicts with A=2, B=0, C=4 because A and D cannot both be 2, so it must be that A=3, B=0, C=9,
and [spoiler]A+B+C=12[/spoiler]
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