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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Each of A, B and C represents a one-digit integer. AB and BA tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## Each of A, B and C represents a one-digit integer. AB and BA ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] Each of A, B and C represents a one-digit integer. AB and BA are two-digit integers, and CAA is a three-digit integer. If BA + AB + AB = CAA, what is the value of A? A. 1 B. 2 C. 3 D. 4 E. 5 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
[GMAT math practice question]

Each of A, B and C represents a one-digit integer. AB and BA are two-digit integers, and CAA is a three-digit integer. If BA + AB + AB = CAA, what is the value of A?

A. 1
B. 2
C. 3
D. 4
E. 5
325 = 100*3 + 10*2 + 5
648 = 100*6 + 10*4 + 8
Generally:
Three-digit integer XYZ = 100X + 10Y + Z

Since BA + AB + AB = CAA, we get:
(10B+A) + (10A+B) + (10A+B) = 100C + 10A + A
12B + 21A = 100C + 11A
12B + 10A = 100C
12B + 10A = MULTIPLE OF 100
Since B and A are digits, the left side will yield a multiple of 100 only if B=5 and A=4, with the result that 12B+10A = (12*5) + (10*4) = 100.
Thus, A=4.

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Equating the units digits of BA + AB + AB and CAA gives either A + B + B = A or A + B + B = 10 + A. So, B = 5 or B = 0.
Since BA is a two-digit integer, we must have B = 5.
After carrying from the addition of the units digits, adding the tens digits yields B + A + A + 1 = 5 + A + A + 1 = 10 + A or A = 4.

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