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Each of A, B and C represents a one-digit integer. AB and BA

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by Max@Math Revolution » Wed May 15, 2019 11:28 pm

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[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
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by GMATGuruNY » Thu May 16, 2019 2:16 am
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.

The correct answer is D.
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by Max@Math Revolution » Sun May 19, 2019 4:56 pm
=>

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.

Therefore, the answer is D.
Answer: D
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