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

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

Archit3110 · Answer

given
 BA + AB + AB = CAA
which can be written as
10b+a+10a+b+10a+b=100c+10a+a
or say
21a+12b=100c+11a
10a+12b=100c
5a+6b=50c

say c=1
so
a=4 & b=6
IMO D ; 4

nick1816 · Answer

If BA is two digit number then B can not equal to 0
Now BA+AB+AB=CAA
That means A+B+B has same unit digit as A
Hence B can either 0 or 5( B can not equal to 0)
B=5
Also B+A+A+1 has same unit digit as A and C is non-zero
hence B+A+A+1= 10+A
5+2A+1=10+A
A=4

GMATGuruNY · Answer

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.

D

MathRevolution · Answer

=>

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

RJ7X0DefiningMyX · Answer

Your derived set of values do not satisfy the equation BA + AB + AB = CAA

What I rather did was after we got 10A + 12B = 100 C

(B has to be 0 or 5 so that B+B+A = A, but B cannot be 0 as BA, in that case, will be a single digit integer), so kept B as 5 in the above equation and got 10A + 60 = 100C, and then you can clearly see a set with A = 4 and C = 1, satisfying 54 + 45 + 45 = 144

Crytiocanalyst · Answer

Only a simplicfication has to be done and then some brute force substituttion

BA + AB + AB = CAA

which when simplified

10b+a+10a+b+10a+b=100c+10a+ a

=>10b +10a +2b =100c

for c=1 , b=2 we get a=4

Therefore IMO D

chetan2u · Answer

Easiest part first: Add the units digit => B+B+A=10+A or B=5
B+B+A cannot be 0+A as BA is a 2-digit number meaning B is not 0.

Now, we can write 5A +A5+A5 =CAA, where C is either 1 or 2.
To ease the calculations further as A is 5 or less from options given, C = 1
5A +A5+A5 =1AA
50+A+10A+5+10A+5=100+10A+A
50+5+10A+5=100
10A=40 or A=4

RC_xx · Answer

Hi  Bunuel , first of all thank for your awsome work, I'm close to exam day, but this kind of question are pretty hard for me, and I'd like to improve my skill, could you link similar question?

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

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

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