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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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MathRevolution
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Each of A, B and C represents a one-digit integer. AB and BA are two-d [#permalink] New post  16 May 2019, 00:36
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65% (02:53) correct 35% (02:40) wrong based on 180 sessions
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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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Archit3110
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Re: Each of A, B and C represents a one-digit integer. AB and BA are two-d [#permalink] New post  16 May 2019, 01:14
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MathRevolution 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


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
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nick1816
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Re: Each of A, B and C represents a one-digit integer. AB and BA are two-d [#permalink] New post  16 May 2019, 01:15
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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
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GMATGuruNY
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Re: Each of A, B and C represents a one-digit integer. AB and BA are two-d [#permalink] New post  16 May 2019, 03:22
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MathRevolution 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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MathRevolution
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Re: Each of A, B and C represents a one-digit integer. AB and BA are two-d [#permalink] New post  19 May 2019, 18:06
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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 \(A = 4.\)

Therefore, the answer is D.
Answer: D
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RJ7X0DefiningMyX
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Re: Each of A, B and C represents a one-digit integer. AB and BA are two-d [#permalink] New post  29 May 2019, 03:18
Archit3110 wrote:
MathRevolution 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


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


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
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Crytiocanalyst
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Re: Each of A, B and C represents a one-digit integer. AB and BA are two-d [#permalink] New post  26 Aug 2021, 07:07
MathRevolution 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


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
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chetan2u
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Re: Each of A, B and C represents a one-digit integer. AB and BA are two-d [#permalink] New post  25 Aug 2023, 19:44
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MathRevolution 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



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
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Re: Each of A, B and C represents a one-digit integer. AB and BA are two-d [#permalink]
25 Aug 2023, 19:44
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