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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
47% (01:59) correct
53%
(02:48)
wrong
based on 265
sessions
History
Date
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Not Attempted Yet
AB
+BA
____
CDC
In the correctly worked addition problem shown, AB and BA are two-digit positive integers, CDC is a three-digit integer, and A, B, C, and D are distinct nonzero digits. How many different values can A * B * C * D take?
A. 2
B. 3
C. 4
D. 6
E. 8
+BA
____
CDC
In the correctly worked addition problem shown, AB and BA are two-digit positive integers, CDC is a three-digit integer, and A, B, C, and D are distinct nonzero digits. How many different values can A * B * C * D take?
A. 2
B. 3
C. 4
D. 6
E. 8
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M46-39
Fri Jul 10, 2026 8:00 am
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GMAT Club Official Solution:
AB
+BA
____
CDC
In the correctly worked addition problem shown, AB and BA are two-digit positive integers, CDC is a three-digit integer, and A, B, C, and D are distinct nonzero digits. How many different values can A * B * C * D take?
A. 2
B. 3
C. 4
D. 6
E. 8
Since the sum of two two-digit numbers is a three-digit number, the hundreds digit C must be 1. The largest possible sum is 99 + 99 = 198, so C cannot be anything greater than 1.
Now look at the units column. Since the units digit of the sum is C = 1, the sum A + B must have units digit 1. Also, since the result is three digits, A + B must be at least 10. Since A and B are digits, A + B cannot be 21 or more. Therefore:
A + B = 11
So the units column gives 1 and carries 1 to the tens column. Then the tens column is:
A + B + 1 = 12
Thus, D = 2.
So C = 1, D = 2, and A + B = 11.
Since A, B, C, and D are distinct nonzero digits, A and B cannot be 1 or 2. The possible ordered pairs for A and B are:
(3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3)
But reversed pairs give the same value of A * B * C * D, so we only need:
(3, 8), (4, 7), (5, 6)
Since C = 1 and D = 2, we get:
A * B * C * D = A * B * 1 * 2
The three possible values are:
3 * 8 * 1 * 2 = 48
4 * 7 * 1 * 2 = 56
5 * 6 * 1 * 2 = 60
So there are 3 different values.
Answer: B.
AB
+BA
____
CDC
In the correctly worked addition problem shown, AB and BA are two-digit positive integers, CDC is a three-digit integer, and A, B, C, and D are distinct nonzero digits. How many different values can A * B * C * D take?
A. 2
B. 3
C. 4
D. 6
E. 8
Since the sum of two two-digit numbers is a three-digit number, the hundreds digit C must be 1. The largest possible sum is 99 + 99 = 198, so C cannot be anything greater than 1.
Now look at the units column. Since the units digit of the sum is C = 1, the sum A + B must have units digit 1. Also, since the result is three digits, A + B must be at least 10. Since A and B are digits, A + B cannot be 21 or more. Therefore:
A + B = 11
So the units column gives 1 and carries 1 to the tens column. Then the tens column is:
A + B + 1 = 12
Thus, D = 2.
So C = 1, D = 2, and A + B = 11.
Since A, B, C, and D are distinct nonzero digits, A and B cannot be 1 or 2. The possible ordered pairs for A and B are:
(3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3)
But reversed pairs give the same value of A * B * C * D, so we only need:
(3, 8), (4, 7), (5, 6)
Since C = 1 and D = 2, we get:
A * B * C * D = A * B * 1 * 2
The three possible values are:
3 * 8 * 1 * 2 = 48
4 * 7 * 1 * 2 = 56
5 * 6 * 1 * 2 = 60
So there are 3 different values.
Answer: B.
General Discussion
Fri Jul 10, 2026 7:12 am
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Here's my solution for this question
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