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16 Mar 2022, 04:30
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D
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Difficulty:
15%
(low)
Question Stats:
79% (01:21) correct
21%
(01:34)
wrong
based on 133
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Is the two-digit positive integer n divisible by 3?
(1) If the digits of n are reversed to produce the two-digit integer m, then m is divisible by 3.
(2) If the digits of n are reversed to produce the two-digit integer m, then m + n is divisible by 3.
(1) If the digits of n are reversed to produce the two-digit integer m, then m is divisible by 3.
(2) If the digits of n are reversed to produce the two-digit integer m, then m + n is divisible by 3.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
19 Mar 2022, 07:46
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If we have a two digit number AB, that number will be divisible by 3 if A+B is divisible by 3. So if, as Statement 1 tells us, the two-digit number BA is divisible by 3, then B+A is divisible by 3, and so is A+B, and the two-digit number AB is divisible by 3. So Statement 1 is sufficient.
For Statement 2, if n = AB (where A and B are digits), then n = 10A + B. If m = BA (where B and A are digits), then m = 10B + A. So n + m = 10A + B + 10B + A = 11A + 11B = 11(A + B). We know that's divisible by 3, and the '11' isn't divisible by 3 at all, so the only possibility is that A+B is divisible by 3, but that's the sum of the digits of AB, so AB is divisible by 3, and Statement 2 is sufficient.
Or if you know remainders really well, you might see that m and n in this question must have the same remainder by 3 since they have the same digit sum, and then since we can add remainders, you can see that they must both have a remainder of zero by 3 if Statement 2 is true. So the answer is D.
For Statement 2, if n = AB (where A and B are digits), then n = 10A + B. If m = BA (where B and A are digits), then m = 10B + A. So n + m = 10A + B + 10B + A = 11A + 11B = 11(A + B). We know that's divisible by 3, and the '11' isn't divisible by 3 at all, so the only possibility is that A+B is divisible by 3, but that's the sum of the digits of AB, so AB is divisible by 3, and Statement 2 is sufficient.
Or if you know remainders really well, you might see that m and n in this question must have the same remainder by 3 since they have the same digit sum, and then since we can add remainders, you can see that they must both have a remainder of zero by 3 if Statement 2 is true. So the answer is D.
29 Nov 2023, 02:01
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Is the two-digit positive integer n divisible by 3?
Let the number be ab, where a and b are digits.
If a+b is divisible by 3, then ab or n is divisible by 3.
(1) If the digits of n are reversed to produce the two-digit integer m, then m is divisible by 3.
Now, m is ba and is divisible by 3, that is b+a is divisible by 3.
b+a is same as a+b, so a+b is also divisible by 3.
Sufficient
(2) If the digits of n are reversed to produce the two-digit integer m, then m + n is divisible by 3.
Now, m is ba and m+n or 10b+a+10a+b or 11(a+b) is divisible by 3, that is a+b is divisible by 3.
Sufficient
D
Let the number be ab, where a and b are digits.
If a+b is divisible by 3, then ab or n is divisible by 3.
(1) If the digits of n are reversed to produce the two-digit integer m, then m is divisible by 3.
Now, m is ba and is divisible by 3, that is b+a is divisible by 3.
b+a is same as a+b, so a+b is also divisible by 3.
Sufficient
(2) If the digits of n are reversed to produce the two-digit integer m, then m + n is divisible by 3.
Now, m is ba and m+n or 10b+a+10a+b or 11(a+b) is divisible by 3, that is a+b is divisible by 3.
Sufficient
D
