Official Guide Explanation:
Data Sufficiency #D25




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Solution and Metadata

Question: D25
Page: 24
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Powers and Roots of Numbers > Powers
Category 2: Arithmetic > Properties of Integers > Other

Explanation: Note from the question that units digit cannot be 0, 1, or 2. Since it's a digit, it must be no greater than 9. Thus, the units digit of n must be between 3 and 9, inclusive.

Statement (1) is insufficient. Consider each of the possibilities from 3 to 9. If the units digit of n is 3, the units digit of n2 is 9, so it can't be 3. If the units digit of n is 4, the units digit of n2 is 6. Continue through the options: if 5, then 5; if 6, then 6; if 7, then 9; if 8, then 4; if 9, then 1. Thus, the units digit of n could be either 5 or 6.

Statement (2) is also insufficient. Again, consider each of the choices. When calculating the cube, don't bother with the actual cube, just focus on the units digit. For instance, if the units digit of n is 9, it doesn't matter that n3 = 729, just that the units digit of n3 is 9. The product of 9 and 9 is 81, so the units digit is 1. The product of 1 and 9 is 9, so the units digit of the cube must be 9.

Working through each of the options: if 3, then 7; if 4, then 4; if 5, then 5; if 6, then 6; if 7, then 3; if 8, then 2; if 9, then 9. Thus, the units digit of 9 could be 4, 5, 6, or 9.

Taken together, the statements are still insufficient. Even knowing both statements, the units digit of n could be 5 or 6. Choice (E) is correct.

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