College of Admission Tests Multan

Principles of Data Sufficiency

Solve the question of and select the option from the choices A through D/E. Check your Answer and view the explanation.

Question: 2

What is the last digit of the positive integer n?

(1) The last digit of n equals the last digit of n2.

(2) n is an even number.

  • Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  • Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  • BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  • EACH statement ALONE is sufficient.
  • Statements (1) and (2) TOGETHER are NOT sufficient.

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Correct Answer: E

The last digit of a positive integer is the same as the last digit of n2 only when the last digit is 0, 1, 5, or 6. For example, The last digit of 10 is 0 and the last digit of 102 (= 100) is also 0. The last digit of 11 is 1 and the last digit of 112 (= 121) is also 1. The last digit of 15 is 5, and the last digit of 152 (= 225) is also 5. The last digit of 16 is 6, and the last digit of 162 (= 256) is also 6. Since we have multiple cases with Statement (1) alone, it is not sufficient.

Now, the last digit of an even number is 0, 2, 4, 6, or 8. Hence, Statement (2) alone is not sufficient.

The common solutions from the two statements are 0 and 6 (which means n ends with either 0 or 6). Since we do not have a single solution, the statements together are not sufficient. The answer is (E).