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Re: If n is an integer such that 3 <= n <= 7, what is the unit’s digit of [#permalink]
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Solution



Given:
    • n is an integer such that 3<=n<=7.

To find:
    • What is the units digit of \(n^2\)?

Statement-1:\((n + 1)^2\) has units digit 6.“

Since 3<=n<=7, 4<=(n+1) <=8

The units digit of all the possible values of \((n+1)^2\) is:
    • \(4^2= 6\)
    • \(5^2=5\)
    • \(6^2=6\)
    • \(7^2=9\)
    • \(8^2=4\)

For (n+1) = 4 and (n+1)=6, the units digit of \((n+1)^2\) is 6.
    • Thus, n= 3 or 5.

We do not have a unique value of n. Thus, Statement 1 alone is not sufficient to answer the question.

Statement-2:\((n - 1)^2\) has units digit 6.“

Since 3<=n<=7, 2<=(n+1) <=6

The units digit of all the possible values of \((n-1)^2\) is:
    • \(2^2= 4\)
    • \(3^2=9\)
    • \(4^2=6\)
    • \(5^2=5\)
    • \(6^2=6\)

For (n-1) = 4 and (n-1)=6, the units digit of \((n-1)^2\) is 6.
    • Thus, n= 5 or 7.

We do not have a unique value of n. Thus, Statement 2 alone is not sufficient to answer the question.

Combining both the statements:

From statement 1, we have:
    • n= 3 or 5

From statement 2, we have:
    • n= 5 or 7

By combining both the statements, the common value of n is 3 and the units digit of \(n^2\) is 9.

Hence, Statement (1) and (2) together are sufficient to answer the question.

Hence, the correct answer is option C.

Answer: C
GMAT Club Bot
Re: If n is an integer such that 3 <= n <= 7, what is the unit’s digit of [#permalink]
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