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# If n is an integer such that 3 <= n <= 7, what is the unit’s digit of

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

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.

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