What is the least value of the positive integer $n?$

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Thu Dec 17, 2020 1:15 pm

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What is the least value of the positive integer $n?$

I. The unit digit of $n$ is equal to the unit digit of the sum of $n$ and $(n + 1).$
II. n is the square of a single-digit odd prime number.

Answer: D

Source: e-GMAT

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Source: Beat The GMAT — Data Sufficiency | Thu Dec 17, 2020 1:15 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: What is the least value of the positive integer $n?$

by deloitte247 » Sun Dec 27, 2020 1:07 am

Statement 1: The unit digit of n is equal to the unit digit of the sum of n and (n+1)
n + (n+1) = 2n + 1 which is an odd number.
So, testing all odd unit integer 1, 3, 5, 7, and 9.
If n=1, then 2n+1 = 3 units are not equal.
$$So,\ n\ne1$$
If n=3, then 2n+1 = 7 units are not equal.
$$So,\ n\ne3$$
If n=5, then 2n+1 = 11 units are not equal.
$$So,\ n\ne5$$
If n=7, then 2n+1 = 15 units are not equal.
$$So,\ n\ne7$$
If n=9, then 2n+1 = 19 units are not equal.
$$So,\ n=9$$

Statement 2: n is the square of a single-digit odd prime number.
Odd prime unit integers are 3, 5, and 7. So,
$$n=3^2\ or\ n=5^2\ or\ n=7^2$$
$$n=9\ or\ n=25\ or\ n=49$$
But among these values the least of them is 9. So, n=9. Hence, statement 2 is SUFFICIENT.

Since each statement alone is SUFFICIENT, the correct answer is option D

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