If n is an integer such that 3

Question

If n is an integer such that 3 <= n <= 7, what is the unit’s digit of n^2?

(1) (n + 1)^2 has units digit 6.
(2) (n - 1)^2 has units digit 6.

kunalcvrce · Answer

n can be 3,4,5,6,7

From1:n can be 3 and 5 ,
for n=3,N+1=3+1=4 ,4^2 unit digit =6
similarly for 5 unit digit will be 6.
insufficient

from2:n can be 5 and 9 
Insufficient

combining both n=5

hence C

DavidTutorexamPAL · Answer

As there are only a small number of options, we'll just write them out.
This is an Alternative approach.

2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 15
6^2 = 36
7^2 = 49
8^2 = 64

(1) is true for 4 and 6 meaning n=3 or 5. In this case the answer to 'what is the units digit of n^2' is '9' or '5'.
Insufficient.

(2) is true for 4 or 6 meaning n=5 or 7. In this case the answer to our question is '5' or '9'.
Insufficient.

Combined.
Combining the above means that n = 5 so our answer is '5'.
Sufficient.

(C) is our answer.

EgmatQuantExpert · Answer

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

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

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