For positive integer x, what is the units digit of x^2?

Question

(1) The units digit of (x+1)^2 is 9.

(2) The units digit of (x−1)^2 is 5.

maxschmid · Answer

Please tell me if my approach is right:

WRONG
(1) try different values for x that fulfill the first condition. 
x = 2: (2+1)^2 = 9 
x = 12: (12+1)^2 = 169

now 2^2 = 4 & 12^2 = 144 -> both have the same units digit. assuming that this will be the same also for greater numbers. (1) is sufficient

(2) again try different values that fulfill the condition
x=6: (6-1)^2 = 25
x=16: (16-1)^2 = 225

now 6^2 = 36 & 16^2 also has a units digit of 6 cause of the characteristics of 6. (2) sufficient

Answer D

There is probably a shorter solution. this took me 2min 30.

quantumliner · Answer

Statement 1) The units digit of (x+1)^2 is 9.

Now If the Units digit of X was 2, then Unit's digit of (x+1)^2 would b 3 ^ 2 = 9

Now If the Units digit of X was 6, then Unit's digit of (x+1)^2 would b 7 ^ 2 = 9

Since we have two values, this statement is not sufficient.

Statement 2) The units digit of (x−1)^2 is 5.

Now If the Units digit of X was 6, then Unit's digit of (x-1)^2 would b 5 ^ 2 = 5

Therefore Statement 2 is sufficient.

Answer is B

JeffTargetTestPrep · Answer

We need to determine the units digit of x^2.

Statement One Alone:

The units digit of (x+1)^2 is 9.

We should recognize that there are two ways to obtain a units digit of 9 when squaring a positive integer: when the integer has a units digit of 3 or when the integer has a units digit of 7.

Thus, x itself could have a units digit of 2 and x^2 would have a units digit of 4, or x itself could have a units digit of 6 and x^2 would have a units digit of 6. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The units digit of (x−1)^2 is 5.

We should recognize that the only way to obtain a units digit of 5 when squaring a positive integer is if the integer has a units digit of 5. Thus, x itself MUST have a units digit of 6 and x^2 MUST have a units digit of 6. Statement two alone is sufficient to answer the question.

Answer: B

ion · Answer

Take into acount 6 (6+1)^2 = 7^2 > 49. And 6^2 = 36. So you have two options

ashikaverma13 · Answer

Hi, Instead of testing values, you can just check out which numbers between 1 to 9 end with a unit's digit of 9 when squared. (this approach helps because no matter what number you take, the unit's digit will always be sqaure of any digit between 1 to 9 or 0 but that will always result in zero) So, between 1 to 9 there are two numbers which when squared result in 9 i.e. 3 and 7. therefore, x could either be 2 or 6. hence, statement A is NOT SUFFICIENT. For statement 2, you know that only 5 or any number ending with a 5 results in units digit of 5. therefore, x would be 6. hence, statement B is SUFFICIENT. If it helps, kindly help me with kudos. Thanks.

harikrish · Answer

Statement : Unit's digit of x+1=3, ie x=2 or Unit's digit of x+1=7,ie x=6 . As we are getting 2 values of x, this statement is insufficient.
Statement 2:Unit's digit of x-1=5, Therefore x has to be 6.

Therefore answer is B

pushpitkc · Answer

Since we know that x is positive, all we need to find is the units digit of x^2.

(1) The units digit of (x+1)^2 is 9.
If the units digit of (x+1)^2 is 9, x could be 2 or 6, because 3^2 is 9 AND 7^2 is 49.
2^2 = 4 and 6^2 is 36(whose units digit is 6). Clearly insufficient.

(2) The units digit of (x−1)^2 is 5
This is possible only when x=6, because 5^2 is the only number whose square yields a 5 in the units digit.
Hence, sufficient(Option B)

goalMBA1990 · Answer

Statement 1: Since unit digit of x+1 is 9, x can be either no. with unit digit 2 or no. with unit digit 6. So x^2 will have either 4 or 6 as a unit digit. So not sufficient.

Statement 2: unit digit of (x-1)^2 is 5. So x must no. with unit digit 6. So x^2 will have unit digit 6 only. Sufficient to answer.

So B is the answer.

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JeffTargetTestPrep · Answer

We need to determine the units digit of x^2.

Statement One Alone:

The units digit of (x+1)^2 is 9.

Using the information in statement one, we see that the units digit of x can be 2 or 6. However, 2^2 has a units digit of 4 and 6^2 has a units digit of 6, so we cannot determine a unique value for the units digit of x^2. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The units digit of (x−1)^2 is 5.

Using the information in statement two, we see that x can be 6 or any positive integer with a units digit of 6. Thus, x^2 will have a units digit of 6. Statement two alone is sufficient to answer the question.

Answer: B

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For positive integer x, what is the units digit of x^2?

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