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Math Expert V
Joined: 02 Sep 2009
Posts: 58135
For a certain integer x, the units digit of (x+2)^2 is 9. Which of the  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 70% (01:55) correct 30% (02:07) wrong based on 795 sessions

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For a certain integer x, the units digit of (x+2)^2 is 9. Which of the following could be the units digit of |x+1|?

A. 0
B. 3
C. 4
D. 5
E. 7

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Re: For a certain integer x, the units digit of (x+2)^2 is 9. Which of the  [#permalink]

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Bunuel wrote:
For a certain integer x, the units digit of (x+2)^2 is 9. Which of the following could be the units digit of |x+1|?

A. 0
B. 3
C. 4
D. 5
E. 7

The only way to get a units digit of 9 when squaring an integer is for the original integer to have a units digit of 3 or 7. Thus, since (x+2)^2 has a units digit of 9, x could be 1, 5,-5, or -9. Let’s plug each value into |x + 1|.

When x = 1, |x + 1| = 2, which is not an answer choice.

When x = 5, |x + 1| = 6, which is not an answer choice.

When x = -5, |x + 1| = |-4| = 4, which IS an answer choice.

When x = -9, |x + 1| = |-8| = 8, which is not an answer choice.

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Re: For a certain integer x, the units digit of (x+2)^2 is 9. Which of the  [#permalink]

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Bunuel wrote:
For a certain integer x, the units digit of (x+2)^2 is 9. Which of the following could be the units digit of |x+1|?

A. 0
B. 3
C. 4
D. 5
E. 7

(x+2)^2 = 9

So, Units digit of (x+2) will be 3 or 7

Thus, the units digit of x can be either 1 or 5

Quote:
the units digit of |x+1|

Units digit of |x+1| must be 4 or 6

Among the given option only (C) is possible, hence this is our answer...
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Intern  B
Joined: 02 Feb 2013
Posts: 16
For a certain integer x, the units digit of (x+2)^2 is 9. Which of the  [#permalink]

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1
I'll bet my uncle's beer-can collection it's C; i.e., x = -5, -15, etc.
Manager  B
Joined: 08 Sep 2016
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Re: For a certain integer x, the units digit of (x+2)^2 is 9. Which of the  [#permalink]

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1
X= -5

-5 + 1 = -4
Absolute value = 4

Manager  B
Joined: 06 Dec 2016
Posts: 243
Re: For a certain integer x, the units digit of (x+2)^2 is 9. Which of the  [#permalink]

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x could be 5 or 1.
If x is one, then we get a result of 4. Therefore the answer is C.
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Re: For a certain integer x, the units digit of (x+2)^2 is 9. Which of the  [#permalink]

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if the unit digit of square of the number is 9, the unit digit will be either 3 or 7 if x is positive and 5 and 9 if x is negative
hence the unit digit of x will be either 1 or 5 if x is positive and 5 and 9 if x is negative
hence |x+1| will yield the unit digit as 2 or 6 if x is positive and 4 and 8 if x is negative.

looking at the option we can see that 4 is the only option

Option C
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Re: For a certain integer x, the units digit of (x+2)^2 is 9. Which of the  [#permalink]

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(x+2)^2=9
it's supposed to end 3 or 7

I tried negative numbers: -5+3=-3^2=9
|-5+1|=4
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Re: For a certain integer x, the units digit of (x+2)^2 is 9. Which of the  [#permalink]

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A. 0
B. 3
C. 4
D. 5
E. 7

Unit digit on squaring any number can be 9 if and only if unit number of which we are squaring, must be either 3 or 7

And to have 7 or 3 at unit digit x can be 1,5,-5,-9

When x = 1, |x + 1| = 2,

When x = 5, |x + 1| = 6,

When x = -5, |x + 1| = |-4| = 4,

When x = -9, |x + 1| = |-8| = 8,
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Director  G
Joined: 09 Mar 2018
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Re: For a certain integer x, the units digit of (x+2)^2 is 9. Which of the  [#permalink]

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Bunuel wrote:
For a certain integer x, the units digit of (x+2)^2 is 9. Which of the following could be the units digit of |x+1|?

A. 0
B. 3
C. 4
D. 5
E. 7

Key word : certain integer x

(x+2)^2 is 9

x= -9 or x = -5 or x = 5 or x = 1

Only value which is present after using the above values in |x+1|

4

C
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Re: For a certain integer x, the units digit of (x+2)^2 is 9. Which of the  [#permalink]

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(x+2)^2 = 9, means --> last digit of x must be -5,(-5+2=3)
|x+1|--> _/(x+1)^2 or, x+1-->therefore last digit 4 (|-5+1|=4)
Manager  S
Joined: 27 Mar 2018
Posts: 79
Location: India
Re: For a certain integer x, the units digit of (x+2)^2 is 9. Which of the  [#permalink]

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Solution to this problem has already been discussed in detail. Just want to add another slightly different approach to select from the available options-

Unit digit of (x+2)^2 is 9, so x has to be an odd number and therefore |x+1| has to be an even number, which is only one of the available option, i.e. 4
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Thank you for the kudos. You are awesome!  Re: For a certain integer x, the units digit of (x+2)^2 is 9. Which of the   [#permalink] 01 May 2019, 09:35
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# For a certain integer x, the units digit of (x+2)^2 is 9. Which of the

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