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# x and y are integers. If the units digit of x^2 is 9, and the units

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Math Expert
Joined: 02 Sep 2009
Posts: 52108
x and y are integers. If the units digit of x^2 is 9, and the units  [#permalink]

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11 Apr 2017, 22:23
1
5
00:00

Difficulty:

25% (medium)

Question Stats:

73% (02:04) correct 27% (02:18) wrong based on 103 sessions

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x and y are integers. If the units digit of x^2 is 9, and the units digit of y^2 is 9 as well, which of the following CANNOT be (x−y)?

A) -4
B) 4
C) 6
D) 10
E) 18

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WE: Engineering (Energy and Utilities)
Re: x and y are integers. If the units digit of x^2 is 9, and the units  [#permalink]

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11 Apr 2017, 22:58
Option E

$$X^2$$ = abc9 & $$Y^2$$ =lmn9 [a,b,c,l,m,n are arbitrarily assumed digits]

There two possibilities for unit's digit value of each of X & Y i.e., 3 or 7. For e.g. any number of the form p3 or p7, will result in q9 or q9 upon squaring. Where p & q are arbitrarily assumed digits. Now, coming back to Q.

So, X = g3 or g7 & similarly, Y = h3 or h7 [g,h arbitrarily assumed digits].

Now, we can see the possible value for (X - Y) could be = 0 (13 -13 or 17 - 17); 4/-4 (17 - 13 or 13 - 17); 10 (27-17 or 37-27 etc.)

Hence, (X-Y) can never be 18.
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Re: x and y are integers. If the units digit of x^2 is 9, and the units  [#permalink]

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12 Apr 2017, 06:06
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1
Bunuel wrote:
x and y are integers. If the units digit of x² is 9, and the units digit of y² is 9 as well, which of the following CANNOT be (x−y)?

A) -4
B) 4
C) 6
D) 10
E) 18

We know that 3² = 9, and 7² = 49. BOTH of these values yield a value with 9 in the units position.
So, some possible values of x include: 3, 7, 13, 17, 23, 27, 33, 37, etc
Likewise, some possible values of y include: 3, 7, 13, 17, 23, 27, 33, 37, etc

Which of the following CANNOT be (x−y)?
A) -4. If x = 3 and y = 7, then x - y = 3 - 7 = -4. ELIMINATE
B) 4. If x = 7 and y = 3, then x - y = 7 - 3 = 4. ELIMINATE
C) 6. If x = 13 and y = 7, then x - y = 13 - 7 = 6. ELIMINATE
D) 10. If x = 13 and y = 3, then x - y = 13 - 3 = 10. ELIMINATE

By the process of elimination, the correct answer must be E

Cheers,
Brent
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Joined: 21 Mar 2016
Posts: 523
Re: x and y are integers. If the units digit of x^2 is 9, and the units  [#permalink]

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12 Apr 2017, 07:36
units digit will 9 only for 3^2 and 7^2

hence 3,-3,7,-7 are the possibilites..

18 is not possible out of th egiven choices,,
ans E
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Re: x and y are integers. If the units digit of x^2 is 9, and the units  [#permalink]

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19 Apr 2017, 15:03
1
Bunuel wrote:
x and y are integers. If the units digit of x^2 is 9, and the units digit of y^2 is 9 as well, which of the following CANNOT be (x−y)?

A) -4
B) 4
C) 6
D) 10
E) 18

If the units digits of x^2 and y^2 are both 9, the units digit of x and y could be: 3, -3, 7, or -7.

Thus, some possible values of x - y are:

3 - 7 = -4

7 - 3 = 4

3 - (-3) = 6

3 - (-7) = 10

However, x - y cannot equal 18.

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Re: x and y are integers. If the units digit of x^2 is 9, and the units &nbs [#permalink] 19 Apr 2017, 15:03
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