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The following addition operation shows the sum of the twodigit positi
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24 Sep 2018, 00:17
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The following addition operation shows the sum of the twodigit positive integers XY and YX. If the threedigit integer XXZ, and X, Y , and Z are different digits, what is the value of the integer Z? XY +YX _____ XXZ (A) 8 (B) 7 (C) 2 (D) 1 (E) 0
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The following addition operation shows the sum of the twodigit positi
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24 Sep 2018, 03:59
Bunuel wrote: The following addition operation shows the sum of the twodigit positive integers XY and YX. If the threedigit integer XXZ, and X, Y , and Z are different digits, what is the value of the integer Z?
XY +YX _____ XXZ
(A) 8 (B) 7 (C) 2 (D) 1 (E) 0 Given the options , we want the units digit of XXZ consider 10 10 can be written as 19, 91 19+91= 110 Therefore E



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Re: The following addition operation shows the sum of the twodigit positi
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24 Sep 2018, 09:59
Bunuel wrote: The following addition operation shows the sum of the twodigit positive integers XY and YX. If the threedigit integer XXZ, and X, Y , and Z are different digits, what is the value of the integer Z?
XY +YX _____ XXZ
(A) 8 (B) 7 (C) 2 (D) 1 (E) 0
\(X,Y\,\,\, \in \,\,\,\,\left\{ {1,2, \ldots ,9} \right\}\) \(Z \in \,\,\,\,\left\{ {0,1,2, \ldots ,9} \right\}\) \(X,Y,Z\,\,\,{\text{distinct}}\) \(? = Z\) \(\left\langle {XXZ} \right\rangle = \left\langle {XY} \right\rangle + \left\langle {YX} \right\rangle < 99 + 99 < 200\,\,\,\,\,\,\, \Rightarrow \,\,\,\,X = 1\) \(\left\langle {1Y} \right\rangle + \left\langle {Y1} \right\rangle = \left\langle {11Z} \right\rangle \,\,\,\,\, \Rightarrow \,\,\,Y = 9\,\,\,\,\,\,\left( {18 + 81 < 100} \right)\) \(\left\langle {11Z} \right\rangle = 19 + 91 = 110\,\,\,\,\, \Rightarrow \,\,\,Z = 0\,\,\,\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
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The following addition operation shows the sum of the twodigit positi
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24 Sep 2018, 12:20
Bunuel wrote: The following addition operation shows the sum of the twodigit positive integers XY and YX. If the threedigit integer XXZ, and X, Y , and Z are different digits, what is the value of the integer Z?
XY +YX _____ XXZ
(A) 8 (B) 7 (C) 2 (D) 1 (E) 0 XXZ has to be a multiple of 11 with a 100s digit of 1 and a matching tens digit the only possibility is 110 0 E



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Re: The following addition operation shows the sum of the twodigit positi
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05 Oct 2018, 09:16
Considering the stem, the sum of twodigit integer must result in a threedigit integer with the first 2 digits of this integer being similar. The only case possible is for X to equal one (for example no two digit integer can sum above 198), hence we now have 1Y+Y1 = 11Z Which leave us with the only option possible for Y to yield a three digit number : 9 (for example 8 for Y would yield : 18+81= 99) Finally : 19+91=110
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Re: The following addition operation shows the sum of the twodigit positi
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06 Oct 2018, 08:51
fskilnik wrote: Bunuel wrote: The following addition operation shows the sum of the twodigit positive integers XY and YX. If the threedigit integer XXZ, and X, Y , and Z are different digits, what is the value of the integer Z?
XY +YX _____ XXZ
(A) 8 (B) 7 (C) 2 (D) 1 (E) 0
\(X,Y\,\,\, \in \,\,\,\,\left\{ {1,2, \ldots ,9} \right\}\) \(Z \in \,\,\,\,\left\{ {0,1,2, \ldots ,9} \right\}\) \(X,Y,Z\,\,\,{\text{distinct}}\) \(? = Z\) \(\left\langle {XXZ} \right\rangle = \left\langle {XY} \right\rangle + \left\langle {YX} \right\rangle < 99 + 99 < 200\,\,\,\,\,\,\, \Rightarrow \,\,\,\,X = 1\) \(\left\langle {1Y} \right\rangle + \left\langle {Y1} \right\rangle = \left\langle {11Z} \right\rangle \,\,\,\,\, \Rightarrow \,\,\,Y = 9\,\,\,\,\,\,\left( {18 + 81 < 100} \right)\) \(\left\langle {11Z} \right\rangle = 19 + 91 = 110\,\,\,\,\, \Rightarrow \,\,\,Z = 0\,\,\,\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. Can you explain how u got the below plzz? ⟨XXZ⟩=⟨XY⟩+⟨YX⟩<99+99<200⇒X=1⟨XXZ⟩=⟨XY⟩+⟨YX⟩<99+99<200⇒ X=1??? ⟨1Y⟩+⟨Y1⟩=⟨11Z⟩⇒ Y=9???(18+81<100)



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Re: The following addition operation shows the sum of the twodigit positi
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06 Oct 2018, 19:13
ias882000 wrote: fskilnik wrote: Bunuel wrote: The following addition operation shows the sum of the twodigit positive integers XY and YX. If the threedigit integer XXZ, and X, Y , and Z are different digits, what is the value of the integer Z?
XY +YX _____ XXZ
(A) 8 (B) 7 (C) 2 (D) 1 (E) 0
\(X,Y\,\,\, \in \,\,\,\,\left\{ {1,2, \ldots ,9} \right\}\) \(Z \in \,\,\,\,\left\{ {0,1,2, \ldots ,9} \right\}\) \(X,Y,Z\,\,\,{\text{distinct}}\) \(? = Z\) \(\left\langle {XXZ} \right\rangle = \left\langle {XY} \right\rangle + \left\langle {YX} \right\rangle < 99 + 99 < 200\,\,\,\,\,\,\, \Rightarrow \,\,\,\,X = 1\) \(\left\langle {1Y} \right\rangle + \left\langle {Y1} \right\rangle = \left\langle {11Z} \right\rangle \,\,\,\,\, \Rightarrow \,\,\,Y = 9\,\,\,\,\,\,\left( {18 + 81 < 100} \right)\) \(\left\langle {11Z} \right\rangle = 19 + 91 = 110\,\,\,\,\, \Rightarrow \,\,\,Z = 0\,\,\,\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. Can you explain how u got the below plzz? ⟨XXZ⟩=⟨XY⟩+⟨YX⟩<99+99<200⇒ X=1??? ⟨1Y⟩+⟨Y1⟩=⟨11Z⟩⇒ Y=9???(18+81<100) Hi, ias882000 ! Thank you for your interest in my solution. 1st doubt: <XXZ> is a positive 3digit number less than 200, therefore X must be 1. 2nd doubt: If Y is 8 or less, ⟨1Y⟩+⟨Y1⟩ would be 18+81 or less, hence it would not be a threedigit number. It must be, to be equal to ⟨11Z⟩. Regards, Fabio.
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Re: The following addition operation shows the sum of the twodigit positi
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19 Dec 2018, 13:21
Bunuel wrote: The following addition operation shows the sum of the twodigit positive integers XY and YX. If the threedigit integer XXZ, and X, Y , and Z are different digits, what is the value of the integer Z?
XY +YX _____ XXZ
(A) 8 (B) 7 (C) 2 (D) 1 (E) 0 Dear Moderator, This same problem has been duplicated in the link below, you may wish to merge the same, Thank you. https://gmatclub.com/forum/inthecorre ... ml#p384737
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Re: The following addition operation shows the sum of the twodigit positi
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