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In the correctly-worked addition of the two-digit numbers below, each
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09 Feb 2022, 05:15
09 Feb 2022, 05:15
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Question Stats:
42% (02:10) correct
57% (02:17) wrong based on 21 sessions
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In the correctly-worked addition of the two-digit numbers below, each letter represents a different positive integer less than 10. Which of the following could represent the number \(1SK\)?
\(XY+\)
\(YY\)
-------
\(1SK\)
I. 178
II. 134
III. 120
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
\(XY+\)
\(YY\)
-------
\(1SK\)
I. 178
II. 134
III. 120
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
Show: ::
digit search
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Re: In the correctly-worked addition of the two-digit numbers below, each
[#permalink]
05 Mar 2022, 00:50
05 Mar 2022, 00:50
Carcass wrote:
In the correctly-worked addition of the two-digit numbers below, each letter represents a different positive integer less than 10. Which of the following could represent the number \(1SK\)?
\(XY+\)
\(YY\)
-------
\(1SK\)vf
I. 178
II. 134
III. 120
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
\(XY+\)
\(YY\)
-------
\(1SK\)vf
I. 178
II. 134
III. 120
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
Show: ::
digit search
XY can be written as 10X + Y
YY can be wtitten as 10Y + Y
Sum (1SK) = 10X + 12Y
Let's check the option choices;
I. 178 = 10X + 12Y
X = 9, Y = \(\frac{88}{12}\) - NO
X = 8, Y = \(\frac{98}{12}\) - NO
X = 7, Y = 9 - YES
II. 134 = 10X + 12Y
X = 9, Y = \(\frac{44}{12}\) - NO
X = 8, Y = \(\frac{54}{12}\) - NO
X = 7, Y = \(\frac{64}{12}\) - NO
X = 6, Y = \(\frac{74}{12}\) - NO
X = 5, Y = 7 - YES
III. 120 = 10X + 12Y
X = 9, Y = \(\frac{30}{12}\) - NO
X = 8, Y = \(\frac{40}{12}\) - NO
X = 7, Y = \(\frac{50}{12}\) - NO
X = 6, Y = 5 - YES
Hence, option E
General Discussion
Re: In the correctly-worked addition of the two-digit numbers below, each
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14 Sep 2023, 16:12
14 Sep 2023, 16:12
KarunMendiratta wrote:
Carcass wrote:
In the correctly-worked addition of the two-digit numbers below, each letter represents a different positive integer less than 10. Which of the following could represent the number \(1SK\)?
\(XY+\)
\(YY\)
-------
\(1SK\)vf
I. 178
II. 134
III. 120
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
\(XY+\)
\(YY\)
-------
\(1SK\)vf
I. 178
II. 134
III. 120
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
Show: ::
digit search
XY can be written as 10X + Y
YY can be wtitten as 10Y + Y
Sum (1SK) = 10X + 12Y
Let's check the option choices;
I. 178 = 10X + 12Y
X = 9, Y = \(\frac{88}{12}\) - NO
X = 8, Y = \(\frac{98}{12}\) - NO
X = 7, Y = 9 - YES
II. 134 = 10X + 12Y
X = 9, Y = \(\frac{44}{12}\) - NO
X = 8, Y = \(\frac{54}{12}\) - NO
X = 7, Y = \(\frac{64}{12}\) - NO
X = 6, Y = \(\frac{74}{12}\) - NO
X = 5, Y = 7 - YES
III. 120 = 10X + 12Y
X = 9, Y = \(\frac{30}{12}\) - NO
X = 8, Y = \(\frac{40}{12}\) - NO
X = 7, Y = \(\frac{50}{12}\) - NO
X = 6, Y = 5 - YES
Hence, option E
The question says that "each letter represents a different positive integer." The problem with I. (178) is that if X=7 and Y=9 then that means S=7, which wouldn't work, right? Can someone explain what I am missing? Thanks!
