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X, Y, and Z are unique digits in the correctly-worked subtraction prob
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10 Feb 2022, 08:15
10 Feb 2022, 08:15
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Question Stats:
58% (02:18) correct
41% (01:54) wrong based on 24 sessions
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X, Y, and Z are unique digits in the correctly-worked subtraction problem below. Which decimal is closest to the decimal represented by \(0.XYZ\)?
\(8.740-\)
\(3.XYZ\)
------------------
\(4.XYZ\)
(A) 0.620
(B) 0.770
(C) 0.870
(D) 0.920
(E) 0.970
\(8.740-\)
\(3.XYZ\)
------------------
\(4.XYZ\)
(A) 0.620
(B) 0.770
(C) 0.870
(D) 0.920
(E) 0.970
Re: X, Y, and Z are unique digits in the correctly-worked subtraction prob
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10 Feb 2022, 14:10
10 Feb 2022, 14:10
1
We try plugging in the options here
Let's try C as it's the choice in the middle
If Z=0, our subtraction remains intact,
We plug in Y=7, then 14 - 7= 7, so we still are on the right track,
Now plug in X=8, we carry 1 and add it to X, so X=8+1=9
And, 17-9=8, voilà!
Our answer choice would be (C)
Visual representation here,
8.740
-3.870
______
4.870
Let's try C as it's the choice in the middle
If Z=0, our subtraction remains intact,
We plug in Y=7, then 14 - 7= 7, so we still are on the right track,
Now plug in X=8, we carry 1 and add it to X, so X=8+1=9
And, 17-9=8, voilà!
Our answer choice would be (C)
Visual representation here,
8.740
-3.870
______
4.870
Re: X, Y, and Z are unique digits in the correctly-worked subtraction prob
[#permalink]
29 Oct 2022, 08:53
29 Oct 2022, 08:53
1
We can think about this problem in an algebraic way as well:
8.740 − 3.XYZ = 4.XYZ
8.740 − 3 − 0.XYZ = 4 + 0.XYZ
8.740 − 3 − 4 = 0.XYZ + 0.XYZ
1.74 = 2 x 0.XYZ
0.XYZ = 1.74/2
0.XYZ = 0.87
8.740 − 3.XYZ = 4.XYZ
8.740 − 3 − 0.XYZ = 4 + 0.XYZ
8.740 − 3 − 4 = 0.XYZ + 0.XYZ
1.74 = 2 x 0.XYZ
0.XYZ = 1.74/2
0.XYZ = 0.87
