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01 Sep 2022, 02:26
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
70% (01:35) correct
30%
(01:42)
wrong
based on 221
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\(x_1+x_2+...+x_{100} = 1\);
\(x_1+x_2+...+x_{99} = 2\);
\(x_1+x_2+...+x_{98} = 3\);
...
\(x_1= 100\).
What is the value of \(x_1*x_2*...*x_{100} \)?
A. -100
B. -1
C. 0
D. 1
E. 100
Fresh GMAT Club Tests' Question
\(x_1+x_2+...+x_{99} = 2\);
\(x_1+x_2+...+x_{98} = 3\);
...
\(x_1= 100\).
What is the value of \(x_1*x_2*...*x_{100} \)?
A. -100
B. -1
C. 0
D. 1
E. 100
Fresh GMAT Club Tests' Question
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01 Sep 2022, 02:47
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Bunuel
\(x_1+x_2+...+x_{100} = 1\);
\(x_1+x_2+...+x_{99} = 2\);
So \(2+x_{100}=1……x_{100}=-1\)
\(x_1+x_2+...+x_{99} = 2\);
\(x_1+x_2+...+x_{98} = 3\);
So, \(3+x_{98}=2………x_{98}=-1\)
...
and so on till \(x_2=1\)
Also, \(x_1= 100\).
Thus, \(x_1*x_2*...*x_{100}=100*-1*-1….*-1=100*(-1)^{99}=100*(-1)=-100 \)
A
01 Sep 2022, 02:54
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x1+x2+...+x100=1x1+x2+...+x100=1; -------A
x1+x2+...+x99=2x1+x2+...+x99=2;--------B
x1+x2+...+x98=3x1+x2+...+x98=3;---------C
NOW A-B
GIVES YOU X100=-1
B-C GIVES YOU X99=-1
SO ON.....
ALSO GIVEN X1=100
THEREFORE
100 *(-1)(-1)......(-1)
SINCE -1 ARE ODD NO OF TERMS
THEREFORE -100
CORRECT OPTION A
x1+x2+...+x99=2x1+x2+...+x99=2;--------B
x1+x2+...+x98=3x1+x2+...+x98=3;---------C
NOW A-B
GIVES YOU X100=-1
B-C GIVES YOU X99=-1
SO ON.....
ALSO GIVEN X1=100
THEREFORE
100 *(-1)(-1)......(-1)
SINCE -1 ARE ODD NO OF TERMS
THEREFORE -100
CORRECT OPTION A
