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May 1308:30 AM PDT
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In Episode 4 of our GMAT Ninja CR series, we tackle the most intimidating CR question type: Boldface & "Legalese" questions. If you've ever stared at an answer choice that reads, "The first is a consideration introduced to counter a position that...- May 12
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Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products.- May 14
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Most GMAT test-takers are intimidated by the hardest GMAT Verbal questions. In this session, Target Test Prep GMAT instructor Erika Tyler-John, a 100th percentile GMAT scorer, will show you how top scorers break down challenging Verbal questions.. - Jun 10
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03 Mar 2023, 22:13
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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. \(100\)
\(x_1+x_2+...+x_{99} = 2\);
\(x_1+x_2+...+x_{98} = 3\);
\(...\)
\(x_1= 100\).
What is the value of \(x_1*x_2*...*x_{100}\)?
A. \(-100\)
B. \(-1\)
C. \(0\)
D. \(1\)
E. \(100\)
11 Mar 2023, 02:52
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Official Solution:
\(x_1+x_2+...+x_{100} = 1\);
\(x_1+x_2+...+x_{99} = 2\);
\(x_1+x_2+...+x_{98} = 3\);
\(...\)
\(x_1= 100\).
What is the value of \(x_1*x_2*...*x_{100}\)?
A. \(-100\)
B. \(-1\)
C. \(0\)
D. \(1\)
E. \(100\)
By subtracting the second equation from the first, we obtain \((x_1+x_2+...+x_{100})-(x_1+x_2+...+x_{99}) = 1-2\), which simplifies to \(x_{100}= -1\).
Similarly, subtracting the third equation from the second yields \((x_1+x_2+...+x_{99}) -(x_1+x_2+...+x_{98}) = 2-3\), which simplifies to \(x_{99}= -1\).
By repeating this process for each successive pair of equations, we can determine that every term up to \(x_1\) is also equal to -1.
Therefore, \(x_1*x_2*...*x_{100}=100(-1)(-1)(-1)...(-1)=100(-1)^{99}=-100\).
Answer: A
\(x_1+x_2+...+x_{100} = 1\);
\(x_1+x_2+...+x_{99} = 2\);
\(x_1+x_2+...+x_{98} = 3\);
\(...\)
\(x_1= 100\).
What is the value of \(x_1*x_2*...*x_{100}\)?
A. \(-100\)
B. \(-1\)
C. \(0\)
D. \(1\)
E. \(100\)
By subtracting the second equation from the first, we obtain \((x_1+x_2+...+x_{100})-(x_1+x_2+...+x_{99}) = 1-2\), which simplifies to \(x_{100}= -1\).
Similarly, subtracting the third equation from the second yields \((x_1+x_2+...+x_{99}) -(x_1+x_2+...+x_{98}) = 2-3\), which simplifies to \(x_{99}= -1\).
By repeating this process for each successive pair of equations, we can determine that every term up to \(x_1\) is also equal to -1.
Therefore, \(x_1*x_2*...*x_{100}=100(-1)(-1)(-1)...(-1)=100(-1)^{99}=-100\).
Answer: A
05 May 2024, 19:47
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How are you solving for the values for X sub2 thru X sub97 without making the assumption of a repeating pattern?
For instance how do you know that the value of X sub97 is -1? Could X sub 2 thru 96 all be zero and then X sub97 be -96?
It seems like we are assuming something that can't be proven.
For instance how do you know that the value of X sub97 is -1? Could X sub 2 thru 96 all be zero and then X sub97 be -96?
It seems like we are assuming something that can't be proven.
