Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included!
03 Mar 2023, 22:13
Kudos
Bookmarks
\(x_1+x_2+...+x_{100} = 1\);
\(x_1+x_2+...+x_{99} = 2\);
\(x_1+x_2+...+x_{98} = 3\);
\(...\)
\(x_1= 100\).
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
Kudos
Bookmarks
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
Kudos
Bookmarks
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.
