Finding the Number Equidistant from 75 and 117
The problem asks for a number that is the same distance away from 75 as it is from 117. This means the number is exactly in the middle of 75 and 117.
Method 1: Using Algebra
- Let the unknown number be $x$.
- According to the problem, the number is as much greater than 75 as it is smaller than 117. We can write this as an equation: $x - 75 = 117 - x$
- To solve for $x$, first add $x$ to both sides: $x + x - 75 = 117 - x + x$ $2x - 75 = 117$
- Next, add 75 to both sides: $2x - 75 + 75 = 117 + 75$ $2x = 192$
- Finally, divide by 2: $x = \frac{192}{2}$ $x = 96$
Method 2: Calculating the Average
The number that is exactly in the middle of two other numbers is their average (mean).
- Add the two given numbers: $75 + 117 = 192$.
- Divide the sum by 2 to find the average: $\frac{192}{2} = 96$.
Both methods show that the number is 96.
Check: Is 96 greater than 75 by the same amount it is smaller than 117? Difference 1: $96 - 75 = 21$ Difference 2: $117 - 96 = 21$ The differences are equal, confirming the answer.
The number is 96.
Important Questions from Numerical Computation
In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is 1/4th of the number of students who like other branches. The number of students who like both their core and other branches is 500.
The number of students who like their core branches is$A$ is an ($n \times n$) matrix. Consider the following two statements
Statement 1: Columns of matrix $A$ are linearly independent
Statement 2: Inverse of matrix $A$ exists
Which one of the following statements is TRUE?
- Consider the function $G(x, y, z) = 0$. This function allows us to implicitly define each of three variables as a function of the other two variables. Assume that all partial derivatives of the function $G(x, y, z)$ exist everywhere. Then, the value of $\left(\frac{\partial z}{\partial x} \times \frac{\partial x}{\partial y} \times \frac{\partial y}{\partial z}\right)$ is _________ (in integer)
- Levenshtein distance is used to measure the minimum edit distance between two strings by counting the minimum number of editing operations (such as, insertions, deletions, substitutions) required to transform one string to another. Consider an alternative version of the Levenshtein distance in which each insertion and each deletion has a cost of 1 and substitutions are not allowed.
Based on this alternative version, the Levenshtein distance between the strings, word and work is ______ (Answer in integer). - In a given collection of documents, let $N$ be the total number of documents and let $d$ be the number of documents in which the term $t$ occurs.
Which ONE of the following fractions is used to define the inverse document frequency (idf) of the term $t$?
