CAT Quant Formulas Quiz

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Questions and Answers

Which representation correctly denotes a ratio?

a + b

a:b (correct)

a - b

a * b

What term is used for the first number in a ratio?

Antecedent (correct)

Fraction

Consequence

Denominator

What is a necessary condition for defining a ratio?

The quantities should be of the same nature. (correct)

The quantities must be whole numbers.

The quantities must be of different types.

The quantities must be in percentage.

In the equation for a ratio a:b, what does 'b' symbolize?

Consequent Signup and view all the answers

If the length of a rod is represented as 'a' cm and the area of a square is 'b' sq.km, how can their ratio be defined?

By expressing it as a:b. Signup and view all the answers

Why are fundamentals of ratio and proportion important?

They help answer questions in conjunction with other concepts. Signup and view all the answers

Which of the following is an incorrect comparison for defining a ratio?

Length of a rod to area of a square. Signup and view all the answers

Which formula would be appropriately used to express the ratio of two quantities?

a/b Signup and view all the answers

What can be concluded if a system of equations has n variables and n-1 equations?

The solution is indeterminate. Signup and view all the answers

Under what condition can a system of n variables with n-1 equations potentially have a definite solution?

If all variables are integers. Signup and view all the answers

What does it indicate if the determinant D = 0 and at least one of the determinants Dx, Dy, or Dz is also zero?

No solutions exist. Signup and view all the answers

Which of the following conditions must hold for a system of equations to have infinitely many solutions?

Determinant D = 0 and all of Dx, Dy, Dz are zero. Signup and view all the answers

What is the result when the determinant D of a system of equations is not equal to zero?

The equations have a unique solution. Signup and view all the answers

In the context of equations with three variables, what is the significance of matrices at play?

They provide a way to organize coefficients for analysis. Signup and view all the answers

How do you calculate the determinant D for a 3-variable equation system?

Using the formula involving cross-multiplication of coefficients. Signup and view all the answers

What happens to the solution set of a system of equations if the determinants for all variables are found to be zero?

There are infinitely many solutions. Signup and view all the answers

What is the formula to calculate the time 'y' after which a clock that gains time will show the same time again?

$y = \frac{720}{60 + x}$ Signup and view all the answers

If a clock shows the correct time at 'Q' and it gains time, how is the time 'T' shown by the clock represented after 'h' hours?

$T = Q + (h \times x)$ Signup and view all the answers

When two people are running on a circular track in opposite directions, how many distinct meeting points will they have?

$a + b$ Signup and view all the answers

What is the first meeting time for two runners on a circular track with speeds 'm' and 'n' running in opposite directions?

$\frac{I}{m + n}$ Signup and view all the answers

If two runners P and Q meet after time 't', what does 't' equal?

$t = x \times y$ Signup and view all the answers

If a clock loses time, how is the formula for 'y' represented?

$y = \frac{720}{60 - x}$ Signup and view all the answers

What is the formula for the time it takes for two runners to meet when running in the same direction?

$\frac{I}{|m - n|}$ Signup and view all the answers

When two individuals start from points A and B and meet after a time 't', which variable represents the time taken by P to reach B?

x Signup and view all the answers

What characteristic defines a surd?

An irrational number involving a root Signup and view all the answers

Which of the following expressions is equivalent to $X^m \cdot X^n$?

$X^{m+n}$ Signup and view all the answers

If $X$ and $Y$ are positive real numbers and $a$ is a rational number, which statement is true?

$X^a \cdot Y^a = (XY)^a$ Signup and view all the answers

What is the result of $X^{m-n}$ if $X > 0$ and $m, n$ are rational numbers?

$\frac{X^m}{X^n}$ Signup and view all the answers

What is required for two surds to be considered like surds?

They must have the same number under the radical sign Signup and view all the answers

Which of the following expressions demonstrates the property of a power with a negative exponent?

$X^{-m} = \frac{1}{X^m}$ Signup and view all the answers

In the context of logarithms, what does the equation $X^m = n$ imply about $X$?

$X = n^{1/m}$ Signup and view all the answers

What does the equation $\frac{1}{a} X^a = X$ imply?

$a = 1$ Signup and view all the answers

What is the result of adding the surds $6\sqrt{2}$ and $3\sqrt{2}$?

$9\sqrt{2}$ Signup and view all the answers

If $N = a$, how is $x$ defined?

$x = log_a(N)$ Signup and view all the answers

What is the value of $log_a(1)$ for any base $a$?

$0$ Signup and view all the answers

What is the conjugate of the expression $a + b$?

$a - b$ Signup and view all the answers

If $0 < a < 1$, how does $log_a(x)$ compare to $log_a(y)$ when $x > y$?

$log_a(x) < log_a(y)$ Signup and view all the answers

What is the relationship between the logarithms $log_a(b)$ and $log_b(a)$?

$log_a(b) \cdot log_b(a) = 1$ Signup and view all the answers

What is the result of $log_a(x)$ when $x = a$?

$1$ Signup and view all the answers

When adding two variables $x$ and $y$, what should be the correct form if $x = m + n$?

$x + y = m + n + 2mn$ Signup and view all the answers

If $a = 2$, what can be concluded about $log_a(a^c)$?

$c$ Signup and view all the answers

For the expression $\frac{log_b(y)}{log_a(b)}$, what is it equal to?

$log_a(y)$ Signup and view all the answers

Study Notes

Overview of CAT Quantitative Formulas

CAT exam covers various mathematical topics, essential for scoring high percentiles.
Important topics include Ratio and Proportion, Mixtures, Profit and Loss, Interest, Speed and Distance, and Geometry.

Key Topics and Their Importance

Ratio and Proportion
- Fundamental for understanding other concepts like mixtures and similar triangles.
- Ratios can be expressed as fractions (a/b) or in the form a:b.
Mixtures and Alligations
- Useful in problems combining different quantities or percentages.
Profit and Loss, Discount
- Vital for real-world application in financial calculations.
Interests (Simple and Compound)
- Key concepts for financial literacy and evaluating investments over time.
Time, Speed, Distance & Work
- Essential for solving questions involving motion and productivity.

Quadratic Equations

Essential topic for quick problem-solving; includes fundamental formulas and methods.
Techniques like option elimination and value substitution facilitate faster solutions.

Logarithms, Surds, and Indices

Relatively straightforward with limited question types but requires understanding various properties.
Logarithmic identities include:
- loga(xy) = loga(x) + loga(y)
- loga(x^m) = m * loga(x)

Geometry

Consists of numerous formulas that require significant preparation.
Understanding how and when to apply formulas is crucial; practice using different problem sets enhances proficiency.

Time Calculation with Erroneous Clocks

If a clock gains time:
- Actual time ( T = Q - (h \times x) )
If a clock loses time:
- Actual time ( T = Q + (h \times x) )

Circular Motion Problems

When two runners are on a circular track with speeds in the ratio a:b:
- They meet at ( a + b ) points if running in opposite directions.
- They meet at ( |a - b| ) points if running in the same direction.

System of Equations

A system with n variables and n-1 equations is indeterminate.
Conditions or additional equations can sometimes determine unique solutions.
The determinant condition determines solution type:
- Unique solution if ( \text{Determinant} D \neq 0 )
- No solution if ( D = 0 ) and at least one of ( Dx, Dy, Dz ) is zero.

Success Stories and Faculty Expertise

High success rates of students achieving top percentiles attest to the effectiveness of the preparation programs.
Experienced faculty members available for assistance.

Preparation Recommendations

Practice extensively to familiarize with concepts and formulas.
Use visual aids to comprehend geometric principles.
Regularly solve varied problems to apply learned formulas effectively.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your knowledge on essential quantitative formulas for the CAT exam. This quiz covers key topics such as Ratio and Proportion, Mixtures and Allegations, Profit and Loss, and more. Perfect for aspirants looking to refine their quantitative skills.