Muhammad Imdad Ullah

Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, Python, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

GRE Mathematics 2

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The GRE mathematical reasoning section tests your knowledge of arithmetic, basic algebra, applied mathematics, elementary geometry, and common graphs and charts. Let Starts with the GRE Mathematics quiz.

1. In a cafeteria, the people are either faculty members or students. The number of faculty members is 15% of the total number of people in the cafeteria. After some of the students leave, the total number of persons remaining in the cafeteria is 50% of the original total. The number of students who left is what fractional part of the original number of students?

 
 
 
 
 

2. ABC works two part-time jobs. One week ABC worked 8 hours at one job, earning $\$150$, and $4.5$ hours at the other job, earning $\$90$. What were his average hourly earnings for the week?

 
 
 
 
 

3. If the value of a piece of the property decreases by 10% while the tax rate on the property increases by 10%, what is the effect on the taxes?

 
 
 
 
 

4. For how many 3-digit whole numbers is the sum of the digits equal to 3?

 
 
 
 
 

5. In a certain population, 40% of all people have biological characteristics $X$; the others do not. if 8000 people have characteristic $X$, how many people do not have $X$?

 
 
 
 
 

6. If $7-x=0$, then $10-x=$?

 
 
 
 
 

7. If the radius of a circle is increased by 1 unit, the ratio of the new circumference to the new diameter is:

 
 
 
 

8. If $x=k+\frac{1}{2}=\frac{k+1}{2}$, then $x=$?

 
 
 
 
 

9. If $6k^2+k= 2$ and $k>0$, then $k$ must equal which of the following?

 
 
 
 

10. $2000 amount is deposited into a savings account that earns interest at the rate of 10% per year, compounded semi-annually. How much money will there be in the account at the end of one year?

 
 
 
 
 

11. If $x=\frac{y}{7}$ and $7x=12$, then $y=?$

 
 
 
 
 

12. If $x+y=8$ and $2x-y=10$ then $x=$?

 
 
 
 
 

13. A car dealer who gives a customer a 20% discount on the list price of a car still realizes a net profit of 25% of the cost. If the dealer’s cost is $4800 what is the usual list price of the car?

 
 
 
 
 

14. A certain photo state machine produces 13 copies every 10 seconds. If the machine operates without interruption, how many copies will it produce in an hour?

 
 
 
 
 

15. If $3x-5=x+11$, then $x=$?

 
 
 
 
 

GRE Mathematics Test with Answers

MCQs GRE Mathematics with Answers

  • ABC works two part-time jobs. One week ABC worked 8 hours at one job, earning $\$150$, and $4.5$ hours at the other job, earning $\$90$. What were his average hourly earnings for the week?
  • In a cafeteria, the people are either faculty members or students. The number of faculty members is 15% of the total number of people in the cafeteria. After some of the students leave, the total number of persons remaining in the cafeteria is 50% of the original total. The number of students who left is what fractional part of the original number of students?
  • In a certain population, 40% of all people have biological characteristics $X$; the others do not. if 8000 people have characteristic $X$, how many people do not have $X$?
  • If $3x-5=x+11$, then $x=$?
  • If $x+y=8$ and $2x-y=10$ then $x=$?
  • $2000 amount is deposited into a savings account that earns interest at the rate of 10% per year, compounded semi-annually. How much money will there be in the account at the end of one year?
  • A car dealer who gives a customer a 20% discount on the list price of a car still realizes a net profit of 25% of the cost. If the dealer’s cost is $4800 what is the usual list price of the car?
  • If the value of a piece of property decreases by 10% while the tax rate on the property increases by 10%, what is the effect on the taxes?
  • A certain photo state machine produces 13 copies every 10 seconds. If the machine operates without interruption, how many copies will it produce in an hour?
  • If $x=\frac{y}{7}$ and $7x=12$, then $y=?$
  • If $x=k+\frac{1}{2}=\frac{k+1}{2}$, then $x=$?
  • If $7-x=0$, then $10-x=$?
  • For how many 3-digit whole numbers is the sum of the digits equal to 3?
  • If $6k^2+k= 2$ and $k>0$, then $k$ must equal which of the following?
  • If the radius of a circle is increased by 1 unit, the ratio of the new circumference to the new diameter is:

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Number System Test 3

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The Post is about the Number System Test from Mathematics of Intermediate Part-I (First Year). Let us start with the Online Number System Quiz with Answers. MCQs are about the number system Test for the preparation of mathematics.

Please go to Number System Test 3 to view the test

A numeral system is a way of expressing numbers; that is, it is a mathematical writing system or notation used to represent the numbers of a given set consistently by using either digits or other symbols. The same sequence of symbols may represent different numbers in different numeral systems.

Number System

Decimal Number System

The commonly used number system is the decimal positional numeral system. The decimal refers to 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to construct all numbers.

In mathematics courses you have heard about number systems of whole numbers and real numbers, however, in the context of computer systems, the other types of number systems are (i) The decimal number system, (ii) The binary number system, (iii) The octal number system and, (iv) The hexadecimal number system.

MCQs Number system Test

  • If $a+ib$ is a complex number then its conjugate is
  • If $a+ib$ is a complex number then its conjugate is
  • If $z$ is any real number then its conjugate is
  • If $k$ is any real number and $a+ib$ is a complex number then
  • The additive identity in a set of complex numbers is
  • The multiplicative identity of a complex number is
  • The additive inverse of $(a, -b)$ is
  • The multiplicative inverse of $(a, -b)$ is
  • (0, 1) is equal to
  • $(0, 1)^2$ is equal to
  • $(0, 1)^3$ is equal to
  • $(0, 1)^4$ is equal to
  • $(-i)^{19}$ is equal to
  • $(-1)^{-\frac{21}{2}}$ is equal to
  • (0, 3) (0, 5) is equal to
  • The sum of two conjugate complex numbers is
  • The product of two conjugate complex numbers is
  • The multiplicative inverse of $(-4, 7)$ is
  • The factors of $3(x^2+y^2)$ are
  • The real part of $\frac{2+i}{i}$ is equal to

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MCQs Econometrics Statistics 4

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This quiz is about MCQs Econometrics Statistics, which covers the topics of Regression analysis, correlation, dummy variables, multicollinearity, heteroscedasticity, autocorrelation, and many other topics. Let’s start with the MCQs Econometric Statistics Quiz.

Please go to MCQs Econometrics Statistics 4 to view the test

An application of different statistical methods applied to the economic data used to find empirical relationships between economic data is called Econometrics.

Econometrics means “Economic Measurement”. Econometrics is the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of statistical inference.

Econometrics can also be defined as the empirical determination of economic laws. Econometrics can be classified as (i) Theoretical Econometrics and (ii) Applied Econometrics.

(i) Theoretical Econometrics

Theoretical econometrics is concerned with developing appropriate methods for measuring economic relationships specified by econometric models. Theoretical econometrics leans heavily on mathematical statistics and must spell out the assumptions of methods (such as Least Squares), their properties, and what happens to these properties when one or more of the assumptions of the technique are not fulfilled.

(ii) Applied Econometrics

In applied econometrics, the tools of theoretical econometrics are used to study special fields(s) such as production function, investment function, demand and supply function, portfolio theory, etc.

MCQs Econometrics Statistics

  • Which one of the following is not a plausible remedy for near multicollinearity?
  • Which of the following could be used as a test for autocorrelation up to third order?
  • If we omit a relevant variable from the model ———-
  • Autocorrelation may be the result of ———-
  • One can test the pure randomness of residual from ———-
  • The term Heteroscedasticity means ———-
  • Collinearity or multicollinearity occurs whenever ———-
  • If there is no overlapping between regressors then ———-
  • What does a VIF of 1 mean?
  • Autocorrelation is most likely occurred in ———- data?
  • If measurement errors are present only independent variable, then the estimate remains:
  • The presence of heteroscedasticity does not destroy the ———- of OLS estimators.
  • The Durbin-Watson d test has no ———- for the rejection of the null hypothesis.
  • If the value of R-square between $X_2$ and $X_3$ approaches 1 then ———-.
  • Which of the following is an indication of the existence of multicollinearity?
  • The generalized least square estimators are also called:
  • Robust standard errors are the ones that are corrected by ———-.
  • In the case of multicollinearity, the confidence interval tends to be much ———-, leading to the acceptance of a zero null hypothesis.
  • Which of the following is an indication of the existence of multicollinearity?
  • One can test the pure randomness of residuals from

Types of Econometrics Data

Different type of data is used in Econometrics. There are three important types of data for empirical analysis:

  • Time Series Data
    A time series data is a set of observations on the values that a variable takes at different times. The time series data may be collected at regular time intervals such as daily, weekly, monthly, quarterly, or annually, etc.
  • Cross-Sectional Data
    Cross-sectional data are data on one or more variables collected at the same point in time. Cross-sectional data has a problem of heterogeneity.
  • Pooled Data
    Pooled data is a combination of both time series and cross-sectional data.
MCQs Econometrics Statistics

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Basic Econometrics MCQs 3

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This quiz is about Basic Econometrics MCQs with Answers, which cover the topics of Regression analysis, correlation, dummy variable, multicollinearity, heteroscedasticity, autocorrelation, and many other topics. Let’s start with the Basic Econometrics MCQs with Answers Quiz.

Please go to Basic Econometrics MCQs 3 to view the test

An application of different statistical methods applied to the economic data used to find empirical relationships between economic data is called Econometrics.

Econometrics means “Economic Measurement”. Econometrics is the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of statistical inference.

Econometrics can also be defined as the empirical determination of economic laws. Econometrics can be classified as (i) Theoretical Econometrics and (ii) Applied Econometrics.

(i) Theoretical Econometrics

Theoretical econometrics is concerned with developing appropriate methods for measuring economic relationships specified by econometric models. Theoretical econometrics leans heavily on mathematical statistics and must spell out the assumptions of methods (such as Least Squares), their properties, and what happens to these properties when one or more of the assumptions of the technique are not fulfilled.

(ii) Applied Econometrics

In applied econometrics, the tools of theoretical econometrics are used to study special fields(s) such as production function, investment function, demand and supply function, portfolio theory, etc.

Basic Econometrics MCQs

  • The rule of thumb is if k is between 100 and 1000 then there is _______ multicollinearity?
  • A system which has an infinite number of solutions has ______.
  • The existence of a perfect or near-to-exact linear relationship among some or all explanatory variables of a regression model is called
  • If $\rho$ is zero, then there is
  • Zero tolerance or VIF equal to one indicate
  • The log transformation is __________ if some of the $Y$ and $X$ values are zero or negative.
  • In the case of perfect multicollinearity, the OLS estimates are
  • In case of perfect or near-to-perfect multicollinearity, the OLS estimates are
  • The Glejser test is similar to _________.
  • If the calculated value of tolerance is 1, then there is an issue of
  • If $d*<d_l$ then we
  • An assumption about underlying the d statistics “The explanatory variable $X$’s are non-stochastic or fixed in __________”
  • Which combination of regressors might lead to perfect collinearity?
  • In the case of perfect multicollinearity, the $X’X$ is a ___________.
  • Durbin and Watson have suggested a test to detect the presence of autocorrelation which applies to
  • Which one assumption is not related to an error in the independent variable
  • The existence of a perfect or near-to-exact linear relationship among some or all explanatory variables of a regression model is called
  • What is the meaning of the term heteroscedasticity?
  • The generalized least square (GLS) is an efficient procedure that weights each squared residual by:
  • In a regression model with 3 explanatory variables, there will be __________ auxiliary regressions.

Types of Econometrics Data

Different type of data is used in Econometrics. There are three important types of data for empirical analysis:

  • Time Series Data
    A time series data is a set of observations on the values that a variable takes at different times. The time series data may be collected at regular time intervals such as daily, weekly, monthly, quarterly, annually, etc.
  • Cross-Sectional Data
    Cross-sectional data are data on one or more variables collected at the same point in time. Cross-sectional data has a problem of heterogeneity.
  • Pooled Data
    Pooled data is a combination of both time series and cross-sectional data.
Basic Econometrics MCQs

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