Thursday, December 31, 2015

Hard GMAT Problem Solving : Inequalities & Number Properties

An interesting number properties question that tests your understanding of odd numbers, even numbers and inequalities.

If x is a positive integer such that (x-1)(x-3)(x-5)....(x-93) < 0, how many values can x take?
A. 47
B. 23
C. 46
D. 21

E. 22

Explanation Video

Correct Answer: Choice B

Thursday, March 27, 2014

GMAT Number Theory LCM HCF

An interesting Problem Solving question from Number Theory

If the LCM of two numbers a and b is 1104 and their HCF is 4, which of the following MUST be true?

I. a * b = 4416 
II. a and b are both divisible by 8 
III. a : b = 48 : 23

A. I only
B. II only
C. I and III only
D. II and III only
E. I, II, and III

Inequalities and Number Properties DS

Inequalities and Number Properties Data Sufficiency Question

If m,n ≠0, is m^n > n^n? 
(1) |m| = n
(2) m < n

Simple Number Properties Question

If the integer N = 139,k50 where k is the hundreds digit, N can NEVER be divisible by which of the following?
A. 2
B. 3
C. 4
D. 6
E. 9

Monday, March 17, 2014

GMAT Mixtures - Problem Solving Question

60% of the students in a class are instate students. 60% of the students in the class are women. If there are twice as many instate men in the class as are instate women, and the number of instate men exceeds instate women by 12, how many more women in the class are not instate women?
A. 12
B. 60
C. 48
D. 24
E. 0

Data Sufficiency : Number Properties and Probability

A Data Sufficiency Question - Number properties and Probability

Set A contains distinct integers: A = {2,4,6,-8,x,y}. When two numbers from this set are picked and multiplied, what is the probability that the product is less than zero?

(1) x*y is not equal to zero.
(2) |x| = |y|

Correct Answer is choice B. Statement 2 alone is sufficient.

Explanatory Answer

Alternatively, here is the text based explanation for the question.

The product of two numbers picked will be less than zero if one of the numbers is positive and the other is negative.

Statement 1 clearly indicates that neither x nor y is 0.

However, that alone is not sufficient because the probability of the product being less than 0 is dependent on how many of the 6 numbers is negative.

So, statement 1 is NOT sufficient.

Statement 2 points to the fact that the magnitude of x an y are same. 
Both could be positive, both negative, one negative and the other positive or both zeroes. 

However, the possibility of both being simultaneously positive or negative or zero can be eliminated as the question stem states that these are distinct integers. So, one of x or y has to be positive and the other negative.

So, we know that there are 4 positive numbers and 2 negative numbers. 

Hence, we can determine the probability.

So, statement 2 is alone is sufficient.

Combining the two statements, we have no additional information other than what we have from statement 1.

Hence, choice B is the answer.

Additional Data Sufficiency Practice @

Saturday, March 15, 2014

Arithmetic Mean - Data Sufficiency

Here is an easy Descriptive Statistics Data Sufficiency Question

What is the median of a set of 10 positive integers?
1. The numbers are in an AP with the first term being 10
2. The arithmetic mean of these 10 numbers is 55

Answer - Choice C

Explanatory Answer

Break down the process of solving any DS question into 3 mandatory steps and 1 optional step.

Step 1 : Get an idea about the answer : Answering this question is providing with one single value for the median of 10 positive integers. This number will be a positive number - may or may not be an integer.

Step 2 : Evaluate Statement 1 alone. 

The numbers are in an AP with the first term being 10.

If there are 10 terms, then the median is the arithmetic mean of the 5th and the 6th term.

From statement 1 we know that the first term is 10. However, there is no information about the subsequent terms - information about the common difference is missing.

Hence, we will not be able to find the 5th and the 6th term. 

Data is Not Sufficient.

Step 3 : Evaluate Statement 2 alone.

The arithmetic mean of these 10 numbers is 55.

The arithmetic mean of the numbers may or may not be equal to the median. 

The arithmetic mean will be the median too if the distribution is symmetric about the mean.

Statement 2 alone is Not Sufficient.

Step 4 : Combine statement 1 and statement 2.

The necessity to combine the two statements arises only when the two statements independently do not provide you with an answer.

Step 4, therefore, is not mandatory for all questions. In fact, do not combine the two statements if you get an answer from these statements independently.

Combining the statements, we can deduce that the terms are in an AP and their mean is 55. 

If terms are in an AP, the mean and the median are the same.

Hence, we can deduce the median to be 55.

Statements 1 and 2 together are sufficient to answer the question.

Choice C is the answer.

More Descriptive Statistics questions @

Friday, February 28, 2014

Problem Solving - Equations

GMAT Problem Solving Question

In a test comprising 50 questions, a student attempts all questions. For every correct answer the student is awarded 1 mark. She will get negative marks for incorrect answers as per the following rule.

1. 0.25 negative mark for each of the first 10 incorrect answer.
2. 0.5 negative mark for each incorrect answer, from the 11th to the 20th.
3. 0.75 negative mark for each incorrect answer, from the 21st.

What is the minimum number of questions that the student should get right to get a non-negative score?

A. 22
B. 18
C. 23
D. 21
E. 17

Correct Answer : Choice B. Minimum of 18 questions correct. 

Explanatory Answer

The student has to get a non-negative mark. 

The quickest way to solve this question is to back substitute answers.

Let us start with the smallest number in the given set. 17 questions correct and 33 incorrect.

If she had got 17 questions correct, she will get 17 * 1 - (10 * 0.25 + 10 * 0.5 + 13 * 0.75)

i.e., she will get 17 - (2.5 + 5 + 9.75) = 17 - 17.25 = -0.25 marks.

So, if she got only 17 questions correct she will end up with a negative mark.

If she had got 18 questions correct, then she will get -0.25 + 1.75 = 1.5 mark, a non-negative mark.

Correct answer is choice B.

Monday, January 27, 2014

Number Properties Problem Solving : Factors

Here is an interesting GMAT number property problem solving question. Concept tested : number of factors.

Integer x has n factors; 3x has 3 factors; Which of the following values can n take?

I. 1
II. 2
III. 3

A. I only
B. II only
C. I or II
D. II or III
E. I or III

Saturday, December 14, 2013

GMAT Problem Solving : Descriptive Statistics

Here is a simple descriptive statistics question.

When a student Joe, weighing 41 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left to the weight of Joe?
1. 11 kg
2. 5.5 kg
3. 71 kg
4. 36.5 kg
5. 30 kg