# GMAT Number Properties Live Sessions

#### GMAT LCM HCF Lesson Videos | Aug 4, 2017 | youtube.com/wizako

Welcome to the live session of GMAT Number Properties and GMAT Number Theory. The questions discussed on August 4, 2017 during the live session follow the embedded video. The video link next to each question will take you to the start of the part of the video where that specific question is discussed. Click the video embedded below to watch the entire session.

### GMAT Questions Discussed in the Youtube Live Session

#### Problem Solving Questions

1. 136 blue marbles, 192 red marbles, 72 green marbles, 216 black marbles, and 144 yellow marbles must be packed into packets containing equal number of marbles with the packets containing only marbles of the same colour. What is the minimum number of packets required?

Hint to solve this GMAT Question

The keyword in this question is that we are packing the given marbles into packets containing equal number of marbles. And each packet contains only marbles of the same color. Use this information to solve the question.

2. If x and y are two distinct positive integers and their sum is 360, what is the largest possible value of the HCF of the two numbers?

Hint to solve this GMAT Number Properties Question

Let the two integers be x and y. So, x + y = 360. Let 'h' be the HCF of the two numbers. Express x and y in terms of 'h' and compute the largest possible value of h.

3. What is the smallest number that leaves a remainder of 2 when divided by 3, 3 when divided by 4, 4 when divided by 5, 5 when divided by 6, and 6 when divided by 7?

Hint to solve this GMAT Question

A remainder of 2 when divided by 3 is the same as the number being 1 short of a multiple of 3. A remainder of 3 when divided by 4 is the same as the number being 1 short of a multiple of 4. The same holds good for the next 3 pieces of information. Use this framework to solve the question.

4. If the product of 2 positive integers is 144, which of the following could be the LCM and HCF of the two numbers? Mark all answers that are correct.

1. {72, 2}
2. {48, 6}
3. {18, 8}
4. {24, 6}
5. {16, 9}
Key Points to remember while solving this GMAT Number Theory Question

Point 1: The product of the two numbers is equal to the product of the LCM and HCF of the two numbers.
Point 2: The HCF of the two numbers should be a factor of the LCM of the two numbers.

#### Data Sufficiency

1. If ‘x’ is a positive integer, what is the value of x?

1. The LCM of x and 72 is 144
2. The HCF of x and 72 is 8
Approach to solve this GMAT Question

Statement 1: Will help get an understanding of how high the value of 'x' can be and the highest power of 2 and 3 that x can contain.
Statement 2: Will help understand whether 'x' is a multiple of 3.
Combine the two statements and determine whether we have adequate information to determine a unique value for x.

2. If a and b are positive integers, what is the HCF of (a, b)?

1. The product ab is ‘a’ more than the square of ‘a’
2. Twice the value of ‘a’ is one less than the sum of ‘a’ and ‘b’
Approach to solve this GMAT DS Question

Statement 1: Frame an equation based on the information given in this statement to express b in terms of a.
Statement 2: Frame an equation based on the information given in this statement to express b in terms of a.
Concept: The HCF of two consecutive positive integers is 1.

3. If ‘a’ is a positive integer, what is the HCF of (a, 32)?

1. 'a' has exactly 3 factors
2. 2a has twice as many factors as ‘a’ has
Approach to solve this GMAT Number Theory DS Question

Statement 1: The question for which you need to have an answer to evaluate this statement: What kind of a number has exactly 3 factors?
Statement 2: The question to ask to evaluate this statement: If 2a has twice as many factors as 'a' has, is 2 a factor of a?

4. If ‘a’ and ‘b’ are positive integers, what is the HCF (a, b)?

1. HCF(3a, b) is 15
2. HCF(a, 2b) is 30
Hint to solve this GMAT HCF Data Sufficiency Question

Statement 1: 15 is a factor of 3a. So, what can be definitely deduced about 'a'? Also note that 15 is a factor of b.
Statement 2: 30 is a factor of a. 30 is a factor of 2b. So, what can be definitely deduced about b.
Will either of the statements alone or together help determine the HFC (a, b)?

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