Logical Reasoning and Inequalities

The video tutorial covers a series of GMAT problems, focusing on inequalities, integer properties, and algebraic equations. Each problem is analyzed using given statements to determine the sufficiency of information provided. The tutorial emphasizes logical reasoning and mathematical problem-solving skills.

In problem 16, which statement is sufficient to determine if x is greater than 1.8?

• Statement 1: x is greater than 1.7

• Statement 2: x is greater than 1.9

• Both statements together

• Neither statement

For problem 17, if n plus 1 is odd, what can be inferred about n?

• n is odd

• n is even

• n is a prime number

• n is greater than 10

In problem 17, which statement is sufficient to determine if n plus 1 is odd?

• Neither statement

• Statement 1: n plus 2 is even

• Statement 2: n minus 1 is odd

• Both statements together

In problem 18, what is the combined range of x when both statements are considered?

• 0 < x < 3

• 1 < x < 2

• x > 1

• x < 2

For problem 18, are the statements sufficient to determine if x is between 1 and 2?

• Only statement 1 is sufficient

• No, neither statement is sufficient

• Yes, both statements together are sufficient

• Only statement 2 is sufficient

In problem 19, what is the rate at which water is increasing in the tank?

• 4 gallons per minute

• 6 gallons per minute

• 10 gallons per minute

• 0 gallons per minute

For problem 19, which statement is sufficient to determine the rate of water increase?

• Both statements together

• Neither statement

• Statement 2: Water is pumped in at 10 gallons per minute and out at 4 gallons per minute

• Statement 1: Initial water is 200 gallons

In problem 20, what can be concluded if 9x is greater than 10x?

• x is positive

• x is zero

• x is greater than 10

• x is negative

For problem 21, what does the equation 6m = 9n imply?

• 2m = 3n

• m is less than n

• m is greater than n

• m = n

In problem 21, which statement is sufficient to determine if 2m - 3n equals zero?

• Neither statement

• Both statements together

• Statement 2: 6m equals 9n

• Statement 1: m does not equal 0