(1) x is to the right of -7 on the number line.
x can be to the right or left of 5
Insufficient

(2) x is between -4 and -3 on the number line.
x is certainly to the right of 5
B

Target question: Is x to the right of -5 on the number line?
This is a good candidate for rephrasing the target question.

Key concept: If a number is TO THE RIGHT of another number on the number line, then that number is GREATER THAN that number.
For example, since 10 is to the right of 3 on the number line, we know that 10 is greater than 3.

So we can, rephrase the target question as follows:
REPHRASED target question: Is x > -5?

Aside: the video below has tips on rephrasing the target question


Statement 1: x is to the right of -7 on the number line
In other words, x > -7
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 0 (this satisfies statement 1, since 0 > -5. In this case, the answer to the REPHRASED target question is YES, it is the case that x > -5
Case b: x = -6 (this satisfies statement 1, since -6 > -5. In this case, the answer to the REPHRASED target question is NO, it is not the case that x > -5
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is between -4 and -3 on the number line
In other words, -4 < x < -3
Since we also know that -5 < -4, we can add this information to our given inequality to get: -5 < -4 < x < -3
From this we can conclude with certainty that -5 < x
The answer to the REPHRASED target question is YES, it is the case that x > -5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

RELATED VIDEO:

_________________

Target question: Is x to the right of -5 on the number line?
This is a good candidate for rephrasing the target question.

Key concept: If a number is TO THE RIGHT of another number on the number line, then that number is GREATER THAN that number.
For example, since 10 is to the right of 3 on the number line, we know that 10 is greater than 3.

So we can, rephrase the target question as follows:
REPHRASED target question: Is x > -5?
Aside: the video below has tips on rephrasing the target question

Statement 1: x is to the right of -7 on the number line
In other words, x > -7
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 0 (this satisfies statement 1, since 0 > -7. In this case, the answer to the REPHRASED target question is YES, it is the case that x > -5
Case b: x = -6 (this satisfies statement 1, since -6 > -7. In this case, the answer to the REPHRASED target question is NO, it is not the case that x > -5
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is between -4 and -3 on the number line
In other words, -4 < x < -3
Since we also know that -5 < -4, we can add this information to our given inequality to get: -5 < -4 < x < -3
From this we can conclude with certainty that -5 < x
The answer to the REPHRASED target question is YES, it is the case that x > -5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

RELATED VIDEO:

_________________