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Re: Is x to the right of -5 on the number line?
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20 Apr 2020, 07:50
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rraman wrote:
Is x to the right of -5 on the number line?
(1) x is to the right of -7 on the number line. (2) x is between -4 and -3 on the number line.
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
Re: Is x to the right of -5 on the number line?
[#permalink]
20 Apr 2020, 07:51
Expert Reply
Top Contributor
rraman wrote:
Is x to the right of -5 on the number line?
(1) x is to the right of -7 on the number line. (2) x is between -4 and -3 on the number line.
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
Re: Is x to the right of -5 on the number line?
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06 Jun 2021, 10:59
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