DS Qn Please help
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Source: Beat The GMAT — Data Sufficiency |
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Ian Stewart
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Ian Stewart
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Okay, hope this works:
First, note that x+1 must be positive. Otherwise 1/(x+1) would be negative, and couldn't lie within the given range.
So,
1/2 > 1/(x+1)
x+1 > 2
x > 1
Note that we can multiply both sides of the inequality by x+1 without needing to worry about whether we need to reverse the inequality, because we know x+1 is positive. We also have:
1/5 < 1/x+1
x+ 1 < 5
x < 4
So 1 < x < 4, and x could be 2 or 3. You don't actually need to do all this work. If you look again at the original inequality: 1/5 < 1/(x+1) < 1/2, then x+1 must be between 2 and 5, which gives two possible integer values, 2 or 3.
From Statement 2, (x-3)(x-4)=0, we know that (x-3) times (x-4) is 0. If you ever multiply two things and get zero, you must have multiplied by zero. Thus x-3 = 0, or x-4 = 0, and x = 3 or 4. Note that this is the basis of the mathematical technique called 'factoring', when solving quadratic equations, and it's the reason we always set one side to be equal to zero before factoring a quadratic. It's a very important idea to understand for the GMAT. So, we again get two possible solutions.
Together, the only possible value that is consistent with both statements is x=3. So the answer should be C.
First, note that x+1 must be positive. Otherwise 1/(x+1) would be negative, and couldn't lie within the given range.
So,
1/2 > 1/(x+1)
x+1 > 2
x > 1
Note that we can multiply both sides of the inequality by x+1 without needing to worry about whether we need to reverse the inequality, because we know x+1 is positive. We also have:
1/5 < 1/x+1
x+ 1 < 5
x < 4
So 1 < x < 4, and x could be 2 or 3. You don't actually need to do all this work. If you look again at the original inequality: 1/5 < 1/(x+1) < 1/2, then x+1 must be between 2 and 5, which gives two possible integer values, 2 or 3.
From Statement 2, (x-3)(x-4)=0, we know that (x-3) times (x-4) is 0. If you ever multiply two things and get zero, you must have multiplied by zero. Thus x-3 = 0, or x-4 = 0, and x = 3 or 4. Note that this is the basis of the mathematical technique called 'factoring', when solving quadratic equations, and it's the reason we always set one side to be equal to zero before factoring a quadratic. It's a very important idea to understand for the GMAT. So, we again get two possible solutions.
Together, the only possible value that is consistent with both statements is x=3. So the answer should be C.
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gabriel
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Just check in the "Disable HTML in this post" option when you post and you should be able to post without any problem.Ian Stewart wrote:Edit: The forum keeps corrupting my message, so I'm going to start again!
GMAT/MBA Expert
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Ian Stewart
- GMAT Instructor
- Posts: 2623
- Joined: Mon Jun 02, 2008 3:17 am
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- GMAT Score:780
Thanks Gabriel- that was definitely the issue.gabriel wrote:Just check in the "Disable HTML in this post" option when you post and you should be able to post without any problem.Ian Stewart wrote:Edit: The forum keeps corrupting my message, so I'm going to start again!
