Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Solution: 10sec. Traditional 3-steps method is too time-consume technique. First of all we find length (9-1)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.

Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner

For any |x-a|<b a is a center and b is a half of length. So, |x-5|<8/2 represents our inequality (answer D)

Problems in our app are the most difficult problems from GMAT Club's Tests. Maybe it would be useful for you to take a look at math-absolute-value-modulus-86462.html _________________

Problem: 1<x<9. What inequality represents this condition?

A. |x|<3 B. |x+5|<4 C. |x-1|<9 D. |-5+x|<4 E. |3+x|<5 Solution: 10sec. Traditional 3-steps method is too time-consume technique. First of all we find length (9-1)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.

Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner

Posted from my mobile device

You can also think of this the way manhattan suggest. Think of D on a number line. For l x-5 l the a center point of the line is at positive 5. The difference from this point must be less than 4. so the x would have to be between 1 and 9.

When you look at B it has a center point at negative 5. The difference from this point must be less than 4. So you know x would be between -9 and -1
_________________

Problem: 1<x<9. What inequality represents this condition?

A. |x|<3 B. |x+5|<4 C. |x-1|<9 D. |-5+x|<4 E. |3+x|<5 Solution: 10sec. Traditional 3-steps method is too time-consume technique. First of all we find length (9-1)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.

Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner

[size=80]Posted from my mobile device

You can also think of this the way manhattan suggest. Think of D on a number line. For l x-5 l the a center point of the line is at positive 5. The difference from this point must be less than 4. so the x would have to be between 1 and 9.

When you look at B it has a center point at negative 5. The difference from this point must be less than 4. So you know x would be between -9 and -1

I am understanding why all points must be 4 away, but why is the center point the one that sets the left side to zero. Ie 5

imagine if you had the inequality l x l = y . Your graph would start at 0,0 and be a v shape. Now imagine you had the graph at l x - 2 l = y. The graph is now shifted over 2 units to the right because now you have to have 2 more units of x to get the same y value. For example F(4) for the first equation is l 4 l = 4 . For the second equation, you would need F(6) = l (4+2) -2 l = 4 to get the same y value.

The answers above follow the same principle because now you have to compensate by more points to get the same values. The centers is 5 for l x-5l because you now have to have 5 more x's to get the same y value. In relation to l xl. The same logic works for l x + 5l You now have compensate by moving 5 units back
_________________

one thing i don't understand is that we can get the answer by simply solving the ineqs which takes less than a minute. Why are we trying to make it more complicated? or am i missing something here?

We are all different and it's always better to know another way to solve a problem. For example, I can't solve 5 inequalities for less than 1 minute but the approach described above allows me to solve the problem over 10sec. It works for me but it doesn't work for you and that's ok.
_________________

Hey, I was just trying to find out the plus point of using the alternative method. That is the reason why i wrote " i don't understand........am i missing sth here....." We're all different and have different point of views therefore, we're here to learn from each other. I didn't know we could solve the problem in that way...i'll use that method from now on. thx.

Sorry Bibha, I misunderstood you. Yeah, the more ways to solve a problem we know the better. At the same time not all ways work for everybody. For example, I love graphic approach to inequities, but there is a lot of people who find it more difficult in use.

Problem: 1<x<9. What inequality represents this condition?

A. |x|<3 B. |x+5|<4 C. |x-1|<9 D. |-5+x|<4 E. |3+x|<5 Solution: 10sec. Traditional 3-steps method is too time-consume technique. First of all we find length (9-1)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.

Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner

me too, because there is no condition where answer C is insufficient or wrong.

Problem: 1<x<9. What inequality represents this condition?

A. |x|<3 B. |x+5|<4 C. |x-1|<9 D. |-5+x|<4 E. |3+x|<5 Solution: 10sec. Traditional 3-steps method is too time-consume technique. First of all we find length (9-1)=8 and center (1+8/2=5) of the segment represented by 1<x<9. Now, let's look at our options. Only B and D has 8/2=4 on the right side and D had left site 0 at x=5. Therefore, answer is D.

Can someone please explain the logic here in detail I think I am missing what makes b and d finalists then d the winner

me too, because there is no condition where answer C is insufficient or wrong.