Problem Solving

Which of the following inequalities has a solution set that, when graphed on the number line, is a single line segment of finte length??

x^4>1

x^3>=27

2<=|x|<+5

2<=3x+4<=6

I think this one is B - X^3=27. As you go through the inequalities, think about which values of x will satisfy them and then imagine plotting these x values on a number line.

X^4>1...for this equation, raising a negative number to an even power will make the number positive. For example, (-2)^4 = 16 = 2^4. Therefore, this inequality will hold true whenever x is greater than 1 or less than -1. If you plotted this on a number line, you would have a line starting at -1 and going off to negative infinity and a line starting at 1 and going off to positive infinity. So this yields 2 seperate line segments of infinite length.

X^3>=27...since negative numbers raised to an odd power will be negative, we know this can never be true for negative values of x. In addition, we know that 3^3=27, so x must be >=3. Plotting x>=3 on the number line, we get a line starting at 3 and going to infinity in the positive direction. This is a single line segment of infinite length.

2<=|x|<=5...for this to be true, x must be between 2 and 5 or between -2 and -5. Plotting this on the number line yields two line segments of finite length (one between -5 and -2 and another between 2 and 5)

2<=3x+4<=6...by subtracting 4 from each expression, this becomes -2=3x<=2. Dividing by 3 yields -2/3<=x<=2/3. Plotting this on a number line gives a single line segment of finite length between -2/3 and 2/3.

answer is E actually.

can someone explain why D is not a good answer?

alexdallas wrote:answer is E actually.

can someone explain why D is not a good answer?

Since the OP only contains 4 answers, gonna be hard to field this question!

Was this a roman numeral question and the correct answer is II and IV only?

oops

i meant to say:

the correct answer is D (4th choice).
i don't understand why C is(3rd answer choice) not correct.

alexdallas wrote:oops

i meant to say:

the correct answer is D (4th choice).
i don't understand why C is(3rd answer choice) not correct.

b/c we can have 2 different solutions... it asks for only one

ok. tks.

alexdallas wrote:oops

i meant to say:

the correct answer is D (4th choice).
i don't understand why C is(3rd answer choice) not correct.

Absolute value will give us both a positive and a negative range. Since the question clearly asks for "a single line segment of finite length", and the 3rd choice gives us two line segments of finite length, it doesn't match what the question demands.

The reason why x^3 >= 27 is incorrent is because it gives us a single line segment of infinite length - another mismatch.

Only the 4th option is both single and finite.

All that said, what happened to the 5th choice? If this isn't a real GMAT question, the original poster should clearly indicate that so we know how much value to give it.

there was no 5th choice.

i think i was doing too many RC exercises at the time, and got confused.

thanks Stuart

moneyman wrote:Which of the following inequalities has a solution set that, when graphed on the number line, is a single line segment of finte length??

x^4>1

x^3>=27

2<=|x|<+5

2<=3x+4<=6

The missing answer choice (c) is x^2 >= 16

Also answer choice
(a) x^4 >= 1
(b) x^3 <= 27
(d) 2 <= |x| <= 5