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If the vertical tick marks on the number line

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If the vertical tick marks on the number line

by vinni.k » Mon Jan 23, 2012 12:55 am
If the vertical tick marks on the number line in the diagram shown are equally spaced one from another and a and b are the values at the tick marks indicated, what is the value of b?

(1). a = -0.875
(2). |a - b| = 0.625

Answer is D

Thanks & Regards
Vinni
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Source: — Data Sufficiency |

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by Anurag@Gurome » Mon Jan 23, 2012 1:01 am
vinni.k wrote:If the vertical tick marks on the number line in the diagram shown are equally spaced one from another and a and b are the values at the tick marks indicated, what is the value of b?

(1). a = -0.875
(2). |a - b| = 0.625
From the figure it is clear that a and b are 7 and 2 units away to the left of zero on the number line respectively.

Statement 1: a = -0.875 = 7 units
Hence, b = 2 units = (-0.875/7)*2 = -0.250

Sufficient

Statement 2: |a - b| = distance between a and b = absolute value of 5 units = 0.625
Hence, absolute value of 2 b = absolute value of 2 units = (0.625/5)*2 = 0.250

As b lies on the left of zero on the number line, b = -0.250

Sufficient

The correct answer is D.
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by vinni.k » Mon Jan 23, 2012 1:54 am
Anurag@Gurome wrote:
Statement 2: |a - b| = distance between a and b = absolute value of 5 units = 0.625
Hence, absolute value of 2 b = absolute value of 2 units = (0.625/5)*2 = 0.250

As b lies on the left of zero on the number line, b = -0.250

Sufficient
The correct answer is D.
Wow that was quick. Thanks Anurag.
Well here's my reasoning for B because of which I selected only A as the answer.

(2). |a - b| = 0.625
If i open the absolute values, then this will be:-

a - b = 0.625 and a - b = -0.625
We know that a and b are on the negative side of the number line i.e < 0
I am taking x as an interval

So, |-7x - (-2x)| = 0.625 and |-7x - (-2x)| = -0.625
Solving for 1st
|-7x + 2x| = 0.625
|-5x| = 0.625
5x = 0.625
x = 0.125
b = 2x = 2 * 0.125
b = 0.25

Now solving for 2nd
|-7x - (-2x)| = -0.625
|-7x + 2x| = -0.625
|-5x| = -0.625
5x = -0.625
x = -0.125
Now, b = 2x = 2*(-0.125)
b = -0.25

We have got 2 values for B

The absolute value of |a - b| = 1 always gives 2 results
a - b = 1 and a - b = -1

This was the reason I selected A. So, my method was not correct ?

Regards
Vinni
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by Anurag@Gurome » Mon Jan 23, 2012 2:00 am
vinni.k wrote:|a - b| = 0.625
If i open the absolute values, then this will be:-

a - b = 0.625 and a - b = -0.625
From the given diagram note that, a < b ---> (a - b) < 0
Hence, (a - b) cannot be equal to 0.625. So there is no point in considering that as a potential equation.
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by vinni.k » Mon Jan 23, 2012 2:12 am
Anurag@Gurome wrote: From the given diagram note that, a < b ---> (a - b) < 0
Hence, (a - b) cannot be equal to 0.625. So there is no point in considering that as a potential equation.
Got it. Makes sense. Thanks for the nice explanation.
:D

Regards
Vinni
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by GMATGuruNY » Tue Jan 24, 2012 8:16 am
vinni.k wrote:If the vertical tick marks on the number line in the diagram shown are equally spaced one from another and a and b are the values at the tick marks indicated, what is the value of b?

(1). a = -0.875
(2). |a - b| = 0.625

Answer is D

Thanks & Regards
Vinni
Another approach:

Since a is 7 spaces to the left of 0 and b is 2 spaces to the left of 0, a/b = 7/2.

Statement 1: a = -.875.
Since a/b = 7/2 and a = -.875, we can solve for b.
SUFFICIENT.

Statement 2: |a-b| = .625.
In other words, the distance between a and b is .625.
Since we know that a and b are both negative, that the distance between them = .625, and that their ratio = 7/2, we can solve for b.
SUFFICIENT.

Ideally, we wouldn't do any math for this problem. We would simply recognize that the question stem gives us one linear equation and that each statement gives us a second linear equation, making it possible to solve for b.

The correct answer is D.
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by vinni.k » Tue Jan 24, 2012 11:31 am
GMATGuruNY wrote:
Another approach:

Since a is 7 spaces to the left of 0 and b is 2 spaces to the left of 0, a/b = 7/2.

Statement 1: a = -.875.
Since a/b = 7/2 and a = -.875, we can solve for b.
SUFFICIENT.

Statement 2: |a-b| = .625.
In other words, the distance between a and b is .625.
Since we know that a and b are both negative, that the distance between them = .625, and that their ratio = 7/2, we can solve for b.
SUFFICIENT.

Ideally, we wouldn't do any math for this problem. We would simply recognize that the question stem gives us one linear equation and that each statement gives us a second linear equation, making it possible to solve for b.

The correct answer is D.
Hey Mitch, good one and it will definitely save time.

Liked it. Thanks :D

Regards
Vinni
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by ArunangsuSahu » Tue Jan 24, 2012 12:27 pm
Equally spaced

SO (D) is the answer
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