On the number line above, the distance between any two vertical. . .

Question

https://e-gmat.com/blogs/wp-content/uploads/2016/11/03_01-e1478607410846.png On the number line above, the distance between any two vertical bars is constant and the distance between any two circles is also constant. Starting from zero, the vertical bars and the circles coincide at regular intervals. What is the value of D? (1) The value of B is \frac{1}{12} units greater than the value of A. (2) The value of B is 50 % smaller than the value of C. Take a stab at this fresh question from e-GMAT. Post your analysis below. Official Solution to be provided after receiving some good analyses.

manhasnoname · Answer

Let H represent one unit between 2 successive horizontal bars
Let C represent one unit between 2 successive circles

From the given figure 2H = 3C

from statement (1) -H = -C+(1/12)

2 equations and 2 unknowns. Sufficient.

statement (2) just repeats what is in the question. Not sufficient.

Hence (A).

PKay · Answer

The most important thing to understand is:

Starting from 0, every second vertical line coincides with the every 3rd circular point.
i.e, if we assume the distance between two vertical lines to be x, then the distance between two circular points is 2x/3.

Statement 1- simply states that x-2x/3 = x/3 = 1/12. Finding value of D is a piece of cake now.

Statement 2- simply states what we already understood at the beginning. It expresses the same thing in terms of percentage. Hence this info is not useful to find the value of D.

OA is A.

EgmatQuantExpert · Answer

Solution

Steps 1 & 2: Understand Question and Draw Inferences

Given  :
 
• Let the distance between any 2 consecutive vertical bars be x units
• Let the distance between any 2 consecutive circles by y units
• From the figure, it’s clear that  2x = 3y - - - (I)

https://e-gmat.com/blogs/wp-content/uploads/2016/12/GC_1.jpg

To find  : 
The x – coordinate of point D
 • = distance between point D and 0 on the number line
 o Point D has a vertical bar
o 0 has a vertical bar as well 
• So, the distance between point D and 0 = Distance between 4 consecutive vertical bars

So, to answer the question, we need to find the value of x.

Step 3: Analyze Statement 1 independently

(1) The x-coordinate associated with Point B is  \frac{1}{12}  units greater than the x-coordinate associated with Point A.

• (x- coordinate of point B) = (x – coordinate of point A) +  \frac{1}{12} 
 o Since A and B are on the left hand side of 0, their x – coordinates will be negative
o Looking at the figure above, we can write that:
 • (x- coordinate of point B) = -x
• (x – coordinate of point A) = -2y   
•  -x= -2y+\frac{1}{12} 
•  2y-x=\frac{1}{12} - - - (II)
• Equations (I) and (II) form a system of 2 linear equations having 2 unknowns.

By solving these 2 equations together, we can find a unique value of x

So statement 1 is sufficient to arrive at a unique answer.

Step 4: Analyze Statement 2 independently

(1) The x-coordinate associated with Point B is 50% smaller than the x-coordinate associated with Point C.

• (x- coordinate of point B) = 50% less than the (x – coordinate of point C) 
 o Since B and C are on the left hand side of 0, their x – coordinates will be negative
o Looking at the figure above, we can write that:
 • (x- coordinate of point B) = -x
• (x – coordinate of point C) = -y

• It must be noted that in case of negative numbers, the smaller negative number will have the greater absolute value
 o For example, -4 is less than -2. The absolute value of -4 is 4, which is greater than 2, the absolute value of -2
 • Since 4 is 100% greater than 2, -4 will be 100% smaller than -2 
o The x-coordinate of point B is smaller than the x-coordinate of point C by 50%
o So, the absolute value of the x-coordinate of point B will be greater than that of point C by 50%

•  |-x|=(1+\frac{50}{100})|-y| 
 o  x=\frac{3y}{2}

This equation is a restatement of Equation (I) that we’ve already deduced.

Therefore, statement 2 is not sufficient to arrive at a unique answer.

Hence the correct Answer is A

Thanks,
Saquib
Quant Expert
e-GMAT

To practise ten 700+ Level Number Properties Questions attempt the  The E-GMAT Number Properties Knockout  . Click here.

https://e-gmat.com/blogs/wp-content/uploads/2016/12/NP-Free-Trial-e1481107541356.png

bumpbot · Answer

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On the number line above, the distance between any two vertical. . .

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