Of the four numbers represented on the number line above, is

Question

https://gmatclub.com/forum/download/file.php?id=16740 Of the four numbers represented on the number line above, is r closest to zero? (1) q = –s (2) –t < q Number line.jpg

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=16740 Of the four numbers represented on the number line above, is r closest to zero? (1) q = –s --> -s and s are on opposite sides of zero and zero is halfway between them. We can have two cases: <-------(-s)---(r)---0-------(s)-------(t)-------> <---------(-s)-------0---(r)---(s)-------(t)-------> As you can see in either case r is closest to zero. Sufficient. (2) –t < q --> -t and t are on opposite sides of zero and zero is halfway between them. We can have two cases: <-------(-t)-------(q)------(r)-0-------(s)-------(t)-------> <-------(-t)-------(q)-(r)------0-(s)-------------(t)-------> As you can see in either r or s is closest to zero. Not sufficient. Answer: A.

EMPOWERgmatRichC · Answer

Hi All,

While this question appears layered, it can be solved rather easily by TESTing VALUES and paying attention to the relative 'positions' of the variables on the number line. It's important to note that since this is a DS question, we CANNOT trust the picture. We DO know the "order" of the variables on the number line, but we do NOT know if they are evenly spaced out.

We're asked if R is CLOSEST to 0. This is a YES/NO question.

Fact 1: Q = -S

This tells us that Q and S are opposites. By extension, since they represent 2 DIFFERENT spots on the number line, neither can be 0. Also, since they're opposites and Q is "farther left", then Q is NEGATIVE and S is POSITIVE.

IF....
Q = -1
S = 1
R is BETWEEN -1 and 1, so it IS the closest to 0 and the answer to the question is YES.

IF...
Q = -2
S = 2
R is BETWEEN -2 and 2, so it IS the closest to 0 and the answer to the question is YES.

This pattern is consistent no matter what set of numbers you use for Q and S. The answer is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: -T < Q

IF....
Q = -2
T = 3
We can then place R and S between the two values....

IF....
R = 2.1
S = 2.2
Q is closer to 0 than R is, so the answer to the question is NO

IF....
R = 0
S = 1
R is the closest to 0 (it IS 0), so the answer to the question is YES
Fact 2 is INSUFFICIENT

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

shohrat6383 · Answer

Bunuel,
When -t<q, is it possible that q is closest to zero?

Bunuel · Answer

We are interested whether r closest to zero and for the case when –t < q, we have an YES and a NO answer: <-------(-t)-------(q)------(r)-0-------(s)-------(t)-------> <-------(-t)-------(q)-(r)------0-(s)-------------(t)------->

akumar5 · Answer

As per the question ,r lies somewhere in between q & s .

1) q=-s 
 it implies that the value of r lies somewhere between -s & s . also it will be close to 0 in all situation .
 this part is SUFFICIENT.

2)-t<q
 this part fixes value for t & q resulting :
 - we don't know the location of 0. this leads to many possibilities such as r & s may lie at opposite side of 0 or may lie in the same side.
 so in this scenario r may or may not be close to 0.
 INSUFFICIENT.

ANSWER MUST BE A

justdoitxxxxx · Answer

this question seems weird to me..i don't understand the definition of 'close'..

for statement 1, yes, 0 is in the middle of the distance between S and T and R is between them as well.but how to link it to close to zero as we don't know the value of S and T.

Could be 100 and -100 and R be 99. Does it consider Close? Need help to clarify my doubt...

EgmatQuantExpert · Answer

Hi katzzzz , By closest to zero the question is talking about the distance between zero and the numbers given in the question i.e. q, r, s and t. As per statement-I, zero is the midpoint of q and s and r lies between them. Now, there can be two scenarios: 1. r is closer to q than to s. Let's assume the distance between q and zero and s and zero to be x. Since r lies between s and zero, its distance from zero would be less than x. https://e-gmat.com/blogs/wp-content/uploads/2015/05/GC-NL-e1432317260305.jpg 2. r is closer to s than to q. Similarly in this case, we will have the distance of r from zero less than x. In both the cases we can see that the distance of r from zero is lesser compared to the distance of q and s from zero. Also, t is greater than s and hence is at the greatest distance from zero compared to q, r and s. Hence we can say with certainty that r is the closest to zero. Let me know if you have trouble understanding the analysis of st-II as well. Hope this helps

Regards Harsh

ahmedhammam · Answer

For the first case, I got a little confused because I considered the case of q and s = 0, and accordingly r will be equal to 0 as well.

The given does not mention anything about the values not being equal, does it?

EMPOWERgmatRichC · Answer

Hi ahmedhammam,

This question includes a Number Line with the 4 variables placed at 'hash marks.' However, we don't know the 'scale' of the line (and it's likely that the 4 numbers are NOT evenly spaced out)...

For example, Q R S and T could be 1, 2, 3 and 4

OR

Q R S and T could be -1, 10, 19 and 2000.

We DO know that the 4 numbers are arranged from least to greatest (because that's how a Number Line "works"). By extension, one of the 4 numbers COULD be 0, but two of them cannot (and no two of the variables are the same value).

GMAT assassins aren't born, they're made,
Rich

kuvshah · Answer

is it safe to assume the figure is drawn to the scale and hence if q = -s than r is midpoint for q and s and hence r is 0 or close to it?

Bunuel · Answer

No, you absolutely cannot assume that.

OFFICIAL GUIDE :

Problem Solving 
 Figures:  All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency: 
 Figures: 
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.

BrentGMATPrepNow · Answer

Target question :    Is r closest to zero?

Statement 1 : q = -s   
This tells us that q and s are on opposite sides of zero (i.e., one is positive and one is negative) AND it tells us that  q and s are the same distance from zero.  
So, we get something like this: q.....  0  .....s
Since r is  between  points q and s,  r  must  be the closest point to zero 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : -t < q  
There are several sets of values that satisfy this condition. Here are two: 
Case a: q = -1, r = 0, s = 1 and t = 2, in which case  r IS the closest to zero 
Case b: q = 0, r = 1, s = 2 and t = 3, in which case  r is NOT the closest to zero 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

meenes · Answer

Hi Bunuel,

From the OG statements below regarding DS, how do we derive that figures are  not  drawn to scale?

Bullet 1 says "figures conform to the information given in the question". The question says "of the four numbers  represented on the number line above " -> the word  "represented"  confuses me here

Bullet 3 says "The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero" -> You could use this bullet to argue that the number line in this prompt is therefore not drawn to scale, however the bullet also doesn't say it is NOT drawn to scale.

Generally speaking I'm looking for some clear rules regarding pictures in DS questions. For PS it is crystal clear: drawn to scale unless stated otherwise. What's the general rule for DS? Would it be safe to assume: NOT drawn to scale unless stated otherwise?

Thanks for the clarifications

EMPOWERgmatRichC · Answer

Hi meenes,

As a general rule, you can essentially "trust" a picture in a PS question (unless there's a statement telling you that the picture is NOT drawn to scale), but you should be a bit skeptical of any drawing that appears in a DS question.

This DS question includes a Number Line with the 4 variables placed at 'hash marks.' There are things that we DO know about the Number Line and things that we do NOT know:

We DO know that the 4 numbers are arranged from least to greatest (because that's how a Number Line "works"). However, we don't know the 'scale' of the line (and we have to consider the possibility that the 4 numbers are NOT evenly spaced out)...

For example, Q, R, S, and T could be 1, 2, 3 and 4

OR

Q, R, S, and T could be -1, 10, 19 and 2000.
 
Ultimately, with DS questions, you need facts/information to determine the exact nature of whatever picture is included. For example, if you have a picture of a triangle and you know that the sides of the triangle are 3, 4 and 5, then you know that you are dealing with a right triangle even if that is not clear from the picture (because there's no other type of triangle that can be formed with those 3 side lengths). However, If you have a picture of a right triangle and you know that the hypotenuse has a length of 5, then that does NOT necessary mean that you have a 3/4/5 (the two missing sides could be any two positive numbers that fit the Pythagorean Theorem A^2 + B^2 = 5^2).

GMAT assassins aren't born, they're made,
Rich

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=XfLodzfSPRI

ScottTargetTestPrep · Answer

Solution:

Question Stem Analysis:

We need to determine whether r is closest to zero.

Statement One Alone:
 
With statement one, we see that q and s are both equidistant from 0. Therefore, any point not between q and s is further away from 0 than either q or s. However, any point between q and s is closer to 0 than either q or s. Since r is between q and s (and t is not), then r is closest to 0.

Statement one alone is sufficient.

Statement Two Alone:

Statement two does not allow us to determine which point (and r in particular) is closest to 0. For example, if q = -1, r = 0, s = 1, and t = 2, then r is closest to 0. However, if q = 1, r = 2, s = 3, and t = 4, then q (not r) is closest to 0. Statement two alone is not sufficient.

Answer: A

GMATinsight · Answer

Answer: Option A

Video solution by  GMATinsight

https://www.youtube.com/watch?v=3MoIPYVzQb4

Hoozan · Answer

BrentGMATPrepNow   avigutman  isn't it true that in Geometry, Co-ordinate and Number lines (unless stated otherwise) the diagram is drawn to scale? And hence in this question, we can assume all for points to be equidistant from each other?

BrentGMATPrepNow · Answer

The diagrams in  Problem Solving  questions are drawn to scale (unless stated otherwise). However, the diagrams in  Data Sufficiency  questions are not necessarily drawn to scale.

Of the four numbers represented on the number line above, is

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GMAT Data Sufficiency (DS) Questions

Of the four numbers represented on the number line above, is

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