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Manager  Joined: 25 Aug 2011
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Of the four numbers represented on the number line above, is  [#permalink]

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116 00:00

Difficulty:   35% (medium)

Question Stats: 71% (01:31) correct 29% (01:43) wrong based on 2800 sessions

### HideShow timer Statistics Of the four numbers represented on the number line above, is r closest to zero?

(1) q = –s
(2) –t < q

Attachment: Number line.jpg [ 6.28 KiB | Viewed 42619 times ]

Originally posted by devinawilliam83 on 29 Feb 2012, 20:50.
Last edited by Bunuel on 14 Jul 2016, 22:24, edited 2 times in total.
Edited the question and added the diagram
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Of the four numbers represented on the number line above, is  [#permalink]

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33 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.

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Re: Of the four numbers represented on the number line above, is  [#permalink]

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the question is not very clear for me.. i've chosen option E because i put ANY value for each letter, should not the question specify that the relation q<r <s <t has always to be true?
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Re: Of the four numbers represented on the number line above, is  [#permalink]

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lucasITA wrote:
the question is not very clear for me.. i've chosen option E because i put ANY value for each letter, should not the question specify that the relation q<r <s <t has always to be true?

The question says "Of the four numbers represented on the number line above", so the order is what you get by looking at it: $$q<r <s <t$$.
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Re: Of the four numbers represented on the number line above, is  [#permalink]

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1
Bunuel wrote:
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.

Bunuel,
When -t<q, is it possible that q is closest to zero?
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Re: Of the four numbers represented on the number line above, is  [#permalink]

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2
1
shohrat6383 wrote:
Bunuel wrote:
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.

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

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)------->

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Re: Of the four numbers represented on the number line above, is  [#permalink]

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2
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.

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Re: Of the four numbers represented on the number line above, is  [#permalink]

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1
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...
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Re: Of the four numbers represented on the number line above, is  [#permalink]

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2
katzzzz wrote:
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...

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. 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
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Re: Of the four numbers represented on the number line above, is  [#permalink]

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3
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

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Re: Of the four numbers represented on the number line above, is  [#permalink]

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devinawilliam83 wrote:
Attachment:
Number line.jpg
Of the four numbers represented on the number line above, is r closest to zero?

(1) q = –s
(2) –t < q

Am unable to understand the explanation in the OG.

Are we just suppose to believe/assume that all points are equidistant from the other??
There is a better version of this question on page 1 of sub-500 coordinate geometry directory page.
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Re: Of the four numbers represented on the number line above, is  [#permalink]

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LogicGuru1 wrote:
devinawilliam83 wrote:
Attachment:
Number line.jpg
Of the four numbers represented on the number line above, is r closest to zero?

(1) q = –s
(2) –t < q

Am unable to understand the explanation in the OG.

Are we just suppose to believe/assume that all points are equidistant from the other??
There is a better version of this question on page 1 of sub-500 coordinate geometry directory page.

No, we cannot assume that the gaps between two adjacent points are equal. We can infer from the image only the relative position (order) of points.
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devinawilliam83 wrote: Of the four numbers represented on the number line above, is r closest to zero?

(1) q = –s
(2) –t < q

Attachment:
Number line.jpg

Of the four numbers represented on the number line above, is r closest to zero?

See how the question is asking us is r "CLOSER" to zero and not asking us is r "Greater than or Less than zero"
In a number line with no marking for magnitude, it would have been almost impossible to tell whether r is greater than or less than 0

(1) q = –s
Sufficient :- q and s must have a zero in between them and they both will be equidistant from 0
For example q=-5 then s=5
r is between q and s so it can never touch the same magnitude as r or s . It can never be 5. It can be -4.99999....... to 4.99999..... It has to be be anything less than 5 hence it will always be closer to zero compared to q and s.

(2) –t < q
Tells us there is 0 between t and q but there r and s are also between t and q; s we don't know whether r or s is close to 0
INSUFFICIENT

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Re: Of the four numbers represented on the number line above, is  [#permalink]

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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?
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Re: Of the four numbers represented on the number line above, is  [#permalink]

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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).

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Re: Of the four numbers represented on the number line above, is  [#permalink]

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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?
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Re: Of the four numbers represented on the number line above, is  [#permalink]

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kuvshah wrote:
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?

No, you absolutely cannot assume that.

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.
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Re: Of the four numbers represented on the number line above, is  [#permalink]

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HI Experts,
Can someone please help me in knowing in solutions provided above , for option 1, Why we are considering that r will be the mid point of point Q, and S.
it not mentioned in question anywhere. are we depicting it from the Figure?
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Re: Of the four numbers represented on the number line above, is  [#permalink]

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er.arun88 wrote:
HI Experts,
Can someone please help me in knowing in solutions provided above , for option 1, Why we are considering that r will be the mid point of point Q, and S.
it not mentioned in question anywhere. are we depicting it from the Figure?

R is not necessarily the midpoint of QS, it could be though and in this case R would be 0 but R could also be anywhere between Q and S. You could check for example THIS SOLUTION, which does not imply that R is the midpoint.
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Re: Of the four numbers represented on the number line above, is  [#permalink]

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Bunuel wrote: 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.

HOW DO WE KNOW THE NUMBERS ARE EQUALLY SPACED ?

The questions just says 4 numbers are represented in the number line. It can even be decimals right ?in that case this explanation doesn't hold good. I am confused here Re: Of the four numbers represented on the number line above, is   [#permalink] 16 Jul 2018, 08:36

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