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Intern  S
Joined: 02 Jan 2017
Posts: 41
Location: India
WE: Engineering (Telecommunications)
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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KUDOS PLEASE, If my post Helped you.
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Math Expert V
Joined: 02 Sep 2009
Posts: 53709
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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Manager  B
Joined: 15 Jan 2014
Posts: 63
Location: India
GMAT 1: 680 Q48 V35 GPA: 3.79
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
Math Expert V
Joined: 02 Sep 2009
Posts: 53709
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

We cannot assume that the points are equally spaced. None of the solutions here assumes that. Please re-read the thread. Hope it helps.
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Of the four numbers represented on the number line above, is  [#permalink]

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Thanks. Understood the logic now when I substituted numbers .

when s=0.5 , q= -0.5 and since r has to be:

1) behind s and away from q ( say r=0.4 then q is 0.5 away from 0 and r is 0.4 away from 0)

2) ahead of q and away from s ( say r=-0.4 then q is 0.5 away from 0 and r is 0.4 away from 0)

Both case r is closer .

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Joined: 09 Mar 2016
Posts: 1277
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.

Bunuel can you please answer one question why on the mumber line you didnt indicate Q in statement one And how can $$q$$ be equal to $$–s$$ ? these are two different numbers … on the other hand if $$q$$ equals $$–s$$ Then both Q and -S MUST BE THE SAME NUMBER pushpitkc , chetan2u anybody somebody H.................E.......................L.....................P Math Expert V
Joined: 02 Aug 2009
Posts: 7415
Re: Of the four numbers represented on the number line above, is  [#permalink]

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1
dave13 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 can you please answer one question why on the mumber line you didnt indicate Q in statement one And how can $$q$$ be equal to $$–s$$ ? these are two different numbers … pushpitkc , chetan2u anybody somebody H.................E.......................L.....................P 1) how can q=-s
This means q and s are of different signs and |q|=|s| and as q<s on the number line q is negative and s is positive.
Say s=3, so q=-s=-3 and 3 and -3 are different numbers.

2) why q is not marked
Because it is equal to -s and instead of q, we have marked -s..
And centre of s and -s is 0 as same value and different signs will be equidistant from 0
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Posts: 1277
Re: Of the four numbers represented on the number line above, is  [#permalink]

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chetan2u wrote:
dave13 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 can you please answer one question why on the mumber line you didnt indicate Q in statement one And how can $$q$$ be equal to $$–s$$ ? these are two different numbers … pushpitkc , chetan2u anybody somebody H.................E.......................L.....................P 1) how can q=-s
This means q and s are of different signs and |q|=|s| and as q<s on the number line q is negative and s is positive.
Say s=3, so q=-s=-3 and 3 and -3 are different numbers.

2) why q is not marked
Because it is equal to -s and instead of q, we have marked -s..
And centre of s and -s is 0 as same value and different signs will be equidistant from 0

chetan2u thank you very much for taking time to explain Great explanation Intern  B
Joined: 08 Jul 2018
Posts: 9
Re: Of the four numbers represented on the number line above, is  [#permalink]

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Doesn't the GMAT state that all figures are drawn to scale and hence what looks equidistant, is intended to be equidistant. In this case, all points seem to have the same gap between them and hence Statement 2 should be sufficient to confirm that r is closest to 0 (because if s were closer to 0, -t would not be less than q and only r can the the closest to 0)
Please let me know where I'm going wrong.

Thanks!
Math Expert V
Joined: 02 Sep 2009
Posts: 53709
Re: Of the four numbers represented on the number line above, is  [#permalink]

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swank wrote:
Doesn't the GMAT state that all figures are drawn to scale and hence what looks equidistant, is intended to be equidistant. In this case, all points seem to have the same gap between them and hence Statement 2 should be sufficient to confirm that r is closest to 0 (because if s were closer to 0, -t would not be less than q and only r can the the closest to 0)
Please let me know where I'm going wrong.

Thanks!

No you cannot infer that the points are equidistant from the figure.

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. he 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.
_________________ Re: Of the four numbers represented on the number line above, is   [#permalink] 21 Aug 2018, 04:52

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

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