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Intern  Joined: 23 Sep 2015
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Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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3
38 00:00

Difficulty:   35% (medium)

Question Stats: 69% (01:54) correct 31% (01:59) wrong based on 354 sessions

### HideShow timer Statistics Three points T, U and V on the number line have coordinates t, u, and v respectively. Is T between points U and V?

(1) $$t^2<4<u^2<v^2$$

(2) $$u<0<v$$
Math Expert V
Joined: 02 Sep 2009
Posts: 56272
Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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15
24
Three points T, U and V on the number line have coordinates t, u, and v respectively. Is T between points U and V?

(1) $$t^2<4<u^2<v^2$$. Since all parts of the inequality are non-negative, we can safely take the square root from it: $$|t| < 2 < |u| < |v|$$. It's possible that T is between U and V, for example, if t=0, u=-3 and v=4, as well as it's possible that it's not, for example, t=0, u=3 and v=4. Not sufficient.

(2) $$u<0<v$$. Clearly insufficient.

(1) Since from (2) u<0<v, then from (1) we get $$|t| < 2 < -u < v$$. If break it: we'll get $$u<-2$$ (from 2 < -u), $$-2<t<2$$ (from |t| < 2), and $$2<v$$. T is between U and V. Sufficient.

Hope it's clear.
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Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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12
4
St1: t^2 can take values between 0 and 4 --> -2 < t < 2
When u and v have the same sign: v > u > 2 or v < u < -2 --> t does not lie between u and v
When u and v have oppositie sign: u > 2 and v < -u < -2 or u < -2 and v > -u > 2 --> t lies between u and v

Illustrating the above statements:
When t = 1; u = 3; v = 4, t does not lie between u and v
When t = 1; u = -3; v = 4, t lies between u and v
Not Sufficient.

St2: u is -ve and v is positive --> Clearly insufficient as we have no information about t

Combining St1 and St2:
-2 < t < 2;
u is negative --> u < -2
v is positive --> v > -u > 2
As shown in St1, when u and v have opposite signs, t lies between u and v.
Sufficient

##### General Discussion
Manager  S
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Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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Hi Bunuel ,
Is this really a GMAT PREP Question .
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Regards ,
Math Expert V
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Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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abhisheknandy08 wrote:
Hi Bunuel ,
Is this really a GMAT PREP Question .

Hi,
the Q is a bit twisted but tests number properties..
and since it has been shown that the source is GMAT PREP EP2, we should be ready for such Qs
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Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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chetan2u wrote:
abhisheknandy08 wrote:
Hi Bunuel ,
Is this really a GMAT PREP Question .

Hi,
the Q is a bit twisted but tests number properties..
and since it has been shown that the source is GMAT PREP EP2, we should be ready for such Qs

Absolutely sir..i think it should be 700 Q---wrongly tagged i believe.
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Intern  Joined: 23 Sep 2015
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Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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abhisheknandy08 wrote:
Hi Bunuel ,
Is this really a GMAT PREP Question .

Yes, it is from EP 2 (the newly launched EP).

Sent from my SM-G900T using Tapatalk
Intern  Joined: 23 Sep 2015
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Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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If everyone thinks it is 700 level, I will change the tag.

Sent from my SM-G900T using Tapatalk
Math Expert V
Joined: 02 Sep 2009
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Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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mbaspire wrote:
If everyone thinks it is 700 level, I will change the tag.

Sent from my SM-G900T using Tapatalk

No need. the difficulty level is adjusted automatically based on stats from timer.
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Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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1
Tip: I found drawing the number line here instead of trying to write out inequalities got to the correct answer much quicker. ~20-30 seconds
Intern  B
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Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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Bunuel wrote:
Three points T, U and V on the number line have coordinates t, u, and v respectively. Is T between points U and V?

(1) $$t^2<4<u^2<v^2$$. Since all parts of the inequality are non-negative, we can safely take the square root from it: $$|t| < 2 < |u| < |v|$$. It's possible that T is between U and V, for example, if t=0, u=-3 and v=4, as well as it's possible that it's not, for example, t=0, u=3 and v=4. Not sufficient.

(2) u<0<v. Clearly insufficient.

(1) Since from (2) u<0<v, then from (1) we get $$|t| < 2 < -u < v$$. If break it: we'll get $$u<-2$$ (from 2 < -u), $$-2<t<2$$ (from |t| < 2), and $$2<v$$. T is between U and V. Sufficient.

Hope it's clear.

When you take the sq rt of 4 in this, shouldn't the result be +/- 2?
Math Expert V
Joined: 02 Sep 2009
Posts: 56272
Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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ailintan wrote:
Bunuel wrote:
Three points T, U and V on the number line have coordinates t, u, and v respectively. Is T between points U and V?

(1) $$t^2<4<u^2<v^2$$. Since all parts of the inequality are non-negative, we can safely take the square root from it: $$|t| < 2 < |u| < |v|$$. It's possible that T is between U and V, for example, if t=0, u=-3 and v=4, as well as it's possible that it's not, for example, t=0, u=3 and v=4. Not sufficient.

(2) u<0<v. Clearly insufficient.

(1) Since from (2) u<0<v, then from (1) we get $$|t| < 2 < -u < v$$. If break it: we'll get $$u<-2$$ (from 2 < -u), $$-2<t<2$$ (from |t| < 2), and $$2<v$$. T is between U and V. Sufficient.

Hope it's clear.

When you take the sq rt of 4 in this, shouldn't the result be +/- 2?

t^2 < 4

|t| < 2 (which is the same as -2 < t < 2).
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GMAT 1: 580 Q41 V29 GMAT 2: 580 Q43 V27 Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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Bunuel wrote:
ailintan wrote:
Bunuel wrote:
Three points T, U and V on the number line have coordinates t, u, and v respectively. Is T between points U and V?

(1) $$t^2<4<u^2<v^2$$. Since all parts of the inequality are non-negative, we can safely take the square root from it: $$|t| < 2 < |u| < |v|$$. It's possible that T is between U and V, for example, if t=0, u=-3 and v=4, as well as it's possible that it's not, for example, t=0, u=3 and v=4. Not sufficient.

(2) u<0<v. Clearly insufficient.

(1) Since from (2) u<0<v, then from (1) we get $$|t| < 2 < -u < v$$. If break it: we'll get $$u<-2$$ (from 2 < -u), $$-2<t<2$$ (from |t| < 2), and $$2<v$$. T is between U and V. Sufficient.

Hope it's clear.

When you take the sq rt of 4 in this, shouldn't the result be +/- 2?

t^2 < 4

|t| < 2 (which is the same as -2 < t < 2).

Yeah, It is a medium level question. I bit of guess/application work is needed to solve this question. Mentioned question can be solved only if we were given both information A and B.

Intern  B
Joined: 20 Oct 2017
Posts: 27
Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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How do I check the difficult level in terms of 660-650-700-750 level? It just shows easy/ medium on the timer :/
Math Expert V
Joined: 02 Sep 2009
Posts: 56272
Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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kritikalal wrote:
How do I check the difficult level in terms of 660-650-700-750 level? It just shows easy/ medium on the timer :/

We have three grades of difficulty: easy, which corresponds to sub-600; medium, which corresponds to 600-700; and hard, which corresponds to 700+. You can check difficulty level of a question along with the stats on it in the first post. The difficulty level of a question is calculated automatically based on the timer stats from the users which attempted the question.
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Re: Three points T, U and V on the number line have coordinates t, u, and  [#permalink]

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_________________ Re: Three points T, U and V on the number line have coordinates t, u, and   [#permalink] 21 Mar 2019, 14:23
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