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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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20 Apr 2016, 19:20

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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

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
_________________

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.

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

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01 Jun 2017, 04:24

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.

Answer: C.

Hope it's clear.

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

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.

Answer: C.

Hope it's clear.

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

Are you talking about t^2 < 4? What is your question?

t^2 < 4

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

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

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10 Aug 2017, 00:14

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.

Answer: C.

Hope it's clear.

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

Are you talking about t^2 < 4? What is your question?

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.

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