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# Out of three distinct numbers: P, Q, R - is P the smallest? (1) Q =

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Retired Moderator
Joined: 22 Aug 2013
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Out of three distinct numbers: P, Q, R - is P the smallest? (1) Q =  [#permalink]

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05 Apr 2018, 02:05
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Difficulty:

35% (medium)

Question Stats:

74% (01:01) correct 26% (01:11) wrong based on 35 sessions

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Out of three distinct numbers: P, Q, R - is P the smallest?

(1) Q = (P+R)/2

(2) R is not less than Q.
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Joined: 17 Jan 2017
Posts: 60
Out of three distinct numbers: P, Q, R - is P the smallest? (1) Q =  [#permalink]

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05 Apr 2018, 10:07
(1) and (2) alone are clearly insufficient.
Both statement together indicate that P must be the smallest.
I plugged in different numbers.

Retired Moderator
Joined: 27 Oct 2017
Posts: 1256
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Out of three distinct numbers: P, Q, R - is P the smallest? (1) Q =  [#permalink]

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05 Apr 2018, 10:28
2
(1) Q = (P+R)/2
this means that Q is mean of P and R, or in other words,
Q is between P & Q if P & Q are not equal
Q =P=R.(which is not possible as all are distinct)
Clearly insufficient, as P can be smallest or largest.

(2) R is not less than Q.
It is clearly insufficent.

Combing statement 1 & 2, we get
out of P, Q, R: Q is the median. and R is not smaller than Q. hence R is greater than Q.
Thus P is the smallest number,

Sufficient.

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Retired Moderator
Joined: 27 Oct 2017
Posts: 1256
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Out of three distinct numbers: P, Q, R - is P the smallest? (1) Q =  [#permalink]

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05 Apr 2018, 10:33
Dear benejo
it is not recommended to prove something valid by substituting value, as you may miss some values which doesn't hold good for the statement under validation.
Yes invalidity of a statement can be proved by substituting because even a single non satisfying value does prove its invalidity.

benejo wrote:
(1) and (2) alone are clearly insufficient.
Both statement together indicate that P must be the smallest.
I plugged in different numbers.

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Re: Out of three distinct numbers: P, Q, R - is P the smallest? (1) Q =   [#permalink] 05 Apr 2018, 10:33
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