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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If −2 < p < 3 and −1 < q < 10, which of the following expresses the po

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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
If −2 < p < 3 and −1 < q < 10, which of the following expresses the po  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 74% (01:31) correct 26% (01:52) wrong based on 101 sessions

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If −2 < p < 3 and −1 < q < 10, which of the following expresses the possible values of p – q ?

A. −12 < p – q < 4
B. −12 < p – q < 7
C. −3 < p – q < 4
D. −3 < p – q < 7
E. −1 < p – q < 4

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If −2 < p < 3 and −1 < q < 10, which of the following expresses the po  [#permalink]

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Bunuel wrote:
If −2 < p < 3 and −1 < q < 10, which of the following expresses the possible values of p – q ?

A. −12 < p – q < 4
B. −12 < p – q < 7
C. −3 < p – q < 4
D. −3 < p – q < 7
E. −1 < p – q < 4

least value of p -2 and q= 10
max value of p 3 and q= -1
so range would of p-q

-12<p-q<4

option A

Originally posted by Archit3110 on 12 Nov 2018, 02:59.
Last edited by Archit3110 on 13 Nov 2018, 03:02, edited 1 time in total.
Intern  Joined: 24 Oct 2018
Posts: 3
Re: If −2 < p < 3 and −1 < q < 10, which of the following expresses the po  [#permalink]

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1
The question stem does not specify p or q as integers, therefore the values could be -1.99, 2.99, etc.

1) Plug in the highest and lowest possible values.
2) To keep it simple, have p as -2 and q as 10
p-q = -2 - 10 = -12
-12 is the lowest possible number

Now have p = 3 and q = -1
p-q = 3 - (-1) = 3 + 1 = 4
4 is the highest possible number.

3) The possible values are -12 < p - q < 4

If you want to check, try the highest and lowest combinations allowed and list all the values.
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Re: If −2 < p < 3 and −1 < q < 10, which of the following expresses the po  [#permalink]

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Its better to draw a number line to avoid any confusions for these types of questions.

p - q => -2 - 10 =>-12
p - q => 3 + 1 =>4

-12 < p-q < 4

Answer should be A
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Re: If −2 < p < 3 and −1 < q < 10, which of the following expresses the po  [#permalink]

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Bunuel wrote:
If −2 < p < 3 and −1 < q < 10, which of the following expresses the possible values of p – q ?

A. −12 < p – q < 4
B. −12 < p – q < 7
C. −3 < p – q < 4
D. −3 < p – q < 7
E. −1 < p – q < 4

To determine the smallest difference of p and q, we want p to be as small as possible and q to be as large as possible. Thus, we have p - q = -2 - 10 = -12.

To determine the largest difference of p and q, we want p to be as large as possible and q to be as small as possible. Thus, we have p - q = 3 - (-1) = 3 + 1 = 4.

Thus, -12 < p - q < 4.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If −2 < p < 3 and −1 < q < 10, which of the following expresses the po   [#permalink] 21 Jan 2019, 19:29
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If −2 < p < 3 and −1 < q < 10, which of the following expresses the po

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