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# If –3 < x < –1 and 3 < y < 7, which of the following best describes x

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If –3 < x < –1 and 3 < y < 7, which of the following best describes x  [#permalink]

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04 Sep 2017, 00:03
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35% (medium)

Question Stats:

69% (01:38) correct 31% (01:48) wrong based on 75 sessions

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If –3 < x < –1 and 3 < y < 7, which of the following best describes $$\frac{x-y}{2}$$
?

(A) −5 < $$\frac{x−y}{2}$$ < −2
(B) −3 < $$\frac{x−y}{2}$$ < −1
(C) −2 < $$\frac{x−y}{2}$$ < 0
(D) 2 < $$\frac{x−y}{2}$$ < 5
(E) 3 < $$\frac{x−y}{2}$$ < 7

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If –3 < x < –1 and 3 < y < 7, which of the following best describes x  [#permalink]

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04 Sep 2017, 00:24
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Given : –3 < x < –1 and 3 < y < 7
Find (x-y)/2 => (x/2 -y/2)

we can rewrite:
–3 < x < –1 => –3/2 < x/2 < –1/2
3 < y < 7 => 3/2 < y/2 < 7/2

Number line
====-3/2===-1/2===3/2===7/2====

Now (x/2-y/2) ...
we have to find range ie highest and lowest difference
Largest difference = smallest number of x and largest no. of y
= -3/2 - 7/2 = -5

smallest difference = largest number of x and smallest no. of y
= -1/2 - 3/2 = -2

therefore -5< (x-y)/2 <-2

If –3 < x < –1 and 3 < y < 7, which of the following best describes x   [#permalink] 04 Sep 2017, 00:24
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# If –3 < x < –1 and 3 < y < 7, which of the following best describes x

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