If –3

Question

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

Source:   Nova GMAT  
Difficulty Level:   600

Nikkb · Answer

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

Answer: A

CrackverbalGMAT · Answer

This is a problem on finding the range of an algebraic expression. When you have to do this, always determine four numbers by taking the difference of the extremities of the given inequalities.

In this problem, we have -3<x<-1 and 3<y<7. The four numbers I’m talking about would be, 
-3-3 = -6 (note that we are trying to find x-y and hence I have taken the values in the same order).
-3-7 = -10
-1-3 = -4 and
-1-7 = -8

To find the range of (x-y), we need to pick the smallest and the biggest of the four numbers. Therefore, range of (x-y) = -10 < (x-y) < -4 and range of  \frac{(x-y)}{2}  = -5< \frac{(x-y)}{2} <-2. 
 The correct answer option is A .

Remember that the approach defined above to find out the range of an expression holds true regardless of the type of expression given.

Hope that helps!

Kinshook · Answer

Asked: If –3 < x < –1 and 3 < y < 7, which of the following best describes \frac{x-y}{2} ? -1.5 < x/2 < - .5 (1) 1.5< y/2 <3.5 -1.5 > -y/2 > - 3.5 -3.5 < -y/2 < -1.5 (2) (1) + (2) - 5 < (x-y)/2 < -2 IMO A

MHIKER · Answer

The subtractions are : -6, -8, -10, -4
so, 10<x-y<-4
−5 <  \frac{x−y}{2}  < −2

The Answer will A.

ScottTargetTestPrep · Answer

Solution:

If x = -3 and y = 7, then (x - y)/2 = (-3 - 7)/2 = -5. However, since x is greater than -3 and y is less than 7, we see that (x - y)/2 is actually greater than -5.

Similarly, if x = -1 and y = 3, then (x - y)/2 = (-1 - 3)/2 = -2. However, since x is less than -1 and y is greater than 3, then (x - y)/2 is actually less than -2.

Answer: A

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

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