## Question of the Week - 2 (If x and y are non-zero integers )

### GMAT/MBA Expert

GMAT Instructor
Posts: 645
Joined: 26 Jul 2010
Location: US
Thanked: 527 times
Followed by:227 members

### Question of the Week - 2 (If x and y are non-zero integers )

by e-GMAT » Sat Mar 30, 2019 12:59 pm

00:00

A

B

C

D

E

## Global Stats

If x and y are non-zero integers and |x - 3| â‰¤ 2 and -1 â‰¤ y â‰¤ 8 then the least value of x/y lies in which of the following range?
• A. Between -5.5 and -4.5
B. Between -4.5 and -3.5
C. Between -3.5 and -2.5
D. Between -2.5 and -1
E. Greater than -1

### GMAT/MBA Expert

GMAT Instructor
Posts: 645
Joined: 26 Jul 2010
Location: US
Thanked: 527 times
Followed by:227 members
by e-GMAT » Tue Apr 02, 2019 8:45 pm
Solution

Given:
In this question, we are given that
• "¢ The numbers x and y are non-zero integers.
"¢ Also, |x - 3| â‰¤ 2 and -1 â‰¤ y â‰¤ 8.
To find:
We need to determine
• "¢ The least value of x/y lies in which of the given ranges.
Approach and Working:
For the non-zero integer x,
• "¢ |x - 3| â‰¤ 2
Or, -2 â‰¤ x - 3 â‰¤ 2
Or, 1 â‰¤ x â‰¤ 5
Therefore, possible values of x = 1, 2, 3, 4, 5

Similarly, for the non-zero integer y,
• "¢ -1 â‰¤ y â‰¤ 8
Therefore, possible values of y = -1, 1, 2, 3, 4, 5, 6, 7, 8

Now, for x/y to be least, we should take one of them as positive and the other one as negative.
• "¢ As we can see from the derived values of x and y, x can be positive only whereas y can be negative.
"¢ Hence, we should take negative value of y, with maximum possible magnitude, and maximum value of x.
Negative value of y, with maximum magnitude = -1
Maximum value of x = 5
• "¢ Therefore, the minimum value of x/y = 5/-1 = -5
"¢ This value lies between -5.5 and -4.5
Hence, the correct answer is option A.