If x, y, and z are consecutive odd integers and x 0, then

Question

If x, y, and z are consecutive odd integers and x < 0 and z > 0, then what is the range of possible values of xyz

A. 0
B. 1
C. 3
D. 4
E. 6

M37-11

Bunuel · Accepted Answer

Official Solution:

If  x ,  y , and  z  are consecutive odd integers and  x < 0  and  z > 0 , then what is the range of possible values of  xyz  ?

A.  0 
B.  1 
C.  3 
D.  4 
E.  6

Out of three consecutive ODD integers one is negative and one is positive. We can have the following two cases:
 
Two numbers are negative and one number is positive: {-3, -1, 1}. In this case  xyz = 3 .
 
One number is negative and two numbers are positive: {-1, 1, 3}. In this case  xyz = -3 .
 
The range of possible values of  xyz  is therefore,  3- (-3)=6

Answer: E

KSBGC · Answer

consecutive odd integers.

x<0 and z>0 limits the range and the number line.

2 possible conditions:

1) -3 -1 0 1
2) -1 0 1 3

y could both be positive or negative.

possible product : PRODUCT of xyz. and range is based on product.

case 1) -3 * -1 * 1 =3

case 2) -1 *1*3 = -3.

Range :

3 - (-3) = 6.

E is the correct answer.

GMATinsight · Answer

x < 0 and z > 0, and x, y z are consecutive odd integers i.e. they may be either {-3, -1, 1} or {-1, 1, 3}

Possible Values of xyz (Product of 3 values) = 3 and -3

Range = Highest - lowest = 3 - (-3) = 6

Answer: Option E

KanishkM · Answer

Keyword: If x, y, and z are consecutive  odd integers  and x < 0 and z > 0

z will be +ive, x will be -ive

There will be 2 such cases

-3 -1 1
-1 1 3

Range will be HT-LT = 1 + 3 = 4

I just hope xyz is not the product and is just a series of numbers, if that is the case then the range will be 6.

Archit3110 · Answer

set of odd integers ; ( -3,-1,1) or ( -1,1,3)
xyz ; 3 & -3
so range 
3+3 = 6
IMO E

Kinshook · Answer

(x,y,z)={(-3,-1,1),(-1,1,3)}
xyz = 3 or -3
Range of xyz = 6

IMO E

Crytiocanalyst · Answer

The possibilities are -3, -1, 1
=>xyz = 3

-1,1,3
=>xyz= -3

Therefore range =   = 6

Therefore IMO E

rvgmat12 · Answer

xyz = { -1, 1, 3} or { -3, -1, 1}

Range = 3-(-3) = 6

E

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x, y, and z are consecutive odd integers and x < 0 and z > 0, then

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

GMAT Problem Solving (PS) Questions