If a, b, c and d are different integers between -6 and 10 inclusive, what is the least possible value of the product

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Jan 31, 2021 4:49 pm

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If a, b, c and d are different integers between -6 and 10 inclusive, what is the least possible value of the product abcd?

A. -480
B. -720
C. -1200
D. -3600
E. -4320

OA E

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Sun Jan 31, 2021 4:49 pm

swerve: Legendary Member; Posts: 2560; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: If a, b, c and d are different integers between -6 and 10 inclusive, what is the least possible value of the product

by swerve » Mon Feb 01, 2021 11:26 am

BTGmoderatorDC wrote: ↑
Sun Jan 31, 2021 4:49 pm
If a, b, c and d are different integers between -6 and 10 inclusive, what is the least possible value of the product abcd?

A. -480
B. -720
C. -1200
D. -3600
E. -4320

OA E

Source: Magoosh

Value is least when the magnitude is highest with a negative sign

$\Rightarrow$ There should odd number of negative values out of 4 integers
$\Rightarrow$ Assign $3$ positive highest value possible $= {8, 9, 10} $ a negative value with highest magnitude $= {-6}$
$\Rightarrow$ Least value possible $= -6\cdot 8\cdot 9 \cdot 10 = -4320$

Therefore, E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8175; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If a, b, c and d are different integers between -6 and 10 inclusive, what is the least possible value of the product

by Scott@TargetTestPrep » Sat Feb 13, 2021 6:44 am

BTGmoderatorDC wrote: ↑
Sun Jan 31, 2021 4:49 pm
If a, b, c and d are different integers between -6 and 10 inclusive, what is the least possible value of the product abcd?

A. -480
B. -720
C. -1200
D. -3600
E. -4320

OA E

Solution:
The least possible product occurs when a (or any one of the 4 variables) is -6 and the other three are 8, 9 and 10, respectively. Thus, the least value of the product abcd is -6 x 8 x 9 x 10 = -4320.

Answer: E

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