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# What is the least possible product of 4 different integers

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Intern
Joined: 03 Dec 2010
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What is the least possible product of 4 different integers  [#permalink]

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16 Mar 2011, 10:29
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25% (medium)

Question Stats:

74% (01:17) correct 26% (01:34) wrong based on 405 sessions

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What is the least possible product of 4 different integers, each of which has a value between –5 and 10, inclusive?

(A) –5040
(B) –3600
(C) –720
(D) –600
(E) –120

Project PS Butler : Question #76

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Re: What is the least possible product of 4 different integers  [#permalink]

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16 Mar 2011, 10:44
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Select the maximum possible multiple using three biggest possible numbers and negate it by multiplying with maximum -ve.

10*9*8*-5 = -3600

Ans: "B"
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Re: What is the least possible product of 4 different integers  [#permalink]

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10 Nov 2015, 02:38
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Acer86 wrote:
What is the least possible product of 4 different integers, each of which has a value between –5 and 10, inclusive?

(A) –5040
(B) –3600
(C) –720
(D) –600
(E) –120

Point to be noted: Even number of negative integers multiplied gives us a positive integer and odd numbers of negative integers multiplied gives us a negative integer.
Any number of positive integers multiplied, the result is always a positive integer

We need to find the least possible negative integer after selecting 4 "different" integers from -5 to 10
We can do it by multiplying the extremes and then putting other numbers in between.

Select -5 and 10. Now we need to maximize this.
Since, we need different numbers, we can take 9 and 8

Hence the product = -5*8*9*10 = -3600
Option B
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Re: What is the least possible product of 4 different integers  [#permalink]

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17 Mar 2011, 01:16
Maximize the total product with a -ve sign

so -5 * 10 * 9 * 8 = 720 * -5 = -3600

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Re: What is the least possible product of 4 different integers  [#permalink]

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17 Mar 2011, 01:22
greatest product is 10X9X8X7. In negative greater the abs value lesser the number is. so we remove 7, replace it with max possible abs value from the set (5) and put a negative sign that the 5 brought with it. ans -3600
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Re: What is the least possible product of 4 different integers  [#permalink]

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17 Mar 2011, 02:17
Can someone please explain as to why we did not choose -5040?
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Re: What is the least possible product of 4 different integers  [#permalink]

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17 Mar 2011, 20:10
Because we have to actually have a negative number in there, not just add a - sign at the end. As others said, we utilize -5 so we can change the sign of our product, and then we can go use our three largest numbers which are positive 10,9,8.
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Re: What is the least possible product of 4 different integers  [#permalink]

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18 Mar 2011, 09:27
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Re: What is the least possible product of 4 different integers  [#permalink]

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18 Mar 2011, 16:44
because -5040 is not possible.

the least we can get for the product here is (-5)*10*9*8 = -3600

if we choose one negative , three positive, least possible combination
if we choose two negative and two positive , product becomes positive. hence wont be least possible.
if we choose three negative and one positive -4*-3*-2*10 , possible combination , but wont give least possible.
if we choose four negative , the product becomes positive . hence wont be least possible

trick is choose a largest possible negative integer .

Acer86 wrote:
Can someone please explain as to why we did not choose -5040?
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Re: What is the least possible product of 4 different integers  [#permalink]

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07 Apr 2012, 21:21
the OE is -

(-5)*10*9*8=-3600

P.S. I am sorry, but I doubt that ur questions are 700 level.
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Re: What is the least possible product of 4 different integers  [#permalink]

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07 Apr 2012, 21:21
let 4 different integers be a,b,c,d.

since least integer we have to find meaning a = -5 (least number in negative side)

b*c*d = -5 * y

for b. -5 * 8*9*10 = -5 * 720 = -3600
for a -5 * 1080 = -5040 however max number possible = -5 * 10 * 10 * 10 = -5000 hence POE

thus B it is.
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Re: What is the least possible product of 4 different integers  [#permalink]

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10 Feb 2019, 23:04
Acer86 wrote:
What is the least possible product of 4 different integers, each of which has a value between –5 and 10, inclusive?

(A) –5040
(B) –3600
(C) –720
(D) –600
(E) –120

Lets start from the biggest least value, A

Only B satisfies, -5*5*8*9

the condition least possible product of 4 different integers
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Re: What is the least possible product of 4 different integers  [#permalink]

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02 Jul 2020, 03:44
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Re: What is the least possible product of 4 different integers   [#permalink] 02 Jul 2020, 03:44