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605-655 (Medium)|   Math Related|         
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 Updated on: 20 Apr 2026, 22:12
Originally posted by Bunuel on 18 Jul 2024, 06:59.
Last edited by Bunuel on 20 Apr 2026, 22:12, edited 1 time in total.
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Smallest value: -250 Largest negative value: -1
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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45% (medium)

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74% (01:41) correct 26% (02:09) wrong based on 719 sessions

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From the consecutive integers −2 to 5, inclusive, four integers are randomly chosen with repetitions allowed. Select the smallest possible value of the product of the 4 integers for Smallest value, and the largest negative value of the product of the 4 integers for Largest negative value.
Smallest value Largest negative value
-1
-16
-24
-250
-625
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Smallest value: -250 Largest negative value: -1
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 07:02
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Bunuel
From the consecutive integers −2 to 5, inclusive, four integers are randomly chosen with repetitions allowed. Select the smallest possible value of the product of the 4 integers for Smallest value, and the largest negative value of the product of the 4 integers for Largest negative value.

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GMAT Club Official Explanation:



­­Smallest Value: The product will be the smallest when it contains integers with the maximum possible absolute values and an odd number of negative values. The maximum absolute value is 5. To achieve the smallest product, use three 5's and one -2. Hence, the smallest product is -2 * 5 * 5 * 5 = -250.

Largest Negative Value: The product will have the largest negative value when it contains integers with the minimum possible absolute values and an odd number of negative values. The minimum absolute value is 1. So the product is -1 * 1 * 1 * 1 = -1.­
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 07:38
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Given that 4 digits selects randomly (with repetition) from -- -2 to 5 (both inclusive)

now smallest possible value means maximum number in negative sign

we can make from the option (-625 or -250) -625 is not possible as for 625 (5^4 and one 5 must be negative which is not available from the digits (-2 to 5) hence, -250 is possible how?
-- (-2*5*5*5= -250)
hence smallest value is -250

Maximum negative value means least value with negative sign
from option -1 can be max neg value how ?
-1*1*1*1= -1
or -1*-1*-1*1= -1 (repetition allowed not it)

and if we any other option that will no be maximum negative value it will less than -1 then so correct ans is -1

I hope my logic is correct and make sense
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 07:42
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Smallest Value = -250 ( 5*5*5*-2)

Largest negative value =-1 (1*1*1*-1)

1-4 2-1
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 07:48
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From the consecutive integers −2 to 5, inclusive, four integers are randomly chosen with repetitions allowed. Select the smallest possible value of the product of the 4 integers for Smallest value, and the largest negative value of the product of the 4 integers for Largest negative value.­

The smallest value will be the largest negative value hence both the answer will be same. 

And the smallest value will be largest postive value * largest negative value = (5*5*5) * (-2) = -250 (Answer)
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 07:52
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Largest Negative Value of the Product

We need to consider the largest magnitudes while maintaining an odd number of negative integers:

The set of integers includes
−2,−1,0,1,2,3,4,5.
To maximize the magnitude, we avoid 0 and consider
consider the products formed by including the maximum negative number of −2:
Taking only one -ve integer because two -ve integer will become positive when multiplied.

Choosing −2 & since repetition is allowed we take maximum values of set that is 5
−2, 5, 5, and 5:
(−2)×5×5×5=−2×125=−250
This gives us a negative product.
Thus, the largest negative value of the product is:−250

Smallest Possible Value of the Product
Since we can choose integers with repetitions allowed, we should include 0 in our product because any product involving 0 will be 0, which is the smallest possible product.

Therefore, the smallest possible value of the product of four integers chosen from this set is:
0⋅a⋅b⋅c=0
for any integers a, b, and c.

Thus, the smallest possible value is:0

Summary:
Smallest value: 0
Largest negative value: −250
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 08:03
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From the consecutive integers −2 to 5, inclusive, four integers are randomly chosen with repetitions allowed. Select the smallest possible value of the product of the 4 integers for Smallest value, and the largest negative value of the product of the 4 integers for Largest negative value.

Consecutive integers -2 to 5, inclusive = {-2,-1,0,1,2,3,4,5}

Smallest value = (-2) * 5*5*5 = -250

Largest negative value = -1*1*1*1 = -1


Smallest valueLargest Negative Value
-250-1
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 08:15
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smallest value and largest negative value will be the same

Pick 3 largest numbers, and one neg number with highest magnitude


value= 5.5.5.(-2)=-250

D, D
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 08:21
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The smallest value = (-2)*(5)^3 = -250 (obtained by multiplying the numbers which have the highest absolute value and result in negative too.)
The largest negative value = -1 = (-1)*(1)^3 = (1)*(-1)^3 (obtained by multiplying the numbers which have the lowest absolute value.)
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 08:31
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Smallest value for a product is -1 hence products of four integers is -1*-1*-1*-1=-1
Largest negative value for largest negative ie -2 implies -2*5*5*5=-250

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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 08:34
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Largest negetive value will be smallest digit with -ve sign.

So lets see if -1 is possible , 1,1,1,-1 will make -1

Also 5*5*5*-2 will make smallest -ve value of -250
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 08:40
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Bunuel
From the consecutive integers −2 to 5, inclusive, four integers are randomly chosen with repetitions allowed. Select the smallest possible value of the product of the 4 integers for Smallest value, and the largest negative value of the product of the 4 integers for Largest negative value.

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­The question  stem is difficult to understand.
Unable to understand part 1 .
The answer to part 2 is definitely -250.
Explain  elaborately
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 08:45
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Bunuel
From the consecutive integers −2 to 5, inclusive, four integers are randomly chosen with repetitions allowed. Select the smallest possible value of the product of the 4 integers for Smallest value, and the largest negative value of the product of the 4 integers for Largest negative value.

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The smaller number will be highest possible magnitude we can achieve but on the negative side.

The highest possible magnitude will be 5*5*5*5 but this will be positive. We can replace one of the 5s with -2 (the negative number with the highest magnitude) and we will then get:

Smallest value = \(-2*5*5*5 = -250\)

The largest negative value will be the negative value that is closest to 0. That means that the largest possible negative integer is -1 -> let's validate that we can achieve that.

Largest negative value = \(-1*1*1*1 = -1\) -> so yes, it is possible and therefore our answer.

The answers are:

Smallest value: -250
Largest negative value: -1­
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 08:45
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From the consecutive integers −2 to 5, inclusive, four integers are randomly chosen with repetitions allowed. Select the smallest possible value of the product of the 4 integers for Smallest value, and the largest negative value of the product of the 4 integers for Largest negative value.
-2,-1,0,1,2,3,4

from given options set can be ( -1,2,2,4) and (-2,5,5,5)

smallest possible value of the product of the 4 integers for Smallest value -250

the largest negative value of the product of the 4 integers for Largest negative value. -16

-250,-16
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 08:47
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IMO

Smallest value. -250 (5*5*5*-2)

Largest negative value -1 (-1*-1*-1*1)
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 08:53
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Smallest value =5*5*5*-2=-250
Largest negative value= 1*1*1*-1=-1
Ans D, A
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 08:53
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Bunuel
From the consecutive integers −2 to 5, inclusive, four integers are randomly chosen with repetitions allowed. Select the smallest possible value of the product of the 4 integers for Smallest value, and the largest negative value of the product of the 4 integers for Largest negative value.

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­Repetitions allowed 
Product of 4 integers for smallest value
and largest negative value of the product of 4 inteers for largest negative value
-2, -1, 0, 1, 2, 3, 4, 5

Smallest negative value is 5*5*5*-2= -250
Largest negative value is 1*1*1* -1= -1


 
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 09:00
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smallest possible value is possible when when we take 5*5*5* -2 = -250
largest possible negative integer value is -1, which can be obtained by selecting 1*1*1*-1

smallest possible value for the product is -250
largest possible negative product  value is -1

 
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 09:03
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Answer: Smallest: -250; Largest negative value: -1

For smallest we will have: -2*5*5*5 = -250

For largest negative value we will have: 1*1*1*-1 or -1*-1*-1*1 = -1.­
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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5 18 Jul 2024, 09:40
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1. -250
2. -1

1.Smallest value = 5*5*5*-2=-250 (also 625 is not possible at all so)
2. Largest -ve = out of them it is -1 = is it feasible = 1*1*1*-1= so yes.
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