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GMAT Club Olympics 2024 (Day 9): From the consecutive integers 2 to 5

1 2 3 4

BGbogoss

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The smallest possible value would be -2*5*5*5 =-250

The largest negative value would be -1:
-1*1*1*1

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Options: -2, -1, 0, 1, 2, 3, 4, 5

We have to select 4 integers

For smallest possible value: we have to maximize the product with a negative sign
since repetition is allowed, selections: 5 5 5 and -2
Product = -250

For largest negative value, same approach
Product = -250

Smallest value: - 250
Largest negative value: - 250

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Integers: -2, -1, 0, 1, 2, 3 ,4, 5

As there are positive and negative integers, the smallest value of the product must be negative.
We have to choose an odd number of negative integers (1 or 3). Also we have to maximize the absolute value of the product.
smallest value = 5*5*5*(-2) = -250

If the product can be -1 then the largest negative value will be -1.
largest negative value = 1*1*1*(-1) = -1

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Largest Negative value = smallest value = 5*5*5*(-2) = -250

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The least possible number is -250 (On taking 5 three times & multiplying that with the leafs number -2).

The max possible negative values is -1 by taking 1 three times & multiplying it by -1

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Answer:
Smallest value: -1
Largest negative value: -250

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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.

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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Screenshot_20240719_082017_Samsung Notes.jpg [ 103.43 KiB | Viewed 1016 times ]

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the possible values are -2,-1,0,1,2,3,4,5

For the smallest value, it has to have only one negative and it has to be -2 --> this leave us with the answers -16, -24 and -250.
Since there could be repetition, the smallest can be 5*5*5*-2 = -250

For the largest negative, it is -1, because it can be -1*1*1*1

Answer is D and A

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Bunuel

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

We have the following set of integers:
{-2, -1, 0, 1, 2, 3, 4, 5)

For Smallest value:
We’ll take the smallest negative -2, and 5^3, giving -250.

For Largest negative value[i],
The largest possible negative integer product is -1, so if we can make the product -1, that should be the answer, -1 * 1^3 works, giving -1.

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If the repetitions are allowed, I could pick in the following ways

5 * 5 * 5 * 5 = 625
-2 * -2 * -2 * -2 = 16
5 * 5 * 4 * 4 = 400

But we are asked for the smallest possible value of the product of the 4 integers,
Then we could pick in such a way that
5 * 5 * 5 * -2 = -250

From the given choices, rule out the possibility of -625 which is the smallest value in the answer choices.
-625 is not possible because it will need 4 fives and a minus sign.

We are asked for the largest negative value of the product of the 4 integers
Then we could pick in below way
1*1*1*-1 or -1*-1*-1*1
either way we get -1 as the largest negative value.

Therefore, smallest value is -250 and largest negative value is -1.

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In order to get the smallest possible value (which will actually be the same for the biggest negative value), we need to take the biggest possible product of 3 integers and make it negative.
The biggest product is obviosuly 5*5*5, and to make it negative, let's take the 'bigger' number of -2.
Therefore, $5^3*(-2) = -250$

And -250 is the answer for both columns.

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Consecutive integers −2 to 5 are ->>>>(-2,-1,0,1,2,3,4,5)
as Repetation allowed

Smallest possible value of the product of the 4 integers for Smallest value-->> 1*1*1*-1=-1

Largest negative value of the product of the 4 integers for Largest negative value-->> 5*5*5*-2=-250

Ans-AE.

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Numbers- -2,-1,0,1,2,3,4,5

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

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

Ans is

Smallest value=-250

Largest negative value=-1

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Quote:

We have following numbers available to pick: -2, -1, 0, 1, 2, 3, 4, 5

For the smallest value => A negative number with largest magnitude => 5*5*5*(-2) => -250

For the largest negative value => Closer to zero => (-1)*1*1*1 => -1

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The solution here is to actually write down the numbers.
The least number should be negative - so choose -2 as one of the numbers. Now, to make it as small as possible, we need to multiply it by largest positive number 5.
So, $-2*5*5*5=-250$
As for the largets negative value, it's easy to see it'll be $-1*1*1*1=-1$

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Smallest Value: $-2*5*5*5=-250$

Largest Negative Value: $-1*1*1*1=-1$

Answer -250 & -1

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Largest native number is -1, which can be derived by 1x1x1x-1
Smallest number can’t be -625 as -5^4 is not possible within the given range
However, -250 can be derived as 5 x5x5 x-2 . Hence smallest number is -250..

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Bunuel

To get the minimum value,
We can check the options

Lets consider -625
it is not possible to achieve the product -625 by selecting 4 numbers from the given range

Lets consider -250
this can be achieved by taking
5*5*5*-2 = -250

To find the greatest negative number,
we can check the options and see if those can be achieved
let's consider -1
we can get -1 by selecting the numebrs as
1*1*1*-1 = -1

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# set = -2,-1,0,1,2,3,4,5
Four integers are chosen, with repetitionallowed
Smallest value of product of 4 integers = smallest negative number = 5*5*5*(-2)=-250
Largest negative value = -1*1*1*1 0r -1*-1*-1*1= -1

Left column = D; Right column = A