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19 Jul 2024, 01:12
Kudos
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From the question stem,
Available numbers = {-2, -1, 0, 1, 2, 3, 4, 5}
We need to find smallest possible value of the product of the 4 integers for Smallest value, and the largest negative value of the product of the integers for Largest negative value.
Repetation is allowed.
For smallest possible value,
We do know that smallest possible value will be negative.
And we want to make it as small as possible. So, let's start with -2.
Now, for other 3 numbers, we want to maximise their product so when multiplied with -2, they become smallest negative value.
Largest number is 5. So, if we take 5, 3 times then
\(5 * 5 * 5 = 125\)
And now multiplying with -2,
\(-2 * 125 = -250\)
No number can be replace in {-2, 5, 5, 5} which will give us smaller negative value than -250.
Answer - -250 for smallest
For largest negative value,
Among the optoins, largest negative value is -1. Can we get -1?
Yes we can.
If we take -1 odd number of times and take 1 for remaining available slots, we get -1 as final product.
For example,
Taking -1 1 time and 1 3 times = \((-1) * 1 * 1 * 1 = -1\)
No negative integer is larger than -1 as we can only take integers from the given set.
Answer - -1 for largest negative value
Available numbers = {-2, -1, 0, 1, 2, 3, 4, 5}
We need to find smallest possible value of the product of the 4 integers for Smallest value, and the largest negative value of the product of the integers for Largest negative value.
Repetation is allowed.
For smallest possible value,
We do know that smallest possible value will be negative.
And we want to make it as small as possible. So, let's start with -2.
Now, for other 3 numbers, we want to maximise their product so when multiplied with -2, they become smallest negative value.
Largest number is 5. So, if we take 5, 3 times then
\(5 * 5 * 5 = 125\)
And now multiplying with -2,
\(-2 * 125 = -250\)
No number can be replace in {-2, 5, 5, 5} which will give us smaller negative value than -250.
Answer - -250 for smallest
For largest negative value,
Among the optoins, largest negative value is -1. Can we get -1?
Yes we can.
If we take -1 odd number of times and take 1 for remaining available slots, we get -1 as final product.
For example,
Taking -1 1 time and 1 3 times = \((-1) * 1 * 1 * 1 = -1\)
No negative integer is larger than -1 as we can only take integers from the given set.
Answer - -1 for largest negative value
19 Jul 2024, 01:38
Kudos
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The answer to both is -250
taking 3 largest positives and multiplying it with the largest negative number will be the smallest number and the largest negative product of 4 numbers. Hence 5 x 5 x 5 x -2 = -250.
taking 3 largest positives and multiplying it with the largest negative number will be the smallest number and the largest negative product of 4 numbers. Hence 5 x 5 x 5 x -2 = -250.
19 Jul 2024, 02:32
Kudos
Bookmarks
Bunuel
Integers: -2, -1, 0, 1, 2, 3, 4, 5
Smallest Value = -2
Largest -ve value = -1
1st column: smallest possible value of the product of the 4 integers for Smallest value
\(Product = -2 * 5 * 5 * 5 = -250\)
2nd column: largest negative value of the product of the 4 integers for Largest negative value
\(Product = -1 * 1 * 1 * 1 = -1\)
