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18 Jul 2024, 06:59
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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)!
Difficulty:
45%
(medium)
Question Stats:
65% (01:42) correct
35%
(02:06)
wrong
based on 558
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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 |
ShowHide Answer
Official Answer
Smallest value: -250
Largest negative value: -1
18 Jul 2024, 07:02
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Bunuel
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.
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
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
