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If the product of four different integers is -6, which of the followin
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17 Dec 2021, 06:58
17 Dec 2021, 06:58
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If the product of four different integers is -6, which of the following could be the smallest of these integers?
(A) -6
(B) -3
(C) -2
(D) -1
(E) 1
(A) -6
(B) -3
(C) -2
(D) -1
(E) 1
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Re: If the product of four different integers is -6, which of the followin
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17 Dec 2021, 07:27
17 Dec 2021, 07:27
1
Carcass wrote:
If the product of four different integers is -6, which of the following could be the smallest of these integers?
(A) -6
(B) -3
(C) -2
(D) -1
(E) 1
(A) -6
(B) -3
(C) -2
(D) -1
(E) 1
Let's check each answer choice, beginning with the smallest value...
(A) -6
So, we have (-6)(?)(?)(?) = -6
This means (?)(?)(?) = 1
Since the all of the integers must be DIFFERENT, that is no way for (?)(?)(?) to equal 1
Eliminate choice A
(B) -3
So, we have (-3)(?)(?)(?) = -6
Divide both sides by -3 to get: (?)(?)(?) = 2
In this case, notice that (1)(-1)(-2) = 2
So, the four numbers could be -3, -2, -1, and 1.
Answer: B
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Re: If the product of four different integers is -6, which of the followin
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17 Dec 2021, 09:05
17 Dec 2021, 09:05
1
In a case like this, assuming that the answer is negative, you're essentially trying to maximize the absolute value of the smallest number.
The simplest way to do that will be to make as many of the four numbers 1 as possible. However, since they have to be different, that means only one of hem can be four.
So I'd put x*y*z*1. Now note that we can also stick a -1 in here and that won't change the size.
That gives us x*y*(-1)*1, and the answer at this point is negative. The other two numbers must multiply to be +6.
Then, we could put in 2 and 3 OR -2 and -3 to make the -6. The smallest among these is -3. Answer B.
(As noted by GreenlightTestPrep, the only way you'll get the -6 as the lowest is if all the rest have absolute value 1, which means that even if you used -1 and 1 both, you'd have to repeat at least one of them.)
The simplest way to do that will be to make as many of the four numbers 1 as possible. However, since they have to be different, that means only one of hem can be four.
So I'd put x*y*z*1. Now note that we can also stick a -1 in here and that won't change the size.
That gives us x*y*(-1)*1, and the answer at this point is negative. The other two numbers must multiply to be +6.
Then, we could put in 2 and 3 OR -2 and -3 to make the -6. The smallest among these is -3. Answer B.
(As noted by GreenlightTestPrep, the only way you'll get the -6 as the lowest is if all the rest have absolute value 1, which means that even if you used -1 and 1 both, you'd have to repeat at least one of them.)
