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16 Sep 2014, 01:22
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What is the product of three consecutive integers?
(1) At least one of the integers is positive.
(2) The sum of the integers is less than 6.
(1) At least one of the integers is positive.
(2) The sum of the integers is less than 6.
16 Sep 2014, 01:22
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Official Solution:
What is the product of three consecutive integers?
(1) At least one of the integers is positive.
We can have three cases:
(i) All three integers are positive. In this case, the product will obviously be positive.
(ii) Two of the integers are positive: {0, 1, 2}. In this case, the product will be zero.
(iii) Only one of the integers is positive: {-1, 0, 1}. In this case, the product will be zero.
Not sufficient.
(2)The sum of the integers is less than 6.
Clearly insufficient; consider {-1, 0, 1} and {-3, -2, -1}.
(1)+(2) The second statement implies that we cannot have case (i) from (1), since the least sum of three positive consecutive integers is 1+2+3=6. Thus, we have either case (ii) or case (iii). Therefore, the product of the integers is zero. Sufficient.
Answer: C
What is the product of three consecutive integers?
(1) At least one of the integers is positive.
We can have three cases:
(i) All three integers are positive. In this case, the product will obviously be positive.
(ii) Two of the integers are positive: {0, 1, 2}. In this case, the product will be zero.
(iii) Only one of the integers is positive: {-1, 0, 1}. In this case, the product will be zero.
Not sufficient.
(2)The sum of the integers is less than 6.
Clearly insufficient; consider {-1, 0, 1} and {-3, -2, -1}.
(1)+(2) The second statement implies that we cannot have case (i) from (1), since the least sum of three positive consecutive integers is 1+2+3=6. Thus, we have either case (ii) or case (iii). Therefore, the product of the integers is zero. Sufficient.
Answer: C
General Discussion
03 Oct 2014, 05:29
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(iii) Only one of the integers is positive: {-1, 0, 1}. In this case the product will be zero.
The above cam be replaced with
{-3, 1,5} in this case - assuming consecutive positive integers by a difference of 4 instead of difference by 1
sum of the integer is -3+1+5= 3<6
and product is -15 not equal to Zero
so This is answer D
correct me if I am wrong.
The above cam be replaced with
{-3, 1,5} in this case - assuming consecutive positive integers by a difference of 4 instead of difference by 1
sum of the integer is -3+1+5= 3<6
and product is -15 not equal to Zero
so This is answer D
correct me if I am wrong.
