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13 Jun 2023, 01:30
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C
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:
59% (01:23) correct
41%
(01:17)
wrong
based on 59
sessions
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If s denoted the number of terms in set S in which no term is zero. Is the product of all the terms in S negative?
(1) Half of the terms in S are negative
(2) 4 is a divisor of s
(1) Half of the terms in S are negative
(2) 4 is a divisor of s
Updated on: 28 Jun 2023, 06:23
Originally posted by 8.toastcrunch on 13 Jun 2023, 02:17.
Last edited by 8.toastcrunch on 28 Jun 2023, 06:23, edited 1 time in total.
Last edited by 8.toastcrunch on 28 Jun 2023, 06:23, edited 1 time in total.
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Statement 1: Half of the terms in S are negative.
From this statement, we know that exactly half of the terms in S are negative. However, this information alone does not provide any information about the product of all the terms in S or whether it is negative. For example, if the other half of the terms are positive, the product would be positive. On the other hand, if all the terms in S are negative, the product would be negative. Therefore, statement 1 is not sufficient to answer the question.
Statement 2: 4 is a divisor of s.
From this statement, we know that 4 is a divisor of s, which means s is divisible by 4. However, this information alone does not provide any information about the terms in S or their product. It is possible to have a combination of positive and negative terms in S that would result in a positive or negative product, regardless of whether s is divisible by 4. Therefore, statement 2 is not sufficient to answer the question.
Considering both statements together:
Sufficient
C
From this statement, we know that exactly half of the terms in S are negative. However, this information alone does not provide any information about the product of all the terms in S or whether it is negative. For example, if the other half of the terms are positive, the product would be positive. On the other hand, if all the terms in S are negative, the product would be negative. Therefore, statement 1 is not sufficient to answer the question.
Statement 2: 4 is a divisor of s.
From this statement, we know that 4 is a divisor of s, which means s is divisible by 4. However, this information alone does not provide any information about the terms in S or their product. It is possible to have a combination of positive and negative terms in S that would result in a positive or negative product, regardless of whether s is divisible by 4. Therefore, statement 2 is not sufficient to answer the question.
Considering both statements together:
Sufficient
C
13 Jun 2023, 05:57
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Bunuel
Given, s is No. of Terms in Set S where no term is 0.
To Find, Product of Terms is Negative or Positive
Basically we have to find if No. of Negative Terms are Even or Odd, As Product of even no. of Negative Numbers is Positive and odd no. of Negative Numbers is Negative
Statement 1 : Half of the terms in S are negative
From this we know that No. of Negative Terms is half=> s/2
But we do not know the nature of S,
for Example, if s=10, then s/2=5, Which Means Odd no. of Negative Numbers, ie. Negative Product,
Alternatively, if s=8, then s/2=4, Which Means even no. of Negative Numbers, ie. Positive Product
Hence, Statement 1 not sufficient
Statement 2 : 4 is a divisor of s
This Statement itself doesn't help much, we understand the nature of s better, but We still don't know value of S or No. of Negative Numbers, Not Sufficient
Statement 1 and 2 Combined :
Combining both helps the complication in Statement 1
Putting Values, s=8 => even no. of Negative Numbers, ie. Positive Product
s=12 => even no. of Negative Numbers, ie. Positive Product
Hence Correct Answer : C
