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26 May 2022, 03:05
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Difficulty:
35%
(medium)
Question Stats:
73% (01:26) correct
27%
(01:54)
wrong
based on 59
sessions
History
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If z is an integer greater than 1, is z even?
(1) 2z is not a factor of 8
(2) 3z/4 is a factor of 6
(1) 2z is not a factor of 8
(2) 3z/4 is a factor of 6
26 May 2022, 11:52
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Step 1: Analyse Question Stem
z is an integer greater than 1, therefore, z ≠ 1.
We have to find out if z is even.
This is a YES – NO type of DS question.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: 2z is not a factor of 8
The factors of 8 are 1, 2, 4 and 8.
As per the information given in statement 1, 2z cannot be equal to any of the above values.
However, it can be equal to any other integer values which are not factors of 12.
For example, 2z can be 6 or 12. Both of these numbers are not factors of 8.
If 2z = 6, z = 3. Is z even? NO.
If 2z = 12, z = 6. Is z even? YES.
The data in statement 1 is insufficient to answer the question with a definite YES or NO.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: \(\frac{3z}{4}\) is a factor of 6
The factors of 6 are 1, 2, 3 and 6.
So, \(\frac{3z }{ 4}\) should be equal to one or more of these values
If \(\frac{3z }{4}\) = 1, z = \(\frac{4 }{ 3}\), which is not valid since z is an integer as per the question.
If \(\frac{3z }{ 4}\) = 2, z = \(\frac{8 }{ 3}\), which is not valid since z is an integer as per the question.
If \(\frac{3z }{ 4}\) = 3, z = 4. Is z even? YES
If \(\frac{3z }{ 4}\) = 6, z = 8. Is z even? YES
Although there are two values for z, in both cases, z is even.
The data in statement 2 is sufficient to answer the question with a definite YES.
Statement 2 alone is sufficient. Answer option C and E can be eliminated.
The correct answer option is B.
z is an integer greater than 1, therefore, z ≠ 1.
We have to find out if z is even.
This is a YES – NO type of DS question.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: 2z is not a factor of 8
The factors of 8 are 1, 2, 4 and 8.
As per the information given in statement 1, 2z cannot be equal to any of the above values.
However, it can be equal to any other integer values which are not factors of 12.
For example, 2z can be 6 or 12. Both of these numbers are not factors of 8.
If 2z = 6, z = 3. Is z even? NO.
If 2z = 12, z = 6. Is z even? YES.
The data in statement 1 is insufficient to answer the question with a definite YES or NO.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: \(\frac{3z}{4}\) is a factor of 6
The factors of 6 are 1, 2, 3 and 6.
So, \(\frac{3z }{ 4}\) should be equal to one or more of these values
If \(\frac{3z }{4}\) = 1, z = \(\frac{4 }{ 3}\), which is not valid since z is an integer as per the question.
If \(\frac{3z }{ 4}\) = 2, z = \(\frac{8 }{ 3}\), which is not valid since z is an integer as per the question.
If \(\frac{3z }{ 4}\) = 3, z = 4. Is z even? YES
If \(\frac{3z }{ 4}\) = 6, z = 8. Is z even? YES
Although there are two values for z, in both cases, z is even.
The data in statement 2 is sufficient to answer the question with a definite YES.
Statement 2 alone is sufficient. Answer option C and E can be eliminated.
The correct answer option is B.
26 May 2022, 13:35
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Bunuel
From statement 1
2z is not a factor
Factors of 8= 1,2,4,8
Z>1
2 x 2= 4 (factor of 8) not considered
2 x 4= 8 (factor of 8) not considered
2 x 8= 16 ( even number and not a factor of 8)
Sufficient
From statement 2
3/4z is a factor of 6
Factors of 6= 1, 2,3,6
Z>1
3/4 x 2 =3/2 ( not an integer, not a factor of 6)
3/4 x 3=9/4 (not an integer, not a factor of 6)
3/4 x 6= 9/2 (not an integer, not a factor of 6)
Not sufficient
Answer A
Hopefully I'm correct
