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26 May 2021, 16:48
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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:
75%
(hard)
Question Stats:
47% (01:55) correct
53%
(01:25)
wrong
based on 97
sessions
History
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Time
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Not Attempted Yet
x and y are two positive integers. Which number among x and y has more factors?
(1) x is a factor of y
(2) x^3<y^2
(1) x is a factor of y
(2) x^3<y^2
27 May 2021, 21:58
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x and y are two positive integers. Which number among x and y has more factors?
(1) x is a factor of y
(2) x^3<y^2
S1: x is a factor of y. but the question does not say x and y are distinct. if x=y, then they would have same number of factors.
Not sufficient
S2: x^3<y^2; this info clearly says x and y are distinct numbers. but the fact that y^2 is greater than x^3 does not necessarily mean it has more factors. y can be a very large prime number.
Not sufficient
S1 and S2: Sufficient. To complete S1, we only needed the info about the distinctness of x from y.
Answer is C
(1) x is a factor of y
(2) x^3<y^2
S1: x is a factor of y. but the question does not say x and y are distinct. if x=y, then they would have same number of factors.
Not sufficient
S2: x^3<y^2; this info clearly says x and y are distinct numbers. but the fact that y^2 is greater than x^3 does not necessarily mean it has more factors. y can be a very large prime number.
Not sufficient
S1 and S2: Sufficient. To complete S1, we only needed the info about the distinctness of x from y.
Answer is C
22 Aug 2022, 22:45
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Solution:
We are asked which positive integer x or y has more factors
Statement 1: x is a factor of y
If x is a factor of y then there might be cases where \(x = y\) and when \(x<y\)
For example, if y = 25 then x can also be 25 because 25 itself is also a factor of 25
Because of the case where \(x=y\), the number of factors of x will be equal to the number of factors of y
and because of the case where \(x<y\), the number of factors of x will be less than the number of factors of y
Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: \(x^3<y^2\)
This statement will not give us any information on the factors of x and y
Thus, statement 2 alone is also not sufficient
Combining:
From statement 1, we get that x is a factor of y
From statement 2, we have \(x^3<y^2\)
Since x is a factor of y, we can cancel the variables and say \(x<y\). This invalidates \(x=y\) case from statement 1
So, we can say that \(x<y\) and number of factors of x will be less than the number of factors of y
Hence the right answer is Option C
We are asked which positive integer x or y has more factors
Statement 1: x is a factor of y
If x is a factor of y then there might be cases where \(x = y\) and when \(x<y\)
For example, if y = 25 then x can also be 25 because 25 itself is also a factor of 25
Because of the case where \(x=y\), the number of factors of x will be equal to the number of factors of y
and because of the case where \(x<y\), the number of factors of x will be less than the number of factors of y
Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: \(x^3<y^2\)
This statement will not give us any information on the factors of x and y
Thus, statement 2 alone is also not sufficient
Combining:
From statement 1, we get that x is a factor of y
From statement 2, we have \(x^3<y^2\)
Since x is a factor of y, we can cancel the variables and say \(x<y\). This invalidates \(x=y\) case from statement 1
So, we can say that \(x<y\) and number of factors of x will be less than the number of factors of y
Hence the right answer is Option C
