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x is an even integer.
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18 Sep 2018, 10:30
18 Sep 2018, 10:30
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76% (00:45) correct
23% (00:34) wrong based on 68 sessions
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x is an even integer.
Quantity A |
Quantity B |
The number of distinct prime factors of 4x |
The number of distinct prime factors of x |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: x is an even integer.
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18 Sep 2018, 22:19
18 Sep 2018, 22:19
1
Qty A is 4*x
Prime factor of 4 is 2.
Hence qty A is unique prime factors of x + 1(to account for 2 as a factor of 4)
However x is a even number which means x is definately a multiple of 2. Therefore we do not have to add extra 1
From this it follows that unique prime factors of 4x is same as the unique prime factors of x.
Prime factor of 4 is 2.
Hence qty A is unique prime factors of x + 1(to account for 2 as a factor of 4)
However x is a even number which means x is definately a multiple of 2. Therefore we do not have to add extra 1
From this it follows that unique prime factors of 4x is same as the unique prime factors of x.
Re: x is an even integer.
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19 Jul 2021, 10:21
19 Jul 2021, 10:21
2
Given that x is an even integer. So by default 2 is one of the prime factor of x.
Next I tried to identify pattern by assigning few values for x
Let
x= 6 {has 2 and 3 as prime factors}, then 4x = 24 {has only 2 and 3 as prime factors }
x= 10 {has 2 and 5 as prime factors}, then 4x = 40 {has only 2 and 5 as prime factors }
x = 14 {has 2,7 as prime factors}, then 4x = 56 {has only 2 and 7 as prime factors }
x= 30 {has 2,3 and 5 as prime factors} then 4x = 120 {has only 2,3 and 5 as prime factors }
Hence I concluded Number of prime factors are same for x and 4x
Therefor Quantity A = Quantity B
Next I tried to identify pattern by assigning few values for x
Let
x= 6 {has 2 and 3 as prime factors}, then 4x = 24 {has only 2 and 3 as prime factors }
x= 10 {has 2 and 5 as prime factors}, then 4x = 40 {has only 2 and 5 as prime factors }
x = 14 {has 2,7 as prime factors}, then 4x = 56 {has only 2 and 7 as prime factors }
x= 30 {has 2,3 and 5 as prime factors} then 4x = 120 {has only 2,3 and 5 as prime factors }
Hence I concluded Number of prime factors are same for x and 4x
Therefor Quantity A = Quantity B
