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13 Nov 2022, 11:18
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
65% (01:19) correct
35%
(01:01)
wrong
based on 46
sessions
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What is the remainder when the positive integer x is divided by 4?
(1) There is no remainder when 2x is divided by 4.
(2) There is no remainder when x/2 is divided by 4.
(1) There is no remainder when 2x is divided by 4.
(2) There is no remainder when x/2 is divided by 4.
13 Nov 2022, 12:36
Kudos
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Statement 1
(1) There is no remainder when 2x is divided by 4.
It is given that when 2x is divided by 4, the remainder is 0. We cannot be certain that if the multiplication of 2 caused the no remainder or was it because x was a multiple of 4 to start with.
Ex.
Hence the statement is not sufficient and we can eliminate options A and D.
Statement 2
(2) There is no remainder when x/2 is divided by 4.
If x/2 doesn't leave a remainder when divided by 4, then x is a multiple of 4.
Hence x/4 will leave a remainder 0
Statement 2 is sufficient.
Option B
(1) There is no remainder when 2x is divided by 4.
It is given that when 2x is divided by 4, the remainder is 0. We cannot be certain that if the multiplication of 2 caused the no remainder or was it because x was a multiple of 4 to start with.
Ex.
- x = 2
Remainder = 2 - x = 4
Remainder = 0
Hence the statement is not sufficient and we can eliminate options A and D.
Statement 2
(2) There is no remainder when x/2 is divided by 4.
If x/2 doesn't leave a remainder when divided by 4, then x is a multiple of 4.
Hence x/4 will leave a remainder 0
Statement 2 is sufficient.
Option B
13 Nov 2022, 23:04
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Bunuel
(1) There is no remainder when 2x is divided by 4.
Given that 2x is divisible by 4 hence we can be sure that x is a multiple of 2. However, whether it is a multiple of 4 cannot be certain
Basically, this means that x can be all even numbers 2, 4, 6, 8, 10, 12...... etc
However, we can clearly see that 2, 6, 10.... etc would not be divisible by 4, while 4, 8, 12......etc would be.
Yes and No as answers.
Not sufficient.
(2) There is no remainder when x/2 is divided by 4.[/quote]
This suggests that x/2 is divisible by 4
This further implies 'x' must be a multiple of 8 to fulfill this condition
For eg for x/2 = 4, 8, 12....... we have x = 8, 16, 24 etc
Hence x is always divisible by 4 since it will be a multiple of 8
Sufficient.
Option B
