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21 May 2015, 05:43
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If x is a positive integer and 123 divided by x leaves a remainder of 3, what is the value of x?
(1) The remainder when 60 is divided by x is more than or equal to 60.
(2) x is a multiple of 60
(1) The remainder when 60 is divided by x is more than or equal to 60.
(2) x is a multiple of 60
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25 May 2015, 03:06
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Bunuel
If x is a positive integer and 123 divided by x leaves a remainder of 3, what is the value of x?
(1) The remainder when 60 is divided by x is more than or equal to 60.
(2) x is a multiple of 60
(1) The remainder when 60 is divided by x is more than or equal to 60.
(2) x is a multiple of 60
OFFICIAL SOLUTION:
If x is a positive integer and 123 divided by x leaves a remainder of 3, what is the value of x?
The stem says that 123 is 3 more than a multiple of 3: 123 = xq + 3, which gives 120= xq. Therefore x must be a factor of 120 greater than 3 (divisor, x, must be more than the remainder 3). So, x can be: 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 or 120.
(1) The remainder when 60 is divided by x is more than or equal to 60. The remainder, cannot be greater than the dividend, thus the remainder remainder when 60 is divided by x IS 60. Which implies that x is greater than 60. Hence x = 120. Sufficient.
(2) x is a multiple of 60.
x can be 60 or 120. Not sufficient.
Answer: A.
General Discussion
21 May 2015, 08:59
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Question stem : 123 divided by x leaves a remainder of 3
This means that
x * Q + 3 =123 ; where Q is quotient
x * Q = 120
x = 120 / Q
Since Q is an integer possible values of x are factors of 120: 120,60,40,30,24,20,15,12,10,8,6,5,4,2 (123 when divided by 3 &1 leaves no remainder )
Stmt 1 : The remainder when 60 is divided by x is more than or equal to 60.
60 when divided by the possible values of x should give a remainder of 60 or more than 60.
Only one value of x i.e. 120 qualifies. 60/120 gives a remainder of 60. All other values of x leaves a remainder less than 60.
Suff
Stmt 2: x is a multiple of 60.
x can be 60 or 120.
Not suff
Answer : A
Ambarish
This means that
x * Q + 3 =123 ; where Q is quotient
x * Q = 120
x = 120 / Q
Since Q is an integer possible values of x are factors of 120: 120,60,40,30,24,20,15,12,10,8,6,5,4,2 (123 when divided by 3 &1 leaves no remainder )
Stmt 1 : The remainder when 60 is divided by x is more than or equal to 60.
60 when divided by the possible values of x should give a remainder of 60 or more than 60.
Only one value of x i.e. 120 qualifies. 60/120 gives a remainder of 60. All other values of x leaves a remainder less than 60.
Suff
Stmt 2: x is a multiple of 60.
x can be 60 or 120.
Not suff
Answer : A
Ambarish
