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firas92
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01 Jul 2019, 12:20
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B
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Difficulty:
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Question Stats:
28% (02:39) correct
72%
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wrong
based on 155
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Three positive integers a, b and c leave the same remainder y when divided by x, where x is a prime number greater than 3 and y is an integer greater than 1. What is the remainder when x is divided by y?
(1) c + 3 when divided by x yields an integer
(2) a + x - 2 when divided by x yields an integer
(1) c + 3 when divided by x yields an integer
(2) a + x - 2 when divided by x yields an integer
WiziusCareers1
Joined: 27 Apr 2009
Last visit: 19 Nov 2025
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01 Jul 2019, 18:46
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Three positive integers a, b and c leave the same remainder y when divided by x, where x is a prime number greater than 3 and y is an integer greater than 1. What is the remainder when x is divided by y?
(1) c + 3 when divided by x yields an integer
(2) a + x - 2 when divided by x yields an integer
Pre-thinking on the question
x is an odd prime number
y is anything greater than 1.
Nothing much can be said from this information.
Considering Statement (1) alone:
Let c = 18, x = 7 => y = 4
So, when x is divided by y, the remainder is 3.
Let c = 12, x = 5 => y = 2
So, when x is divided by y, the remainder is 1.
INSUFFICIENT
Considering statement (2) alone:
Let a = 12, x = 5 => y = 2
So, when x is divided by y, the remainder is 1.
Let a = 5, x = 3 => y = 2
So, when x is divided by y, the remainder is 1.
Let a = 16, x = 7 => y = 2
So, when x is divided by y, the remainder is 1.
Clearly, the statement means that each of a, b, and c are 2 more than a multiple of x.
SUFFICIENT.
The answer is (B).
(1) c + 3 when divided by x yields an integer
(2) a + x - 2 when divided by x yields an integer
Pre-thinking on the question
x is an odd prime number
y is anything greater than 1.
Nothing much can be said from this information.
Considering Statement (1) alone:
Let c = 18, x = 7 => y = 4
So, when x is divided by y, the remainder is 3.
Let c = 12, x = 5 => y = 2
So, when x is divided by y, the remainder is 1.
INSUFFICIENT
Considering statement (2) alone:
Let a = 12, x = 5 => y = 2
So, when x is divided by y, the remainder is 1.
Let a = 5, x = 3 => y = 2
So, when x is divided by y, the remainder is 1.
Let a = 16, x = 7 => y = 2
So, when x is divided by y, the remainder is 1.
Clearly, the statement means that each of a, b, and c are 2 more than a multiple of x.
SUFFICIENT.
The answer is (B).
02 Jul 2019, 02:11
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a=y mod x
b= y mod x
c= y mod x
x>y and x>3
Statement 1
c+3=0 mod x
(y+3) mod x= 0 mod x
y=-3 or x-3
x=3 mod y when y>3
x= 1 mod y when y<3
insufficient
Statement 2
a + x - 2= 0 mod x
a-2= 0 mod x
(y-2) mod x= 0 mod x
y=2
As x is an odd number, x=1 mod 2
Sufficient
b= y mod x
c= y mod x
x>y and x>3
Statement 1
c+3=0 mod x
(y+3) mod x= 0 mod x
y=-3 or x-3
x=3 mod y when y>3
x= 1 mod y when y<3
insufficient
Statement 2
a + x - 2= 0 mod x
a-2= 0 mod x
(y-2) mod x= 0 mod x
y=2
As x is an odd number, x=1 mod 2
Sufficient
firas92
