x and y are positive odd integer. What is the remainder when the product of xy is divided by 18?
1)When x is divided by 9, the remainder is 3
2) y-1 is a multiple of 6
Interesting GMATFix Problem-46
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- arora007
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- goyalsau
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I think it should be E,
Am i correct?
Am i correct?
Saurabh Goyal
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It is ironic that your approach gives me an idea which proves the answer you suggest is correct but the reasoning presented by you is slightly off (I had solved it using brute force and come to C as well!)selango wrote:Clearly stmt1 and stmt2 alone not sufficient.
combining 1 and 2,
x=9a+3 (21,39,57,75...)
y-1=6b
y=6b+1 (7,13,19,25)
watever the combination we try the remainder is 3.
Pick C
x*y = (9a+3)*(6b+1) = 54a + 18b+9a + 3
When we divide this by 18, we get 0 remainders from the first two terms. As we know a is odd, let a = 2p+1 then the last two terms become 9*(2p+1) + 3 when divided by 18 this will always leave a remainder 12
Hence C
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- arora007
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OA is C
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- selango
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x=9a+3anantbhatia wrote:@MJAs we know a is odd, let a = 2p+1
why have you assumed a as odd?
Given X is odd.So a must be even in order for X to be odd.
So a=2p
Last 2 terms=18p+3[p=1,2...]
Sub any values of p u ll get remainder as 3
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if we pick numbers, we ger remainder 1 when xy is divided by 18.?mj78ind wrote:It is ironic that your approach gives me an idea which proves the answer you suggest is correct but the reasoning presented by you is slightly off (I had solved it using brute force and come to C as well!)selango wrote:Clearly stmt1 and stmt2 alone not sufficient.
combining 1 and 2,
x=9a+3 (21,39,57,75...)
y-1=6b
y=6b+1 (7,13,19,25)
watever the combination we try the remainder is 3.
Pick C
x*y = (9a+3)*(6b+1) = 54a + 18b+9a + 3
When we divide this by 18, we get 0 remainders from the first two terms. As we know a is odd, let a = 2p+1 then the last two terms become 9*(2p+1) + 3 when divided by 18 this will always leave a remainder 12
Hence C
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Hi..
Why cant the values of X be 12,21,30,39 and so on...
So considering this..
X=12,21,30,39....
Y=7,13,19,25 and so on...
Case 1:
xy ie. when x=12 and y =7
SO XY =84 and wen divided by 18 the remninder is 12
Case 2: x=21 and y =7
xy= 147 and wen divided by 18 the reminder is 3.
Pls help.
hz do i answer this.
Why cant the values of X be 12,21,30,39 and so on...
So considering this..
X=12,21,30,39....
Y=7,13,19,25 and so on...
Case 1:
xy ie. when x=12 and y =7
SO XY =84 and wen divided by 18 the remninder is 12
Case 2: x=21 and y =7
xy= 147 and wen divided by 18 the reminder is 3.
Pls help.
hz do i answer this.
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