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# When X is divided by 7 the remainder is U, and when Y is

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When X is divided by 7 the remainder is U, and when Y is [#permalink]

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12 Sep 2008, 06:34
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When X is divided by 7 the remainder is U, and when Y is divided by 7 the remainder is V. What is the value of U+V ?

(1) X+Y is divisible by 7
(2) X-Y is divisible by 7
SVP
Joined: 07 Nov 2007
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Location: New York
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12 Sep 2008, 22:10
dancinggeometry wrote:
When X is divided by 7 the remainder is U, and when Y is divided by 7 the remainder is V. What is the value of U+V ?

(1) X+Y is divisible by 7
(2) X-Y is divisible by 7

X= 7k+U
Y= 7m+V

1)
X+Y = 7 (k+m)+U+V
which is divisible by 7
means U+V must be divisable 7 and also U<7 and V<7
so U+V=7

Sufficient
2)

X-Y = 7(k-m)+(U-V)
This is divisible by 7 when U-V is also divisible by 7
and also U<7 and V<7..

U-V must be zero. i.e U=V

U can be any number between 1 to 7
insuffcient

A
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Joined: 17 Jun 2008
Posts: 1397
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Kudos [?]: 226 [0], given: 0

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14 Sep 2008, 03:15
dancinggeometry wrote:
When X is divided by 7 the remainder is U, and when Y is divided by 7 the remainder is V. What is the value of U+V ?

(1) X+Y is divisible by 7
(2) X-Y is divisible by 7

say,X=7p+u
Y=7q+v
X+Y=7(p-q)+u+v
=> (1) u+v div by 7 => u+v=7
(2)u-v div by 7 => only when u=v then its possible hence multiple values

IMO A
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Director
Joined: 29 Aug 2005
Posts: 877
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Kudos [?]: 291 [0], given: 7

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24 Jan 2009, 13:28
x2suresh wrote:
dancinggeometry wrote:
When X is divided by 7 the remainder is U, and when Y is divided by 7 the remainder is V. What is the value of U+V ?

(1) X+Y is divisible by 7
(2) X-Y is divisible by 7

X= 7k+U
Y= 7m+V

1)
X+Y = 7 (k+m)+U+V
which is divisible by 7
means U+V must be divisable 7 and also U<7 and V<7
so U+V=7

Sufficient
2)

X-Y = 7(k-m)+(U-V)
This is divisible by 7 when U-V is also divisible by 7
and also U<7 and V<7..

U-V must be zero. i.e U=V

U can be any number between 1 to 7
insuffcient

A

I think, answer should be C.
If U and V each can be 0, neither of the statements by itself would be sufficient.
What do you think?
SVP
Joined: 07 Nov 2007
Posts: 1820
Location: New York
Followers: 30

Kudos [?]: 728 [0], given: 5

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24 Jan 2009, 13:59
botirvoy wrote:
x2suresh wrote:
dancinggeometry wrote:
When X is divided by 7 the remainder is U, and when Y is divided by 7 the remainder is V. What is the value of U+V ?

(1) X+Y is divisible by 7
(2) X-Y is divisible by 7

X= 7k+U
Y= 7m+V

1)
X+Y = 7 (k+m)+U+V
which is divisible by 7
means U+V must be divisable 7 and also U<7 and V<7
so U+V=7

Sufficient
2)

X-Y = 7(k-m)+(U-V)
This is divisible by 7 when U-V is also divisible by 7
and also U<7 and V<7..

U-V must be zero. i.e U=V

U can be any number between 1 to 7
insuffcient

A

I think, answer should be C.
If U and V each can be 0, neither of the statements by itself would be sufficient.
What do you think?

good point agreed.

when combined...

U=0 and V=0

U+V=0

C
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Re: Zumit DS 018   [#permalink] 24 Jan 2009, 13:59
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