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both are different two

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by sanju09 » Thu Aug 12, 2010 5:19 am
If a and b both are different two digit numbers and a - b = 11 x, is x an integer?

(1) The tens digit and units digit of a are the same.
(2) a + b is a multiple of 11.


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Source: — Data Sufficiency |
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by gig92 » Thu Aug 12, 2010 5:36 am
sanju09 wrote:If a and b both are different two digit numbers and a - b = 11 x, is x an integer?

(1) The tens digit and units digit of a are the same.
(2) a + b is a multiple of 11.


[spoiler]Source: freegmattest.net[/spoiler]

1) nothing about b, thus INSUFFICIENT

2) nothing about a and b individually, thus INSUFFI

From 1 and 2 combined,
and From question : a-b=11x

it is only possible if (b <0) though it is not given.

So from given a+b is mutilple of 11 (e.g a = 99 and b = -11 we have a+b = 110)

ANS: C
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by clock60 » Thu Aug 12, 2010 6:10 am
we need to know does (a-b)/11=x
or simply does a-b-multiple of 11
(1) from 1 we know that a is multiple of 11 ( a=10p+k, p=k=h, a=11h), but know info about b insuff
(2) (a+b)- multiple of 11 , a+b=11t, a=11t-b
11t-b-b=11t-2b we don`t k now the value of b, it can be multiple or can be not insuff
both
a-multiple of 11
and a+b also , so b must be multiple of 11
it means that (a-b)-multiple of 11 so suff
C
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