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# If x and y are integers between 10 and 99, inclusive

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Manager
Joined: 28 Jun 2005
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If x and y are integers between 10 and 99, inclusive [#permalink]  06 Sep 2005, 11:57
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a. If x and y are integers between 10 and 99, inclusive, is (x-y)/9 an integer?
(1) x and y have the same two digits, but in reverse order.
(2) The tensâ€™ digit of x is 2 more than the units digit, and the tens digit of y is 2 less than the units digit.

b. Pam and Ed are in a line to purchase tickets. How many people are in the line?
(1) There are 20 people behind Pam and 20 people in front of Ed.
(2) There are 5 people between Pam and Ed.
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Re: DS [#permalink]  06 Sep 2005, 12:22
gotoknow3 wrote:
a. If x and y are integers between 10 and 99, inclusive, is (x-y)/9 an integer?
(1) x and y have the same two digits, but in reverse order.
(2) The tensâ€™ digit of x is 2 more than the units digit, and the tens digit of y is 2 less than the units digit.

b. Pam and Ed are in a line to purchase tickets. How many people are in the line?
(1) There are 20 people behind Pam and 20 people in front of Ed.
(2) There are 5 people between Pam and Ed.

a.
(1) is sufficient
(2) is insufficient since (x-y)/9 can yield an integer OR a non-integer
ANS: A

b.
(1) We do not know how many people are in between Pam and Ed -> insufficient
(2) We do not know how many people are ahead/behind of Pam/Ed
(1) + (2) Though at first this might seem to be sufficient Pam has been listed first the entire question; however, Ed could be also ahead of Pam, therefore, this is insufficient as well
ANS: E
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1) A is sufficient

take numbers 13, 31, 14, 41...they always are multiples of 9...

sufficient...
Manager
Joined: 06 Aug 2005
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For the first one, write :

x = 10a + b
y = 10b + a

x-y = 10a + b - 10b - a
x-y = 9a - 9b = 9 (a-b)
(x-y)/9 = a - b

a,b integers
Manager
Joined: 18 Aug 2005
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Location: Italy, Rome caput mundi
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A fort the first Q:

by picking u p a number 45 -54 32 -23 ecc...you always get 9

E for the second Q:

All the problem is resolved by remembering that we can't assume that Pam is in front of Ed nor the reverse.
If we do so we fall in the trap of the wording that put Pam first and Ed second, without giving the actual order....

Ciao
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B also is sufficicent below [#permalink]  01 Sep 2007, 14:30
24. If x and y are integers between 10 and 99, inclusive, is an integer?
(1) x and y have the same two digits, but in reverse order.
(2) The tens’ digit of x is 2 more than the units digit, and the tens digit of y is 2 less than the units digit.

As 53 -35 = 18, 42- 24 = 18 which is divisible by 9
B also is sufficicent below   [#permalink] 01 Sep 2007, 14:30
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