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If x and y are integers between 10 and 99, inclusive, is (x

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If x and y are integers between 10 and 99, inclusive, is (x [#permalink] New post 24 Jul 2006, 04:46
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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 tens’ digit of x is 2 more than the units digit, and the tens digit of y is 2 less than the units digit.
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 [#permalink] New post 24 Jul 2006, 05:05
Picking A.
Statement A is sufficient enough to answer the question. Whatever be the numbers, the difference comes out to be 9.
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Trying hard to conquer Quant.

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 [#permalink] New post 24 Jul 2006, 06:51
Statement 1

Let a and b be the digits

The number can be represented as
x = 10a + b
y = 10b + a

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

Hence the number is always divisible by 9 --- Sufficient

Statement 2

This can be represented as

x = 10(a+2) + a { The tens? digit of x is 2 more than the units digit}
y = 10b + b - 2 { the tens digit of y is 2 less than the units digit }

hence
x - y = 10(a+2) + a - 11b + 2 = 11(a - b) + 18

Nothing can be deduced from this statement.

Hence "A"
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 [#permalink] New post 25 Jul 2006, 01:45
A.

1) Digits of x and y are same but in reverse order.

Lets say x = 12 then y = 21 Difference = 9 Suff
Lets say x = 22 then y =22 difference = 0 suff

2)Let unit digit of x be m
then x = 10(m+2) +m = 11m +20
Let unit digit of y be n
then y = 10(n-2) + n = 11n -20

x-y = 11m-11n+40

It can be divisible by 9 and may not be. Hence not suff
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 [#permalink] New post 25 Jul 2006, 01:56
A it is
From 1,
x=10a+b, y= 10b+a
x-y = 9a-9b = 9(a-b) SUFF
From 2,
x=10a+(a-2)
y=10b+(b+2)

x-y= 10a+a-2 - (10b+b+2)
=11a-2-11b-2
Insuff
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 [#permalink] New post 25 Jul 2006, 08:03
Thanks guys. Clear explanation. Yes. The OA is A.
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 [#permalink] New post 25 Jul 2006, 10:50
Answer: A

S1: Let m & n be the two digits

x = 10m + n
y = 10n + m

x-y = 9m -9n = 9(m-n)

As m and n are integers (x-y)/9 = m-n

Sufficient.

S2: Let x = 10m+n
& y = 10a+b

Given m = n+2
a= b-2

x= 11n+20
y = 11b-20

(x-y) = 11(n-b) + 40

Not sufficient.

Answer: A
  [#permalink] 25 Jul 2006, 10:50
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