Practice GMAT Data Sufficiency Question
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If both x and y are positive integers less than 100 and greater than 10, is the sum x + y a multiple of 11?
 x  y is a multiple of 22
 The tens digit and the units digit of x are the same; the tens digit and the units digit of y are the same
Correct Answer: B
 If both x and y are multiples of 11, then both x + y and x  y will be multiples of 11. In other words, if two numbers have a common divisor, their sum and difference retain that divisor.
In case this is hard to conceptualize, consider the following examples:
42  18 {both numbers share a common factor of 6}
=(6*7)  (6*3)
=6(7  3)
=6(4)
=24 {which is a multiple of 6}
49 + 14 {both numbers share a common factor of 7}
=(7*7) + (7*2)
=7(7+2)
=7*9
=63 {which is a multiple of 7}  However, if x and y are not both multiples of 11, it is possible that x  y is a multiple of 11 while x + y is not a multiple of 11. For example:
68  46 = 22 but 68 + 46 = 114, which is not divisible by 11.
The reason x  y is a multiple of 11 but not x + y is that, in this case, x and y are not individually multiples of 11. 
Evaluate Statement (1) alone.
 Since xy is a multiple of 22, xy is a multiple of 11 and of 2 because 22=11*2
 If both x and y are multiples of 11, the sum x + y will also be a multiple of 11. Consider the following examples:
44  22 = 22 {which is a multiple of 11 and of 22}
44 + 22 = 66 {which is a multiple of 11 and of 22}
88  66 = 22 {which is a multiple of 11 and of 22}
88 + 66 = 154 {which is a multiple of 11 and of 22}  However, if x and y are not individually divisible by 11, it is possible that x  y is a multiple of 22 (and 11) while x + y is not a multiple of 11. For example:
78  56 = 22 but 78 + 56 = 134 is not a multiple of 11.  Statement (1) alone is NOT SUFFICIENT.

Evaluate Statement (2) alone.
 Since the tens digit and the units digit of x are the same, the range of possible values for x includes:
11, 22, 33, 44, 55, 66, 77, 88, 99
Since each of these values is a multiple of 11, x must be a multiple of 11.  Since the tens digit and the units digit of y are the same, the range of possible values for y includes:
11, 22, 33, 44, 55, 66, 77, 88, 99
Since each of these values is a multiple of 11, y must be a multiple of 11.  As demonstrated above, if both x and y are a multiple of 11, we know that both x + y and x  y will be a multiple of 11.
 Statement (2) alone is SUFFICIENT.
 Since the tens digit and the units digit of x are the same, the range of possible values for x includes:
 Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT, answer B is correct.
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