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number properties

by sud21 » Thu Jan 12, 2012 4:34 am
x and y are 2-digt integers. What is the difference between two tens' digit?
1). x-y=27
2). Units' digit of x minus the units' digit of y is greater than 3
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Source: — Data Sufficiency |
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by neelgandham » Thu Jan 12, 2012 8:11 am
x and y are 2-digt integers. What is the difference between two tens' digit?
let x = 10a + b and
let y = 10c + d, then the question can be rephrased to 'What is the value of |a-c| ?
1). x-y=27
x-y = 10(a-c) + (b-d) = 27
10(a-c) + (b-d) = 27 (We know -9<b-d<9)
a-c = 2, b-d = 7 and a-c = 3, b-d = -3 are the solutions.
Insufficent!
2). Units' digit of x minus the units' digit of y is greater than 3
b-d > 3 so (a-c) can be anything
Insufficent!

From 1 and 2
a-c = 2, b-d = 7 Hence sufficient C=[/spoiler][/quote]
Anil Gandham
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by ArunangsuSahu » Thu Jan 12, 2012 8:45 am
Let';s solve by Number plugging

Statement 1:
Case I: x=63,y=27
Case 2 x=37,y=10

INSUFFICIENT

Statement :
Case I: 99-90
Case 2:75-61

Combining (1) and (2) Case 2 of Statement 1 Becomes the only answer

(C) is the choice
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