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20 Dec 2010, 10:08
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
55% (02:01) correct
45%
(01:52)
wrong
based on 182
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A number B is formed by reversing the two digit number A. What are the digits of A?
(1) Difference of A and B lies between 70 and 80
(2) B is a two digit number
(1) Difference of A and B lies between 70 and 80
(2) B is a two digit number
20 Dec 2010, 12:58
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surendar26
A number B is formed by reversing the two digit number A. What are the digits of A?
Every 2-digit number can be expressed as \(10x+y\), where \(x\) will be the tens digit (so between 1 and 9, note it can not be zero as in this case number won't be 2-digt anymore) and \(y\) will be the units digit (so between 0 and 9).
Given: \(a=10x+y\) and \(b=10y+x\).
(1) Difference of A and B lies between 70 and 80 --> \(70<(10x+y)-(10y+x)<80\) --> \(70<9(x-y)<80\) --> there is only one multiple of 9 in this range - 72, so \(9(x-y)=72\) --> \(x-y=8\) --> either \(x=9\) and \(y=1\) or \(x=8\) and \(y=0\), so either \(a=91\) or \(a=80\). Not sufficient.
(2) B is a two digit number --> just tells that \(y>0\). Not sufficient.
(1)+(2) As \(y>0\) then \(x=9\) and \(y=1\), so \(a=91\). Sufficient.
Answer: C.
17 Feb 2014, 07:23
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Can anybody clarify when they say difference of a and b , does it mean a-b or |a-b|
if difference of a and b means |a-b| then a could be 19 and b = 91 or a= 91 and b = 19
in both cases |a-b|= 72
in which case shouldn't the answer be E
if difference of a and b means |a-b| then a could be 19 and b = 91 or a= 91 and b = 19
in both cases |a-b|= 72
in which case shouldn't the answer be E
