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How many three-digit integers can be divided by 2 to produce a new integer with the same tens digit and units digit as the original integer?
A. None
B. One
C. Two
D. Three
E. Four
A. None
B. One
C. Two
D. Three
E. Four
21 Feb 2012, 01:11
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acid_burn
The tens and units digits of a three-digit integer must be 0: X00 (no digit gives the same digit when divided by 2 but 0: 0/2=0). Now, apart from this, X must be even because 300/2=150, not the same tens and units digits. Hence there are following three-digit integers possible: 200, 400, 600, and 800.
Answer: E.
02 Jul 2013, 17:05
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acid_burn
hi,
3 digit number divided by 2==>this will yield either a 2 digit number or a 3 digit number
case1:if it yields a 2 digit number
let three digit number =xyz
therefore 2 digit no.=yz===>as unit and tens digit are same
now
we can write :
100x+10y+z=2*(10y+z)
solving
100x = 10y+z
clearly this is not possible as LHS is a 3 digit number and RHS is a 2 digit number.
case 2: if it yields a 3 digit number lets say ayz
then we can write
100x+10y+z=2(100a+10y+z)
solving
100(x-2a)=10y+z
this is only possible if 10y+z =0...and x-2a=0
it means y=z=0..and x=2a
therefore possible values are
put a=1=>x=2=>number=200
a=2=>x=4=>number=400
a=3=>x=6=>number=600
a=4=>x=8=>number=800
a=5=>x=10=>number=1000(its a 4 digit hence not possible)
so only 4 numbers are possible.
