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number properties

by sud21 » Thu Jan 12, 2012 4:49 am
X, y and z are three digits numbers, and x=y+z. Is the hundreds' digit of x equal to the sum of hundreds' digits of y and z?
1). the tens' digit of x equal to the sum of tens' digits of y and z
2). the units' digit of x equal to the sum of units' digits of y and z
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by neelgandham » Thu Jan 12, 2012 10:53 am
X, y and z are three digits numbers, and x=y+z. Is the hundreds' digit of x equal to the sum of hundreds' digits of y and z?
1). the tens' digit of x equal to the sum of tens' digits of y and z
Sufficient.
2). the units' digit of x equal to the sum of units' digits of y and z
Insufficient

IMO A
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by sud21 » Fri Jan 13, 2012 1:00 pm
neelgandham wrote:X, y and z are three digits numbers, and x=y+z. Is the hundreds' digit of x equal to the sum of hundreds' digits of y and z?
1). the tens' digit of x equal to the sum of tens' digits of y and z
Sufficient.
2). the units' digit of x equal to the sum of units' digits of y and z
Insufficient

IMO A
Can you explain a bit further.
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by pemdas » Fri Jan 13, 2012 1:10 pm
main assumption: all the numbers in this q. are positive
st(1) implies no additional unit is carried onto the hundred's digits of y and z. Sufficient.
st(2) no info about the ten's digits of y and z. Not Sufficient

a
sud21 wrote:X, y and z are three digits numbers, and x=y+z. Is the hundreds' digit of x equal to the sum of hundreds' digits of y and z?
1). the tens' digit of x equal to the sum of tens' digits of y and z
2). the units' digit of x equal to the sum of units' digits of y and z
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by ArunangsuSahu » Fri Jan 13, 2012 1:27 pm
Explanation for the answer Choice (A)

Statement 1:

tens digit of y+tens digit of z=tens digit of x

That means tens digit of x can not be 10 rather less than <10..(0 is different than 10)

so there is no carry of 1 to the Hundred's place

So ,
hundreds digit of y+hundreds digit of z=hundreds digit of x

(A) is Sufficient

Statement 2 :

Insufficient...follow the above process from Units Place

CASE I:
Unit digit of y=6, unit digit of z=9 gives 15..Carry 1 to ten's place

Tens digit of y=7, Ten's digit of z=9 gives (16+1)=17..carry 1 to the hundred's place...
So hundreds digit of y+hundreds digit of z=hundreds digit of x IS NOT VALID

Case II:
Unit digit of y=6, unit digit of z=3 gives 9..NO Carry to ten's place

Tens digit of y=5, Ten's digit of z=4 gives 9....NO carry to the hundred's place...

So,hundreds digit of y+hundreds digit of z=hundreds digit of x IS VALID

So No Definite Solution
(B) is INSUFFICIENT
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