Integers

Both a, b, and c are 3-digits integers, where a=b+c. Is the hundreds' digit of number a equal to sum of that of b and c?

a = xyz
b= lmn
d =opq

so xyz = lmn +nop
i.e 100x + 10y +z = 100l + 10m +n + 100o + 10p +q

1). Tens' digit of a=tens' digit of b+tens' digit of c

i.e y=m+p

so we have

100x + 10p + 10m +z = 100l + 10m +n + 100o + 10p +q

100x +z =100(l+o) + n+q

we cant say z=n+q coz n+q may produce a carry
INSUFF

2). Units' digit of a=units' digit of b + units' digit of c

z= n + q

same as above we wont be able to conclude

INSUFF

combine

we have

100x +n + q =100(l+o) + n+q

so x = l+o

SUFF

C

The fastest line of analysis here would be

1) Tens' digit of a=tens' digit of b+tens' digit of c

This would be true only if tens' digit of b+tens' digit of c does not produce a carry

2) Units' digit of a=units' digit of b + units' digit of c
i.e again it does not produce a carry

so in that case sum of the hunderd's digit of b & c must be equal to that of a coz if not then it would be only if the sum produces a carry which would chabge the nos to 4 digit.

Arocks can u check the OA again.

sameer....your method is correct, however you assume that the sum of hundred's digit of B and C will give only a single digit hundred's place in A. What if there is a carry in the sum of hundred's digit??? we cant depict that info from the given stmts and SO the ans shld be E itself....

arocks...u come up wiith pretty good Qs...wht's the src for these man?? these types can come in real exam...

Hi jangojess,arocks
Well its given in the question that "a, b, and c are 3-digits integers" that's why I think it should be C coz if there is a carry then "a" would be 4 digit nos.

arocks the q says "Both a, b, and c are 3-digits integers" here both refers to a,b,c can u verify this.

u got it sameer...missed tht point...

I get the answer A


a = xyz
b= lmn
c =opq

The only way l + o can be equal to x is when there is no carry from m + p.

Thats exactly what statement 1 says.

Statement 2 tells us abt n + q and thats not sufficient info.

Hi Raul,
I think u are right it should be A, ya m+p should not produce a carry coz then m+p <> y, but this stmt also implicitly states that n + q should not produce a carry, otherwise m+p <> y, Stmt 2 explicitly states this, hence I was more keen for C, however Stmt 1 alone is sufficeint coz it enforces the condition on the units digit as well, so 2 is not explicitly reqd, Thanks for pointing out.

damn.....even i had the same ans....but got confused with sameer's equations and all those stuff...