请教OG13 DS133

jessie201237 · 发表于 2013-10-17 20:37:58

OG13 Ds133
133. If x, y, and z are three-digit positive integers and if
x = y + z, is the hundreds digit of x equal to the sum
of the hundreds digits of y and z ?
(1) The tens digit of x is equal to the sum of the tens
digits of y and z.
(2) The units digit of x is equal to the sum of the
units digits of y and z.
Letting * = 100a + 10b + c, y = lOOp + lOq + r,
and z = 100/ + 10a + v, where a, b, c,p, q, r, t, u,
and v are digits, determine if a =p + t.
(1) It is given that b= q+ u (which implies that
c + v < 9 because if c + v > 9, then in the
addition process a ten would need to be
carried over to the tens column and b would
be q+ u + 1). Since bis a digit, 0 < b< 9.
Hence, 0 <q+u<9, andso0 <10(q +u) <90.
Therefore, in the addition process, there are
no hundreds to carry over from the tens
column to the hundreds column, so a =p +t;
SUFFICIENT
(2) It isgiven that c=r+v. If * =687, y - 231,
and z =456,then,y +2; =231 +456=687=*,
r+v = l +6 = 7 =c, andp + t =2 +4 =6 =a.
On the other hand, if * =637, y =392, and
z =245, theny + z = 392 +245 =637 =*,
r+v =2 +5 = 7 =c, andp +t =3 +2 =5*
6 = a; NOT sufficient.
The correct answer is A;
statement 1 alone is sufficient.
----------------------------------------------请问各位大大，红色部分是怎么imply出来的呢，X=y+z不是应该是r+v≤9吗，怎么是C+v≤9呢？

cs944752731 · 发表于 2013-10-17 21:52:21

个人觉得应该是错了，应为c=r+v<=9,只有这样才合理, 才符合后面解释then in the addition process a ten would need to be carried over to the tens column and b would be q+u+1(个位数之和进十位数）

jessie201237 · 发表于 2013-10-20 16:32:33

cs944752731 发表于 2013-10-17 21:52
个人觉得应该是错了，应为c=r+v

恩恩，我也觉得错了，但毕竟是OG。。。
其他NN怎么看啊？

[原始] 请教OG13 DS133

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