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The numbers x and y are three-digit positive integers, and x

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The numbers x and y are three-digit positive integers, and x [#permalink] New post 27 Aug 2004, 06:22
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E

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67% (02:13) correct 33% (00:01) wrong based on 1 sessions
The numbers x and y are three-digit positive integers, and x + y is a four-digit integer. The tens digit of x equals 7 and the tens digit of y equals 5. If x < y, which of the following must be true?


I. The units digit of x + y is greater than the units digit of either x or y.
II. The tens digit of x + y equals 2.
III. The hundreds digit of y is at least 5.


A. II only
B. III only
C. I and II
D. I and III
E. II and III
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Re: PS: x+y [#permalink] New post 27 Aug 2004, 07:07
marine wrote:
The numbers x and y are three-digit positive integers, and x + y is a four-digit integer. The tens digit of x equals 7 and the tens digit of y equals 5. If x < y, which of the following must be true?


I. The units digit of x + y is greater than the units digit of either x or y.
II. The tens digit of x + y equals 2.
III. The hundreds digit of y is at least 5.


A. II only
B. III only
C. I and II
D. I and III
E. II and III


:?: :?: :!:

I. Not true: eg. 5+6 = 11 and 1< 5 or 6
II. Not true: if units digit sum is > 10, then tens digit = 3
III Not true: x+y needs to be greater than 999 and smaller than 1999. If y hundreds unit =5, x will be <5, and only if hundreds units of x is =, then x+ will have four digits. If x=3,2 or 1, then x+y will have three digits.


If III. were "The hundreds digit of x is at least 5" or the stem said "x>y" then III would be true.

Am I getting something wrong here??
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 [#permalink] New post 27 Aug 2004, 07:28
I believe the answer is B

If the hundred is less than 5 it is not possible to get 4 digits for x + y.

example:
y = 459 (highest possible with hundred digit 4.
x = 379 (highest possible when y has hundred digit 4).

x + y = 838

Correct me if I am wrong.

Regards,

Alex
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 [#permalink] New post 27 Aug 2004, 07:38
B. III Only.

Let Xh = hundredth digit of X. Xd = tenth digit of X. Similarly Yh and Yt for Y.

To get a sum of four digits from two three digit numbers, Xh+Yh should be >=10
You get a carry over of "1" from Xt+Yt (7+5="1"2)
S0, Xh+Yh >=9

Given that X<Y, Xhhas to be lesser than Yh, because the tenth digit of X (7) is greater than that of Y(5))
Hence, Y has to be >=5

For eg: Y=5, X=4 -- Correct
OR Y=6, X=3 -- Correct
OR Y=4, X=3 -- Wrong
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 [#permalink] New post 27 Aug 2004, 08:31
my guess is E

x=475 and y=550
x+y=1025 ..it satisfy 2nd and 3rd statement..

otherwise if we look into stem it says x's tens digit should be 7 and y's 5 if we add it should always be 2 (7+5=12)
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 [#permalink] New post 27 Aug 2004, 11:35
Neelam,

The tens digit of x + y doesnt have to be 2.
It can equal 2 but also it can equal 3. Therefore is not that it must be true.

Example:
x = 478, y = 559, x + y = 1037
x = 475, y = 550, x + y = 1025

Regards,

Alex
  [#permalink] 27 Aug 2004, 11:35
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