Difficult Math Problem #98 - Algebra

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800guy
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Topic: Difficult Math Problem #98 - Algebra
PostFri Feb 16, 2007 12:28 pm
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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

from diff math doc. oa coming after a few people reply. have a nice weekend!!
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banona
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PostFri Feb 16, 2007 1:59 pm
The numbers x and y are three-digit positive integers,
this can be translated to : x = X1X2X3 ; AND y= Y1Y2Y3

* AS x + y is a four-digit integer. This only means that (Y1+X1+1 ) > 10; PROVIDED that y>x; then hundreds digis of y is superior to hundreds digit of x; so the inequality in Blod becomes 2y>9. Then easily Y> ou equal to 5. ( III is true)

* The tens digit of x equals 7 and the tens digit of y equals 5. If x < y, we can not conclude that ten digits of the sum is 2 as it depends on the unit digits of x and y. So II is not true

* Units digit of x + y can be greater than units digit of either x or y but it's not necessary. Fr this, consider three digit numbers x= 552 and y= 579 . It's obvious that the unit digit of the sum is 1 and is inferior to the unit digit of both numbers;

III. The hundreds digit of y is at least 5. only this one is true


B. III only s the naswer

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PostFri Feb 16, 2007 2:46 pm
See Below

Last edited by guynoor on Fri Feb 16, 2007 2:51 pm; edited 1 time in total
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guynoor
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PostFri Feb 16, 2007 2:51 pm
guynoor wrote:
800guy 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

from diff math doc. oa coming after a few people reply. have a nice weekend!!
Suppose X = 275 and Y = 955
X + Y = 1230
Checking conditions in the answer choices........
Hence Answer = B
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800guy
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PostMon Feb 19, 2007 9:14 am
oa:

x= abc
y= def

x = a7c
y= b5f

x > y and x+y = wxyz.

I. The units digit of x + y is greater than the units digit of either x or y.

It can carryover one digit. False

II. The tens digit of x + y equals 2.

It can be 2 or 3. False

III. The hundreds digit of y is at least 5.

a+b+1 >= 10
a >b so a at least 5. True.

Ans: b
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