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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
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
25 Jan 2022, 03:15
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Bunuel
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. 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
Consider if x & Y are three digit nos and X+Y is 4 digit then
considering X= 370 & Y= 650
Statement I & II is not justified
& considering X= 379 & Y= 652
Statement III is not satisfied.
But the stem is asking "Must be TRUE"
@Experts chetan2u plz help
25 Jan 2022, 04:41
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CEO2021
Bunuel
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. 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
Consider if x & Y are three digit nos and X+Y is 4 digit then
considering X= 370 & Y= 650
Statement I & II is not justified
& considering X= 379 & Y= 652
Statement III is not satisfied.
But the stem is asking "Must be TRUE"
@Experts chetan2u plz help
Hi,
The statement III tells us that the hundreds digit of y is AT LEAST 5, so it can be 5, 6, 7, 8 or 9.
So even the example you have taken 652 will adhere to statement III.
x<y…..x-y<0
\(x+y\geq 1000\)
\(x+y+0\geq x-y+1000\)
\(2y\geq 1000\)
\(y\geq 500\)
As y is a three digit number y can be anything from 500 to 999.
