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

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Bunuel
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The numbers x and y are three-digit positive integers, and x + y is a [#permalink] New post   20 Jan 2022, 08:00
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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
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The numbers x and y are three-digit positive integers, and x + y is a [#permalink] New post   25 Jan 2022, 03:15
Bunuel 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



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
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Re: The numbers x and y are three-digit positive integers, and x + y is a [#permalink] New post   25 Jan 2022, 04:41
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CEO2021 wrote:
Bunuel 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



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.
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Re: The numbers x and y are three-digit positive integers, and x + y is a [#permalink] New post   25 Jan 2022, 04:53
chetan2u wrote:
CEO2021 wrote:
Bunuel 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



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.


ohhh...Yesss

I somehow unable to figure that its asking for the 10th digit of only number Y

thanks :)
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Re: The numbers x and y are three-digit positive integers, and x + y is a [#permalink] New post   19 Feb 2022, 07:22
chetan2u Is there any particular method to solve such questions? I am able to solve it but it's almost always by trial and error approach which is time consuming. I would really appreciate if you could share some tips and tricks to solve similar question types. Thanks!
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Re: The numbers x and y are three-digit positive integers, and x + y is a [#permalink]
19 Feb 2022, 07:22
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