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x is a non-negative integer less than 7 and y is a non-positive intege

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Carcass
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x is a non-negative integer less than 7 and y is a non-positive intege [#permalink] New post   22 Apr 2022, 02:00
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x is a non-negative integer less than 7 and y is a non-positive integer greater than -4. For how many cases is the sum of x and y less than 5?

A. 0
B. 9
C. 16
D. 23
E. 25

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E
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GreenlightTestPrep
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Re: x is a non-negative integer less than 7 and y is a non-positive intege [#permalink] New post   22 Apr 2022, 05:15
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Carcass wrote:
x is a non-negative integer less than 7 and y is a non-positive integer greater than -4. For how many cases is the sum of x and y less than 5?

A. 0
B. 9
C. 16
D. 23
E. 25


x is a non-negative integer less than 7
Possible values of x: 0, 1, 2, 3, 4, 5, 6

y is a non-positive integer greater than -4
Possible values of y: 0, -1, -2, -3

For how many cases is the sum of x and y less than 5?
Let's individually examine each possible value of y and determine the number of x-values that go to yield a sum that is less than 5.
If y = 0, then x can equal 0 to 4 inclusive (5 values)
If y = -1, then x can equal 0 to 5 inclusive (6 values)
If y = -2, then x can equal 0 to 6 inclusive (7 values)
If y = -3, then x can equal 0 to 6 inclusive (7 values)

So, the total number of cases: 5 + 6 + 7 + 7 = 25

Answer: E
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Kimberly99
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Re: x is a non-negative integer less than 7 and y is a non-positive intege [#permalink] New post   22 Feb 2023, 12:09
Hi Brent GreenlightTestPrep
Question given x is a non-negative integer less than 7 and y is a non-positive integer greater than -4.
So not sure why 0 is included here as thought 0 is neither positive nor negative?
Could you help clarify? Thanks Brent
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Re: x is a non-negative integer less than 7 and y is a non-positive intege [#permalink] New post   22 Feb 2023, 14:23
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x is a non-negative integer less than 7

means 1,2,3,4,5,6


zero is ZERO. Nothing.

it is neither POSITIVE nor NEGATIVE

in the portion above non-negative means positive
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Re: x is a non-negative integer less than 7 and y is a non-positive intege [#permalink] New post   23 Feb 2023, 00:03
Hi Carcass, thanks for your reply.
Sorry still not quite get it.
Basically x is positive and y is negative here.
If 0 is neither POSITIVE nor NEGATIVE, then my confusion is why is 0 being used here?
Thanks for your time again.
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x is a non-negative integer less than 7 and y is a non-positive intege [#permalink] New post   23 Feb 2023, 01:13
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Yes, I understand. Technically zero should be included but usually when a question like this is formulated the tendency is NOT to consider zero

Quote:
The real numbers can be partitioned into the positive real numbers, the negative real numbers, and zero. A real number is one and only one of those three possibilities. This is called "trichotomy." Non-negative (or, correspondingly, non-positive) means not negative (not positive), so zero or positive (zero or negative).

That is, non-negative includes zero whereas positive does not.

Edit for clarity:

Non-negative means zero or positive.

Non-positive means zero or negative.

That is, non-negative includes zero whereas positive does not and vice versa.


FROM MATH ON STACKEXCHANGE https://math.stackexchange.com/question ... n-negative
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Kimberly99
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Re: x is a non-negative integer less than 7 and y is a non-positive intege [#permalink] New post   23 Feb 2023, 01:22
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Wow what a twisted way of GRE maths language.
Get it now and thank you so much Carcass for great helps always.
Noted down these two lines to prevent any future confusion.

Non-negative means zero or positive.
Non-positive means zero or negative.
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Re: x is a non-negative integer less than 7 and y is a non-positive intege [#permalink]
23 Feb 2023, 01:22
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