If xand yare non-negative integers,x+y11,andxy8, which of the following must be true for all the qualified values of x?a)y 3b)y 2c)2 y 10d)y 2e)y 1Correct answer is option 'E'. Can you explain this answer?

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If x and y are non-negative integers, x+y<11,andx−y>8, which of the following must be true for all the qualified values of x?

a)
y < 3
b)
y > 2
c)
2 < y < 10
d)
y < 2
e)
y < 1

Correct answer is option 'E'. Can you explain this answer?

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If xand yare non-negative integers,x+y<11,andx−y>8, whic...

Step 1: Question statement and Inferences:

We are given two linear inequalities:

x + y < 11 ............................(1)

x - y > 8 .............................(2)

where x and y are non-negative integers.

We have to find the option that is true for all the qualified values of x. Now, if we look at the options we get to know that we have to find the range of y. So, we need to eliminate the variable x from the inequalities so that we can get an inequality in x only.

To perform addition or subtraction options on the inequalities above, first we need to convert them into inequalities with the same sign.

So, by multiplying (2) with -1, we get:

- x + y < - 8 .......................(3)

Also, given that x and y are non-negative integers.

This implies, x and y can be 0 or positive integers.

Step 2: Finding required values

By adding (1) and (3),

y + y < 3

y<32

We know that y is a non-negative integer. So, the possible values of y are only 0 and 1.

Here, it seems that the answer should be option D. However, there is one more condition mentioned in the question. We have to find the value of y for all the qualified values of x.

Now, there are two cases:

Case I: y = 0

x + 0 < 11 .............................(1)

x < 11

x - 0 > 8 ...............................(2)

x > 8

So, x can take only two values i.e. 9 and 10.

Case II: y = 1

x + 1 < 11 ..............................(1)

x < 10

x - 1 > 8 ................................(2)

x > 9

So, per this case the value of x lies in between the integers 10 and 9. However, per the question statement x itself is an integer.

So, there is no integer value of x corresponding to y = 1.

Step 3: Calculating the final answer

Hence, the only possible value of y is 0. This condition is satisfied by option E.

Answer: Option (E)

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If xand yare non-negative integers,x+y<11,andx−y>8, which of the following must be true for all the qualified values of x?a)y < 3b)y > 2c)2 < y < 10d)y < 2e)y < 1Correct answer is option 'E'. Can you explain this answer?

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