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# If x, y, and z are integers, are x and y both less than z?

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If x, y, and z are integers, are x and y both less than z? [#permalink]
RatneshS wrote:
Vyshak wrote:
St1: |x| > z --> Not Sufficient as we do not have information about y

St2: z > y --> Not sufficient as we do not have information about x

Combining St1 and St2: |x| > z > y
Let x = 3, z = 2, y = 1 --> Are x and y both less than z? No
Let x = -3, z = 2, y = 1 --> Are x and y both less than z? Yes
The main culprit here is that x can be either positive or negative
Not Sufficient

Answer: E

Why is B not the answer?
question is is x<z and y<z

B says that y>z
which means that the answer of the question is No. why do we care about x?
suppose x>z or x<z...our conclusion still holds the same.

Please acknowledge

Hi,

St2 states that z > y. You have not interpreted the statement correctly. We need additional information about 'x' for St2 to be sufficient.
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If x, y, and z are integers, are x and y both less than z? [#permalink]
Vyshak wrote:
RatneshS wrote:
Vyshak wrote:
St1: |x| > z --> Not Sufficient as we do not have information about y

St2: z > y --> Not sufficient as we do not have information about x

Combining St1 and St2: |x| > z > y
Let x = 3, z = 2, y = 1 --> Are x and y both less than z? No
Let x = -3, z = 2, y = 1 --> Are x and y both less than z? Yes
The main culprit here is that x can be either positive or negative
Not Sufficient

Answer: E

Why is B not the answer?
question is is x<z and y<z

B says that y>z
which means that the answer of the question is No. why do we care about x?
suppose x>z or x<z...our conclusion still holds the same.

Please acknowledge

Hi,

St2 states that z > y. You have not interpreted the statement correctly. We need additional information about 'x' for St2 to be sufficient.

But it doesn't matter. Even if x<z, Statement 2 is sufficient to say both x and y are NOT less than z.

I would go with B as well.
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Re: If x, y, and z are integers, are x and y both less than z? [#permalink]
unverifiedvoracity wrote:

But it doesn't matter. Even if x<z, Statement 2 is sufficient to say both x and y are NOT less than z.

I would go with B as well.

Question asks whether both x and y are less than z i.e. whether x < z and y < z?

Lets look at St2: z > y --> Its as good as saying y < z
Now we know that y < z but is x < z? We don't know that.

If y < z and x < z then yes both x and y are < z
If y < z and x > z then no both x and y are not < z
Hence St2 is insufficient.
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Re: If x, y, and z are integers, are x and y both less than z? [#permalink]
Vyshak wrote:
unverifiedvoracity wrote:

But it doesn't matter. Even if x<z, Statement 2 is sufficient to say both x and y are NOT less than z.

I would go with B as well.

Question asks whether both x and y are less than z i.e. whether x < z and y < z?

Lets look at St2: z > y --> Its as good as saying y < z
Now we know that y < z but is x < z? We don't know that.

If y < z and x < z then yes both x and y are < z
If y < z and x > z then no both x and y are not < z
Hence St2 is insufficient.

my bad. I misread statement 2, I thought it was y > z. Thanks for clarifying.
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Re: If x, y, and z are integers, are x and y both less than z? [#permalink]
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If x, y, and z are integers, are x and y both less than z?

(1) |x|>z
(2) z > y

(1) ---- |x| > z

=> x > z or
-x > z
=>x < -z. Thus -z > x > z. Further value of y not known. NOT Sufficient

(2) value of x not know. NOT Sufficient

(1) + (2), x has two values. NOT Sufficient
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Re: If x, y, and z are integers, are x and y both less than z? [#permalink]
Why is the answer not A (Statement 1 alone is sufficient)? Since we know that x > z, and that is enough to decide that x and y are not both less than z, regardless of what y is. Since x > z and y < z, the answer would be no, and if x > z and y > z, the answer would also be no.
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Re: If x, y, and z are integers, are x and y both less than z? [#permalink]
Expert Reply
smui0603 wrote:
Why is the answer not A (Statement 1 alone is sufficient)? Since we know that x > z, and that is enough to decide that x and y are not both less than z, regardless of what y is. Since x > z and y < z, the answer would be no, and if x > z and y > z, the answer would also be no.

(1) says that |x| > z, implying the absolute value of x is greater than z, not x > z. Thus, there can be a case where x < z. For instance, consider x = -10 and y = 1.

Hope it helps.
Re: If x, y, and z are integers, are x and y both less than z? [#permalink]
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