If it is true that z < 8 and 2z > -4, which of the following must be

Can you please tell what part of GMAT TIGER's solution didn't you understand?

The point here is that \(z\) is between -2 and 8 (as \(z<8\) and \(2z>-4\) then \(-2<z<8\)). ANY \(z\) from this range satisfies option C: \(z>-8\) or in other words any \(z\) from \(-2<z<8\) is more than -8, so option C is always true.

Answer: C.

Why can't we say A is also true. If z lies between -2 and 8 then A is also true for all values if given range
-8 < z < 4

The question is what MUST be true, not what can be true.
A can be true only for that range but the range of z is bigger, so it is ruled out.

Not so. As \(-2<z<8\) then \(z\) could be more than 4, for example \(z\) could be 5, and in this case \(-8<z<4\) doesn't hold true. So A is not always true.

Note that we are asked which of the following MUST be true.

Given: \(z<8\) and \(2z>-4\), or dividing by 2 \(z>-2\). So we have: \(-2<z<8\).

Now, no matter what \(z\) actually is, since it's in the range \(-2<z<8\) then it'll definitely be more than -8, so C. \(z>-8\) must be true.

Answer: C.

If Z>-8,Z may be any value b/t -7 to infinity then -2<Z<8 condition will fail.

We are told that \(-2<z<8\), so this statement is GIVEN to be true. For example z might be -1, 0, 1.5, 5, ... ANY value of z from this (true) range \(-2<z<8\) will be more than -8.

So when you say that z might for example be -7 it's not true as \(-2<z<8\).

To elaborate more. Question uses the same logic as in the examples below:

If \(x=5\), then which of the following must be true about \(x\):
A. x=3
B. x^2=10
C. x<4
D. |x|=1
E. x>-10

Answer is E (x>-10), because as x=5 then it's more than -10.

Or:
If \(-1<x<10\), then which of the following must be true about \(x\):
A. x=3
B. x^2=10
C. x<4
D. |x|=1
E. x<120

Again answer is E, because ANY \(x\) from \(-1<x<10\) will be less than 120 so it's always true about the number from this range to say that it's less than 120.

Or:
If \(-1<x<0\) or \(x>1\), then which of the following must be true about \(x\):
A. x>1
B. x>-1
C. |x|<1
D. |x|=1
E. |x|^2>1

As \(-1<x<0\) or \(x>1\) then ANY \(x\) from these ranges would satisfy \(x>-1\). So B is always true.

Hope it's clear.

To understand this, take a real life example.

Her weight is more than 120 pounds but less than 130 pounds. Then which of the following is definitely true about her weight?
A. Her weight is 125 pounds.
B. Her weight is more than 110 pounds.

Isn't statement B definitely true about her weight? Since I know her weight is between 120 and 130 pounds, it is more than 110 pounds.

If it is true that z < 8 and 2z > -4, which of the following must be true?

(A) -8 < z < 4
(B) z > 2
(C) z > -8
(D) z < 4
(E) None of the above

\(z < 8\) and \(2z > -4\) (\(z>-2\)), --> \(-2<z<8\).

Only C is always true, as ANY x from the TRUE range \(-2<z<8\) will be greater than -8.


Answer: C.

Similar questions to practice:
if-it-is-true-that-x-2-and-x-7-which-of-the-following-m-129093.html
if-4x-12-x-9-which-of-the-following-must-be-true-101732.html

Hope this helps.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rule #3. Thank you.

hi, THANX FOR THE EXPLANATION, BUT Z>-8 WOULD INCLUDE -7 IN THE SOLUTION,WICH IS OBVIOUSLY NOT TRUE.....AND CAN WE ALSO SAY THAT Z>-1000000 OR ANY SUCH NUMBER IS THEREFORE ALWAYS TRUE

z can not be -7 because we are given that -2<z<8. So, it's vise-versa: since it's given that -2<z<8, then saying that z > -8, or z>-100000 would be true. Any \(z\) from \(-2<z<8\) is more than -8, or more than-10000000.

P.S. Please turn Caps Lock off when posting.

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