If it is true that z -4, which of the following must be

Question

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

GMAT TIGER · Answer

Two points: 1) z < 8 2) 2z > -4 or z > -2 From 1 and 2: -2 < z < 8 (A) is not true because z could be > 4. (B) is not true because z could be < 2. (C) is true because z's value is always > -8. (D) is not true because z could be >4. (E) is not true because C is true.

prashantbacchewar · Answer

vibhaj
can you please post the detailed solution as well

Bunuel · Answer

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 -2-8 or in other words any z from -2

saxenashobhit · Answer

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

shrouded1 · Answer

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.

Bunuel · Answer

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.

Bunuel · Answer

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: -2-8 must be true. Answer: C.

surendar26 · Answer

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

Bunuel · Answer

We are told that -2-10 Answer is E (x>-10), because as x=5 then it's more than -10. Or: If -11 , 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 -11 then ANY x from these ranges would satisfy x>-1 . So B is always true. Hope it's clear.

KarishmaB · Answer

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.

Bunuel · Answer

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.

saurabhsavant · Answer

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

Bunuel · Answer

z can not be -7 because we are given that -2 -8, or z>-100000 would be true. Any z from -2

bumpbot · Answer

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

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