If z + 7 > 2 and z - 3 < 5, then which of the following must be true? : Problem Solving (PS)

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14 Aug 2019, 03:59

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The answer is A .The range we get is -5<z<8 and only A covers that range

LeoN88

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14 Aug 2019, 05:44

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Bunuel

If z + 7 > 2 and z - 3 < 5, then which of the following must be true?

A. -6 < z < 8
B. -5 < z < 2
C. 2 < z < 5
D. 4 < z < 5
E. 5 < z < 8

Clearly -5<z<8,
Now z can be 7.9 so only options available A & E,
However z can also be -4.9 so A gives us the best representation.

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14 Aug 2019, 06:34

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I have a doubt aren't all options other than A valid
As we get -5<z<8
So b, c, d, e all are valid for sure

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LeoN88

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14 Aug 2019, 07:15

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itoyj

I have a doubt aren't all options other than A valid
As we get -5<z<8
So b, c, d, e all are valid for sure

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It's not asking for range; the question is asking under all possible circumstance which option must always be true.

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18 Aug 2019, 19:21

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Bunuel

If z + 7 > 2 and z - 3 < 5, then which of the following must be true?

A. -6 < z < 8
B. -5 < z < 2
C. 2 < z < 5
D. 4 < z < 5
E. 5 < z < 8

Simplifying each inequality, we have:

z > -5

and

z < 8

Thus:

-5 < z < 8, so A must be true.

(Note that the range of values for choice A is wider than the range of values for our calculated range of values. And choice A includes EVERY possible value that our calculated range includes (plus more). The concept can be easily visualized by using a number line, where you can see that every value in our calculated range is included in choice A’s range of values.)

Answer: A

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18 Aug 2019, 19:26

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Bunuel

If z + 7 > 2 and z - 3 < 5, then which of the following must be true?

A. -6 < z < 8
B. -5 < z < 2
C. 2 < z < 5
D. 4 < z < 5
E. 5 < z < 8

If z + 7 > 2 and z - 3 < 5, then which of the following must be true?
z>2-7=-5
z<5+3=8
\(-5 \leq z \leq 8\)

A. -6 < z < 8
B. -5 < z < 2
C. 2 < z < 5
D. 4 < z < 5
E. 5 < z < 8

If z>-5 => z>-6

IMO A

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25 Sep 2019, 23:13

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The range of z is -4 to 7 but according to option A) range is from -5 to 7. -5 should not be there, so why not go with option B) which also has 2nd maximum possible value range, can anyone please explain.

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27 Aug 2024, 04:55

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↧↧↧ Detailed Video Solution to the Problem ↧↧↧

Given that z + 7 > 2 and z - 3 < 5

z + 7 > 2
=> z > 2 - 7
=> z > -5 ...(1)

z - 3 < 5
=> z < 5 + 3
=> z < 8 ...(2)

Combining (1) and (2) we get
-5 < z < 8

Now, whichever answer choice is a superset of this range of z is the solution

A. -6 < z < 8 => This is a superset of -5 < z < 8 and covers all the values of z => TRUE
B. -5 < z < 2 => Does not cover the values of z from 2 to 8 => FALSE
C. 2 < z < 5 => Does not cover the values of z from -5 to 2 and from 5 to 8 => FALSE
D. 4 < z < 5 => Does not cover the values of z from -5 to 4 and from 5 to 8 => FALSE
E. 5 < z < 8 => Does not cover the values of z from -5 to 5 => FALSE

So, Answer will be A
Hope it helps!

Watch the following video to MASTER Inequalities

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04 May 2025, 13:14

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answer can't be A, since if z=-5.2 then the first inequality fails. Apart from option A, the other options can be true.

Krunaal

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04 May 2025, 13:40

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abcd1234!!

answer can't be A, since if z=-5.2 then the first inequality fails. Apart from option A, the other options can be true.

Since, z + 7 > 2 => z > -5 and z - 3 < 5 => z < 8

-5 < z < 8 => This tells us the z is a value that must be between -5 and 8

Now the question is asking, which of the below statements must be true?

Option A tells us z must be in between -6 and 8 => since we know that z is between -5 and 8, it also is in between -6 and 8, thus we can for sure say that this statement must be true.

Whereas in other option B won't hold true if z is 3, and option C, D, and E won't hold true if z is -1.

Hope it helps.

abcd1234!!

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04 May 2025, 13:47

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if z is between -5 and 8 how can we say it has to be between -6 and 8, like I stated, if we take z to be between -6 and 8, we can take z to be -5.2 or -5.4 etc and the first inequality fails.

Krunaal

abcd1234!!

answer can't be A, since if z=-5.2 then the first inequality fails. Apart from option A, the other options can be true.

Since, z + 7 > 2 => z > -5 and z - 3 < 5 => z < 8

-5 < z < 8 => This tells us the z is a value that must be between -5 and 8

Now the question is asking, which of the below statements must be true?

Option A tells us z must be in between -6 and 8 => since we know that z is between -5 and 8, it also is in between -6 and 8, thus we can for sure say that this statement must be true.

Whereas in other option B won't hold true if z is 3, and option C, D, and E won't hold true if z is -1.

Hope it helps.

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04 May 2025, 14:13

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Clearly -5<z<8,
but their is no a exact option

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abcd1234!!

if z is between -5 and 8 how can we say it has to be between -6 and 8, like I stated, if we take z to be between -6 and 8, we can take z to be -5.2 or -5.4 etc and the first inequality fails.

Krunaal

abcd1234!!

answer can't be A, since if z=-5.2 then the first inequality fails. Apart from option A, the other options can be true.

Since, z + 7 > 2 => z > -5 and z - 3 < 5 => z < 8

-5 < z < 8 => This tells us the z is a value that must be between -5 and 8

Now the question is asking, which of the below statements must be true?

Option A tells us z must be in between -6 and 8 => since we know that z is between -5 and 8, it also is in between -6 and 8, thus we can for sure say that this statement must be true.

Whereas in other option B won't hold true if z is 3, and option C, D, and E won't hold true if z is -1.

Hope it helps.

You cannot consider z as -5.2 or -5.4, since the question already mentions that z > -5, and anything > -5 is also > -6. In the options we are not redefining the value of z, but selecting a statement which holds true for the z we already have from the question.

Visualize a number line,

-10---------- -6 ------ -5 --z--z----- 0 ---z-------z-----z--- 8 --------------10

You will have to take z > -5 and < 8 as defined to us in qs., and then if someone asks you is z > -6, answer in yes/no, your answer will be yes.

If z + 7 > 2 and z - 3 < 5, then which of the following must be true?

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If z + 7 > 2 and z - 3 < 5, then which of the following must be true?

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