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# If 6 < (4 - x)/5, which of the following must be true?

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If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:00
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If $$6 < \frac{4 - x}{5}$$, which of the following must be true?

I. $$x < 26$$
II. $$|x + 19| > 7$$
III. $$|x| = -x$$

A. I only
B. II only
C. II and III only
D. I and II only
E. I, II and III only

 This question was provided by Crack Verbal for the Game of Timers Competition

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If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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Updated on: 10 Jul 2019, 11:25
3
Note that we are asked to determine which MUST be true, not could be true.

$$6 < \frac{(4-x)}{5}$$ next $$30<4-x$$ next $$x<-26$$

So we know as a fact that $$x<-26$$. Now, keeping this in mind we should find out which of the following will be true for $$x<−26$$

In other words, wtether any number less than $$-26$$ will make the following true?

I. $$x<26$$ Yes for this interval. Whatever less than $$-26$$ would also be less than $$26$$. Or we can just take any number from $$x<-26$$ and check whether it is true for $$x<26$$. For example, $$-50$$ is less than $$-26$$, now is $$-50$$ also less than $$26$$? Yes.

II. $$|x+19|>7$$ means that we have two cases. Case 1: $$x+19>7$$ or simplfied $$x>-12$$. Case 2: $$-x-19>7$$ or simplified $$x<-26$$. We are given that the second range is true ($$x<−26$$), so this inequality holds true.

III. $$|x|=−x$$ means that $$x\leq{0}$$. Whatever less than $$-26$$ is also less than $$0$$. Thus true. We can see that all the three hold true for $$x<-26$$.

Hence E
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Originally posted by JonShukhrat on 10 Jul 2019, 08:56.
Last edited by JonShukhrat on 10 Jul 2019, 11:25, edited 2 times in total.
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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:16
2
6<4-x/5 or x<-26

I. not possible
2. x>-12 or x<-26. Possible
3. Since x<-26 then |x|=-x. Possible.

Hence IMO C is the answer
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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:18
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$$If 6<\frac{(4−x)}{5}$$, which of the following must be true?
30<4-x
x<-26

I. x<26
If x<-26=>x<26 MUST BE TRUE
II. |x+19|>7
If x<-26, Let us take x = -26-y where y>0
|-26-y+19| = |-7-y|=|7+y| > 7 MUST BE TRUE
III. |x|=−x
If x<-26, Let us take x = -26-y where y>0
|x|= |-26-y| = 26+y = -x MUST BE TRUE

A. I only
B. II only
C. II and III only
D. I and II only
E. I, II and III only

All Statements I, II & III MUST BE TRUE
IMO E
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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:20
The equation given is 6<(4-x)/5
Which gives
X<-26 when we simplify it.

Therefore statement 1 is wrong.
The value of x can be <-26 so it can be something like -27,-28 and so on . If we add 19 to it and take mod of that it's always going to be more than 7 hence statement 2 is true.
Also value of x has to be negative so statement 3 also holds true.

Therefore the answer is c (2 and 3 only)

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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:26
2
4-x > 30
-x > 26

x < -26

Thus all 3 must be true

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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:26
C

From the given equality, we get x < -26

Clearly, first may not be true.

Second is always true, assume x < -19, so we get x+19<-7 or x < -26 (always true)
And, since x is negative third is always true as well.
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If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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Updated on: 10 Jul 2019, 23:26
6 < (4 - x)/5

30 < (4 - x)

x < 4 - 30 => x < -26

None of the options seem to satisfy this condition.

If option I is x < -26, then Option A would be the answer.

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Originally posted by prashanths on 10 Jul 2019, 08:29.
Last edited by prashanths on 10 Jul 2019, 23:26, edited 2 times in total.
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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:33
1
Solving the equation, we get x < -26
If x < -26, then x < 26
If x < -26, then |x + 19| > 7
If x < -26, then |x| = -x

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If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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Updated on: 10 Jul 2019, 08:42
from given relation 6<4-x/5 or say 30<4-x ; or we can say that -26>x so x has to be -27,-28.. so on

#1 x<26
this is true as -26>x so x>26 true always
#2
|x+19|>7
we get two ranges;
x<-26 and x>-12
we get both yes and no ; yes for -26>x and no for x>-12 as x can be +ve also
#3
|x|=−x
in this case x has to be -ve ; but not sufficient

IMO A

If 6<4−x56<4−x5, which of the following must be true?

I. x<26x<26
II. |x+19|>7|x+19|>7
III. |x|=−x

Originally posted by Archit3110 on 10 Jul 2019, 08:34.
Last edited by Archit3110 on 10 Jul 2019, 08:42, edited 1 time in total.
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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:35
Simplifying Question Stem we get x<-26
Therefore 1. is eliminated, eliminating A,D,E

Remaining B,C both has 2. Therefore verify only 3.
3 is True always since x<-26 x is also <0. Therefore, |x| = -x is always true. So, C
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If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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Updated on: 11 Jul 2019, 05:49
2
1
6<4-x/5 (multiply by 5)
30<4-x
4-x>30
-x>26
x<-26, we need to find for which of the following statements this subset falls into.
1) x<26, in this statement, all negative numbers are included, including anything lower than negative 26, thus this one is sufficient, must be true
2) |x+19|>7, we have two cases to solve
2.1) if x is positive, x+19>7, x>-12, but our x must be positive, hence no solution.
2.2) if x is negative, -(x+19)>7, -x-19>7, x<-26, this is exactly what we need to find if x is less than negative 26, and according to this statement, yes, x is less than negative 26. Must be true
3) x|=−x, from this we know that x is not positive, because any number on left will give positive result and to be equal to right, that number must be negative, so that two negatives cancel out and we have both sides positive or equal to 0. Since any number in this set is not positive, then anything less than negative 26 is also in this statement. Must be true

Originally posted by mira93 on 10 Jul 2019, 08:35.
Last edited by mira93 on 11 Jul 2019, 05:49, edited 4 times in total.
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If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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Updated on: 11 Jul 2019, 08:05
1
Given inequality simplifies to x<-26
1. <-26 means also less that 26. True
2. -26.1 +19 =.-7.1..Mod(-7.1) =7.1 Always true(as x+19 is always slightly less than -7 and it's mod always greater than 7
3. Since x is always negative, hence always true

Imo E
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Originally posted by saukrit on 10 Jul 2019, 08:36.
Last edited by saukrit on 11 Jul 2019, 08:05, edited 1 time in total.
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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:36
1
IMO E:

solving the inequality we get x< -26.
This implies from I, x<26
as x<-26, which means that x<26 must be true
from 2: |x+19|>7, given x<-26, distance between -26 and 9 is 7, and this will alwayys be greaater then 7, as x<-26.

from 3: |x| = - x, as x<0, this statement must be true.

Therefore all must be true.

E
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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:40
1
On solving the question stem we get: is x<-26 ?
Let's look at the options.
I. x<26x<26 - Clearly true. if x <26 then x will eventually be less than -26.
II. |x+19|>7|x+19|>7 - Solves to x<-26 & x>-12. Hence true again
III. |x|=−x - This implies x<0. TRUE
Therefore E. all 3 are correct
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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:44
1
If 6<4−x/5, which of the following must be true?

I. x<26
II. |x+19|>7
III. |x|=−x

$$6<(4-x)/5$$ ==> $$30 <4-x$$. ==> $$x<-26$$.

I . True. x is definetly less than 26.

II. |x+19|>7 can be written as X+19 >7 or X+19 < -7

X+19 < -7 ==> x <-26 . This is rephrase of Given statement.

III. Let x = -28 |-28| = -(-28) = 28 . TRUE.

Ans - E
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If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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Updated on: 10 Jul 2019, 08:48
1
x < -26

I Clearly always true for any given value of x

III l -28 l = - (-28), Always true

II. Let x be -26 then l 19-26 l is always 7, since x < -26 so the value of expression will always be >7. Must be true.

I, II and III true under all circumstance. E
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Originally posted by LeoN88 on 10 Jul 2019, 08:46.
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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:47
1
Quote:
If 6<(4−x)/5, which of the following must be true?

I. x<26
II. |x+19|>7
III. |x|=−x

A. I only
B. II only
C. II and III only
D. I and II only
E. I, II and III only

Assuming that the inequality is 6<(4−x)/5… 30-4<-x… x<-26;
I. x<26: this means that x can be anything less than 26 to -infinity, this is true.
II. |x+19|>7: then x>-12 (when x>0), or x<-26 (when x<0), but since x<0 always, then x<-26, true.
III. |x|=−x: since x<-26, then x<0… so, x=-|x| is true.

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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 08:51
6<(4-x)/5
30<4-x
x<-26

I. Is not true
Solving II which is |x+19|>7
yields x<-26, which is valid
And x>-12, which is rejected because it doesn’t satisfy the equation. Hence the answer is B.

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Re: If 6 < (4 - x)/5, which of the following must be true?  [#permalink]

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10 Jul 2019, 09:05
IMO-C

6<(4−x)/5
=> (4-x)>30
=> -x>26
=> x< -26

I. x<26--Incorrect
From above, x<-26
but x<26 need not be true as x cannot take any values between 26 to -26

II. |x+19|>7--- Correct
Now, x<-26
x+19<-7
|x+19|>7

III. |x|=−x- Correct
x<-26 (i.e x is negative)
for all negative numbers, |x|=-x

Therefore, II & III Satisfies the given condition.
Re: If 6 < (4 - x)/5, which of the following must be true?   [#permalink] 10 Jul 2019, 09:05

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