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Which of the following is/are true?

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Which of the following is/are true? [#permalink]

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New post 18 Sep 2017, 08:05
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Which of the following is/are true?

1. |3x-19|>5-x holds for all values of x.
2. There is no value of x for which |2x-10| <4-x holds.
3. -|5x-23| is negative for all values of x.

A. None
B. 1 only
C. 1&2 only
D. 1&3 only
E. 1,2 &3

Source - Expert's Global
[Reveal] Spoiler: OA

Kudos [?]: 19 [0], given: 40

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Joined: 02 Aug 2009
Posts: 4971

Kudos [?]: 5472 [2], given: 112

Re: Which of the following is/are true? [#permalink]

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New post 18 Sep 2017, 08:45
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Expert's post
ManishKM1 wrote:
Which of the following is/are true?

1. |3x-19|>5-x holds for all values of x.
2. There is no value of x for which |2x-10| <4-x holds.
3. -|5x-23| is negative for all values of x.

A. None
B. 1 only
C. 1&2 only
D. 1&3 only
E. 1,2 &3

Source - Expert's Global



hi..

you can easily discard option 3, as at some value it will be 0..
1. |3x-19|>5-x holds for all values of x.
x>5 will make the RHS negative but LHS will always be positive or 0 at x = 19/3.
so LHS>RHS.
At negative x the RHS will increase by just x whereas LHS will increase by 3x..
try any value and it will be TRUE


2. There is no value of x for which |2x-10| <4-x holds.
4-x will be negative for x>4, whereas |2x-10| will be POSITIVE
for all negative values of x, again LHS <RHS
try for 0 to 4 also, the statement will be TRUE

3. -|5x-23| is negative for all values of x.
At x = 23/5, -|5x-23|=0
hence FALSE

ans C
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Which of the following is/are true? [#permalink]

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New post 18 Sep 2017, 08:52
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1. |3x-19|>5-x holds for all values of x.
we can open module:
x>19/3, so 3x - 19 > 5 - x and x > 6 (=18/3) - ok
x=19/3, so 0 > 5 - 19/3 or 0>-4/3 - ок
x<19/3, so - 3x + 19 > 5 - x and 14 > 2x or x < 7 (21/3) - ok
The whole expresion is true


2. There is no value of x for which |2x-10| <4-x holds.
the module is positive, 4 - х will be postivie only for x < 4. We can easaly test value x = 1,2,3 and for x<=0 the module can be opened as -2x+10. From -2x+10 < 4 - x we recieve 6 < x and this contradicts the previous condition.

3. -|5x-23| is negative for all values of x.
it is not mentioned that x must be integer, so for x = 23/5 the expresion will be 0

answer C

Kudos [?]: 6 [1], given: 11

Which of the following is/are true?   [#permalink] 18 Sep 2017, 08:52
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