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If x < 12, then it must be true that

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If x < 12, then it must be true that  [#permalink]

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New post 11 Oct 2013, 16:30
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Question Stats:

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If x < 12, then it must be true that

(a) -x < -12
(b) -x - 2 < 14
(c) -x + 2 < -10
(d) x + 2 < 10
(e) x - 2 < 11
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Re: If x < 12, then it must be true that  [#permalink]

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New post 11 Oct 2013, 16:38
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5
jlgdr wrote:
If x < 12, then it must be true that

(a) -x < -12
(b) -x - 2 < 14
(c) -x + 2 < -10
(d) x + 2 < 10
(e) x - 2 < 11



A. -x < -12 --> x>12. Not true.

B. -x - 2 < 14 --> x>-16. Not true, consider x=-20.

C. -x + 2 < -10 --> x>12. Not true.

D. x + 2 < 10 --> x<8. Not true, consider x=10.

E. x - 2 < 11 --> x<13. Since given that x<12, then x is for sure less than 13. Thus this statement must be true.

Answer: E.
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Re: If x < 12, then it must be true that  [#permalink]

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New post 15 Apr 2015, 08:54
Hi Bunuel,

x<12

From E,we get x<13 ,what if x is 12 .This contradicts the question x<12 right ?

Please clarify
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Re: If x < 12, then it must be true that  [#permalink]

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New post 15 Apr 2015, 09:06
2
janani28 wrote:
Hi Bunuel,

x<12

From E,we get x<13 ,what if x is 12 .This contradicts the question x<12 right ?

Please clarify


It's the other way around. We are told that x is less than 12 (it's given as a fact) and asked which of the options is true. Since x is less than 12, then it must be less than 13 too.
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Re: If x < 12, then it must be true that  [#permalink]

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New post 08 Oct 2017, 11:24
jlgdr wrote:
If x < 12, then it must be true that

(a) -x < -12
(b) -x - 2 < 14
(c) -x + 2 < -10
(d) x + 2 < 10
(e) x - 2 < 11



E wil always hold true.
But so will B???

if x=10, -12 <14 true.
if x=0, -2<14 true
if x=5, -7<14 true

Can someone pls explain where I am going wrong.
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Re: If x < 12, then it must be true that  [#permalink]

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New post 08 Oct 2017, 20:22
doeadoer wrote:
jlgdr wrote:
If x < 12, then it must be true that

(a) -x < -12
(b) -x - 2 < 14
(c) -x + 2 < -10
(d) x + 2 < 10
(e) x - 2 < 11



E wil always hold true.
But so will B???

if x=10, -12 <14 true.
if x=0, -2<14 true
if x=5, -7<14 true

Can someone pls explain where I am going wrong.


B gives: x > -16. If x is less than -16, B won't be right. For example, if x = -100 < 12, then B is not true.
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Re: If x < 12, then it must be true that  [#permalink]

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New post 08 Oct 2017, 23:15
Bunuel wrote:
jlgdr wrote:
If x < 12, then it must be true that

(a) -x < -12
(b) -x - 2 < 14
(c) -x + 2 < -10
(d) x + 2 < 10
(e) x - 2 < 11



A. -x < -12 --> x>12. Not true.

B. -x - 2 < 14 --> x>-16. Not true, consider x=-20.

C. -x + 2 < -10 --> x>12. Not true.

D. x + 2 < 10 --> x<8. Not true, consider x=10.

E. x - 2 < 11 --> x<13. Since given that x<12, then x is for sure less than 13. Thus this statement must be true.

Answer: E.


x<12
A. x<12
-x>-12

B. x<12
-x>-12 , -x -2 > -14

C. -x + 2 > -10

D. x + 2 < 14

E. x < 12 , So, x must be <13. This statement must be true.

Answer E
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Re: If x < 12, then it must be true that  [#permalink]

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New post 19 Jul 2018, 16:23
jlgdr wrote:
If x < 12, then it must be true that

(a) -x < -12
(b) -x - 2 < 14
(c) -x + 2 < -10
(d) x + 2 < 10
(e) x - 2 < 11


Let’s analyze each choice.

A) -x < -12

If we multiply both sides of x < 12 by -1, we will have -x > -12 (notice that we have to switch the inequality sign since we’ve multiplied by a negative number). So A is not correct.

B) -x - 2 < 14

Starting with x < 12, we have:

x < 12

-x > -12

-x - 2 > -14

We see that B is not correct either.

C) -x + 2 < -10

x < 12

-x > -12

-x + 2 > -10

We see that C is not correct either.

D) x + 2 < 10

x < 12

x + 2 < 14

We see that D is not correct either. So the correct answer must be E. But let’s verify it anyway.

E) x - 2 < 11

x < 12

x - 2 < 10

If x - 2 < 10, then x - 2 is less than 11 also. So E is correct.

Answer: E
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Re: If x < 12, then it must be true that &nbs [#permalink] 19 Jul 2018, 16:23
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