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# If |c| < 4 and d = 3c − 2, then which of the following must be true?

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If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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18 Feb 2019, 04:27
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45% (medium)

Question Stats:

61% (01:48) correct 39% (01:53) wrong based on 233 sessions

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If |c| < 4 and d = 3c − 2, then which of the following must be true?

A. −2 ≤ d < 10
B. d ≠ −2
C. d < 0
D. c < d
E. −14 < d

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If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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Updated on: 18 Feb 2019, 04:52
2
Bunuel wrote:
If |c| < 4 and d = 3c − 2, then which of the following must be true?

A. −2 ≤ d < 10
B. d ≠ −2
C. d < 0
D. c < d
E. −14 < d

for |c| < 4
c = +/- ( 0,1,2,3)
d= ( -5,-8,-11,1,7,4)

only option E sufficies
IMO E
-14<d
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Originally posted by Archit3110 on 18 Feb 2019, 04:35.
Last edited by Archit3110 on 18 Feb 2019, 04:52, edited 1 time in total.
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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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18 Feb 2019, 04:47
1
Bunuel wrote:
If |c| < 4 and d = 3c − 2, then which of the following must be true?

A. −2 ≤ d < 10
B. d ≠ −2
C. d < 0
D. c < d
E. −14 < d

Let C=0............d=-2..........Eliminate B, D

Let C =-3.........d=-11.........Eliminate A

Let C =3.........d=7.........Eliminate C

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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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18 Feb 2019, 04:48
Archit3110 wrote:
Bunuel wrote:
If |c| < 4 and d = 3c − 2, then which of the following must be true?

A. −2 ≤ d < 10
B. d ≠ −2
C. d < 0
D. c < d
E. −14 < d

for |c| < 4
c = +/- ( 1,2,3)
d= ( -5,-8,-11,1,7,4)

only option B sufficies
IMO B

Hi,

If C =0..........then b =-2...So choice B is incorrect
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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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18 Feb 2019, 04:52
Mo2men wrote:
Archit3110 wrote:
Bunuel wrote:
If |c| < 4 and d = 3c − 2, then which of the following must be true?

A. −2 ≤ d < 10
B. d ≠ −2
C. d < 0
D. c < d
E. −14 < d

for |c| < 4
c = +/- ( 1,2,3)
d= ( -5,-8,-11,1,7,4)

only option B sufficies
IMO B

Hi,

If C =0..........then b =-2...So choice B is incorrect

Mo2men
yes you are right ; i forgot to take 0
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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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18 Feb 2019, 04:53

-4<c<4

=> -12 < 3c< 12
=> -14 <3c-2 < 10

which gives only the E option
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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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18 Feb 2019, 08:01
Bunuel wrote:
If |c| < 4 and d = 3c − 2, then which of the following must be true?

A. −2 ≤ d < 10
B. d ≠ −2
C. d < 0
D. c < d
E. −14 < d

lcl < 4 --> -4<c<4 --> -14<3c-2<10

so only options (A) lies within this range, hence

correct me [quote="Bunuel"] ,if i am wrong.

Posted from my mobile device
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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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25 Feb 2019, 03:48
mahipal wrote:
Bunuel wrote:
If |c| < 4 and d = 3c − 2, then which of the following must be true?

A. −2 ≤ d < 10
B. d ≠ −2
C. d < 0
D. c < d
E. −14 < d

lcl < 4 --> -4<c<4 --> -14<3c-2<10

so only options (A) lies within this range, hence

correct me
Bunuel wrote:
,if i am wrong.

Posted from my mobile device

I did the same reasoning as you, show us the way to E for guaranteed kudos please
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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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25 Feb 2019, 04:11
paolodeppa
given
|c| < 4 ; so C can be +/-(1,2,3) & 0
now considering values of C test in d = 3c − 2
at c = 0 ; d=-2 ; so option B is out
c=1; d= 1 option C out
c=2;d=4option C out
c=3;d=7option C out
c=-1;d=-5 option d out
c=-2;d=-8 option d out
c=-3;d=-11 option A out

only option E is correct in this case i.e -14<d

hope this helps

paolodeppa wrote:
mahipal wrote:
Bunuel wrote:
If |c| < 4 and d = 3c − 2, then which of the following must be true?

A. −2 ≤ d < 10
B. d ≠ −2
C. d < 0
D. c < d
E. −14 < d

lcl < 4 --> -4<c<4 --> -14<3c-2<10

so only options (A) lies within this range, hence

correct me
Bunuel wrote:
,if i am wrong.

Posted from my mobile device

I did the same reasoning as you, show us the way to E for guaranteed kudos please

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If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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25 Feb 2019, 04:24
1
Bunuel wrote:
If |c| < 4 and d = 3c − 2, then which of the following must be true?

A. −2 ≤ d < 10
B. d ≠ −2
C. d < 0
D. c < d
E. −14 < d

|c|<4

-4<c<4.

d = 3c - 2 .

we will get the range of d if we put the extreme value of c.

d = 3*4 - 2 = 10

d = -4*3 - 2 = -14.

-14<d<10.

assess all the options .

A) Incorrect as per the range we have.

B) d ≠ −2. Nope. d could be -2.

C) d<0. not all the time. d<10.

D)c<d. Not always. could be true. what if d = -12 and c = 3.

E) -14<d. YES . part of the range. Matched.

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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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25 Feb 2019, 07:24
Archit3110 wrote:
paolodeppa
given
|c| < 4 ; so C can be +/-(1,2,3) & 0
now considering values of C test in d = 3c − 2
at c = 0 ; d=-2 ; so option B is out
c=1; d= 1 option C out
c=2;d=4option C out
c=3;d=7option C out
c=-1;d=-5 option d out
c=-2;d=-8 option d out
c=-3;d=-11 option A out

only option E is correct in this case i.e -14<d

hope this helps

Yeah I get this process you outlined above, however if we think about it in terms of ranges it becomes:
-14<d<10
and option A) specifically says -2<= d <10 so I can't see how it doesn't fit in -14<d<10
Please I need to know why option A) is wrong throughout ranges
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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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25 Feb 2019, 07:51
1
paolodeppa
how can values of D which range from -14<d<10
fit in to option A where range is given as -2<= d <10??
option A is till -2 only ; its not considering other values of d viz. -5,-8.....
which is why option A is wrong

paolodeppa wrote:
Archit3110 wrote:
paolodeppa
given
|c| < 4 ; so C can be +/-(1,2,3) & 0
now considering values of C test in d = 3c − 2
at c = 0 ; d=-2 ; so option B is out
c=1; d= 1 option C out
c=2;d=4option C out
c=3;d=7option C out
c=-1;d=-5 option d out
c=-2;d=-8 option d out
c=-3;d=-11 option A out

only option E is correct in this case i.e -14<d

hope this helps

Yeah I get this process you outlined above, however if we think about it in terms of ranges it becomes:
-14<d<10
and option A) specifically says -2<= d <10 so I can't see how it doesn't fit in -14<d<10
Please I need to know why option A) is wrong throughout ranges

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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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25 Feb 2019, 08:09
Archit3110 wrote:
paolodeppa
how can values of D which range from -14<d<10
fit in to option A where range is given as -2<= d <10??
option A is till -2 only ; its not considering other values of d viz. -5,-8.....
which is why option A is wrong

paolodeppa wrote:
Archit3110 wrote:
paolodeppa
given
|c| < 4 ; so C can be +/-(1,2,3) & 0
now considering values of C test in d = 3c − 2
at c = 0 ; d=-2 ; so option B is out
c=1; d= 1 option C out
c=2;d=4option C out
c=3;d=7option C out
c=-1;d=-5 option d out
c=-2;d=-8 option d out
c=-3;d=-11 option A out

only option E is correct in this case i.e -14<d

hope this helps

Yeah I get this process you outlined above, however if we think about it in terms of ranges it becomes:
-14<d<10
and option A) specifically says -2<= d <10 so I can't see how it doesn't fit in -14<d<10
Please I need to know why option A) is wrong throughout ranges

Oh I get it now, It's the other way around:
It's not that the options have to fit the interval instead all the values of d [-14;10] have to fit the options

so E
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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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02 Mar 2019, 09:15
Bunuel wrote:
If |c| < 4 and d = 3c − 2, then which of the following must be true?

A. −2 ≤ d < 10
B. d ≠ −2
C. d < 0
D. c < d
E. −14 < d

Since |c| < 4, then -4 < c < 4. So we have:

-12 < 3c < 12

-14 < 3c - 2 < 10

-14 < d < 10

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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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10 Mar 2019, 02:30
I did the same way, but doesn't our solution put an upper limit - d has to be less than 10?
If we ignore one of the limits then A should be right too.

ScottTargetTestPrep wrote:
Bunuel wrote:
If |c| < 4 and d = 3c − 2, then which of the following must be true?

A. −2 ≤ d < 10
B. d ≠ −2
C. d < 0
D. c < d
E. −14 < d

Since |c| < 4, then -4 < c < 4. So we have:

-12 < 3c < 12

-14 < 3c - 2 < 10

-14 < d < 10

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Posts: 12
Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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10 Mar 2019, 04:45
2
KomalSg

Though I got this question initially wrong ,as i too thought A is the answer , but it is the very common trap for MUST BE TRUE questions.

In order to get these questions right ,you have to change your thought process.

first solve the question, find the possible answer set for the question asked.
then w.r.t to the solution found ,preview all the answer choices one by one.

A. says that (−2 ≤ d < 10) but our answer is (−14 < d < 10),does the Option A covers all the possible values of "d" , no it still leaves some values of "d" smaller than -2 and bigger than -14,so it is not the correct answer.
Similarly B,C,D are all also understood.

Option E says "d">-14, this choice is true as all the possible values of "d" are bigger than -14 and this statement alone is 100 decent true.

regards,
Mahi..
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If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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12 Mar 2019, 05:14
Mo2men wrote:
Bunuel wrote:
If |c| < 4 and d = 3c − 2, then which of the following must be true?

A. −2 ≤ d < 10
B. d ≠ −2
C. d < 0
D. c < d
E. −14 < d

Let C=0............d=-2..........Eliminate B, D

Let C =-3.........d=-11.........Eliminate A

Let C =3.........d=7.........Eliminate C

I thought since we are dealing with a modulus of C so you cant let c=-3 meaning all the values of C have to be positive hence making A Correct. kindly correct me where am wrong
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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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12 Mar 2019, 06:44
bridgetnamugga

If i may,

I would like to bring few things to your understanding.
Here we are dealing with a modulus of C as well as C also.

mod of C can't be negative
but C can be negative as well as positive, there are no restrictions to it .

So as explained by Mo2men , you can very well take -3 as "C" since "C" lies between(-4,4).

Hope my understandings are clear to you.
If so do give kudos.

Regards,
Mahi..
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Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?  [#permalink]

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12 Mar 2019, 06:52
mahipal wrote:
bridgetnamugga

If i may,

I would like to bring few things to your understanding.
Here we are dealing with a modulus of C as well as C also.

mod of C can't be negative
but C can be negative as well as positive, there are no restrictions to it .

So as explained by Mo2men , you can very well take -3 as "C" since "C" lies between(-4,4).

Hope my understandings are clear to you.
If so do give kudos.

Regards,
Mahi..

Thanks for clearing my query
Re: If |c| < 4 and d = 3c − 2, then which of the following must be true?   [#permalink] 12 Mar 2019, 06:52
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