If |c|

Question

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

Archit3110 · Answer

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

only option E sufficies
IMO E
-14<d

Mo2men · Answer

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

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

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

Answer: E

Mo2men · Answer

Hi,

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

Archit3110 · Answer

Mo2men 
yes you are right ; i forgot to take 0

kumarankit01 · Answer

answer must be E. -4 -12 < 3c< 12 => -14 <3c-2 < 10 which gives only the E option

mahipal · Answer

lcl < 4 --> -4 -14<3c-2<10 so only options (A) lies within this range, hence Answer is A) correct me ,if i am wrong. Posted from my mobile device

paolodeppa · Answer

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

Archit3110 · Answer

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

KSBGC · Answer

|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.

E is the correct answer.

paolodeppa · Answer

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

Archit3110 · Answer

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 · Answer

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   have to fit the options

so E

ScottTargetTestPrep · Answer

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

-12 < 3c < 12

-14 < 3c - 2 < 10

-14 < d < 10

Answer: E

KomalSg · Answer

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.

mahipal · Answer

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.

Hope my understandings help you, if so give me kudos .

regards,
Mahi..

bridgetnamugga · Answer

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

mahipal · Answer

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..

bridgetnamugga · Answer

Thanks for clearing my query

luisdicampo · Answer

Deconstructing the Question

We are given:

|c| < 4

This means:

-4 < c < 4

Also:

d = 3c - 2

The goal is to determine what must always be true about  d .

Step-by-step

Start with:

-4 < c < 4

Multiply all parts by  3 :

-12 < 3c < 12

Subtract  2 :

-14 < 3c - 2 < 10

Since  d = 3c - 2 , we get:

-14 < d < 10

Now evaluate the choices.

Choice A:  -2 ≤ d < 10

This is too restrictive, since  d  can be less than  -2 .

Choice B:  d ≠ -2

If  c = 0 , then  d = -2 , so this is false.

Choice C:  d < 0

Not always true, since  d  can be positive.

Choice D:  c < d

Not always true, depends on the value of  c .

Choice E:  -14 < d

This is always true.

Answer E

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

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GMAT Problem Solving (PS) Questions

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

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