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12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p|

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Bhartii
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 10:02
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option E.
solving x=4p+10 we get p in terms of x:
p=x-10/4
then putting above equation of p in 2nd equation i.e modp<7
solving we get:
-18<x<38
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 10:07
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Kudos
Answer is E
If x = 4p + 10 and |p| < 7, which of the following represents the correct range of values of x ?

-7 < p < 7 --> -28 < 4p < 28 --> -18< 4p + 10 < 38
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 10:47
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Kudos
|p|=7
Therefore -7<p<7
x=4p+10
(-7)*4+10<x<(7)*4+10
-28+10<x<38
-18< x <38
Ans should be E

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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 10:48
1
Kudos
If x = 4p + 10 and |p| < 7, which of the following represents the correct range of values of x ?

A. -7 < x < 7
B. x > -18
C. x < 38
D. -38 < x < 18
E. -18 < x < 38
-----------------------------------------

IMO E

-7<p<7
at -7, x= -18
at 7, x=38

so, -18 < x < 38
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 11:16
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Kudos
|p|<7 means -7<p<7.

x=4p+10 so,
-7*4+10<x<7*4+10
-18<x<38.

Hence, IMO E.
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 11:26
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|p| < 7

-7<p<7
-28<4p<28
-18<4p+10<38

Option E
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 11:48
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Kudos
|p|<7 => -7 < p < 7

x = 4p + 10
If p = 7 then x = 4*7+10 = 28 + 10 = 38
If p = -7 then x = 4*-7+10 = -28 + 10 = -18

Hence, possible range of values of x => -18<x<38

Answer: E
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 11:59
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Kudos
Bunuel wrote:
12 Days of Christmas GMAT Competition with Lots of Fun

If x = 4p + 10 and |p| < 7, which of the following represents the correct range of values of x ?

A. -7 < x < 7
B. x > -18
C. x < 38
D. -38 < x < 18
E. -18 < x < 38


|p| tells that -7 < p < 7

substituting the min and max of p in the equation x = 4p + 10
gives us the answer - option E.
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 12:20
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Kudos
First of all based on the prompt |p| < 7 :
|p| can either be p or -p , so

Situation 1:
p < 7 --> good as it is

Situation 2:
-p<7 --> here based on the rules of inequalities we move the negative sign to the 7 and flip the inequality sign --> p> -7
so from the prompt we get -7< p < 7

then we have been told that x = 4p + 10 --> lets rearrange this to get p alone --> (x - 10) / 4 = p

putting this all together we get - 7 < (x-10)/4 < 7

Situation 1:
- 7 < (x-10)/4 --> multiply both sides by 4
-28 < x - 10 ---> add 10 to both sides
-18 < x

Situation 2:
(x-10)/4 < 7 --> multiply both sides by 4
x - 10 < 28 --> add 10 to both sides
x < 38

therefore, E is the answer which is all the above steps put together giving -18<x<38
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 12:33
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x=4p+10
x-10/4=p

Therefore abs(x-10/4)<7

Case 1:
x-10/4<7
x-10<28
x<38

Case 2:
-(x-10/4)<7
x-10/4>-7
x-10>-28
x>-18

combine the two
-18<x<38

E.
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 14:25
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If x = 4p + 10 and |p| < 7

given -7<p<7
then we put the p in the range in the equation above we will get;
4(-7)+10<x<4(7)+10
-18<x<38

hence, answer is E
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 15:56
1
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Bunuel wrote:
12 Days of Christmas GMAT Competition with Lots of Fun

If x = 4p + 10 and |p| < 7, which of the following represents the correct range of values of x ?

A. -7 < x < 7
B. x > -18
C. x < 38
D. -38 < x < 18
E. -18 < x < 38


 


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|P|<7 can be re-written as
-7<p<7

if p =-7, x = -28+10 =-18, i.e. since p is greater than -7, thus x will be greater than -18
if p = 7, x =28+10 =38, ie. since p is greater than 7, thus x will be greater than 38

-18<x<38

thus correct option is answer choice E
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 18:11
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Bunuel wrote:
12 Days of Christmas GMAT Competition with Lots of Fun

If x = 4p + 10 and |p| < 7, which of the following represents the correct range of values of x ?

A. -7 < x < 7
B. x > -18
C. x < 38
D. -38 < x < 18
E. -18 < x < 38


 


This question was provided by Experts'Global
for the 12 Days of Christmas Competition

Win $25,000 in prizes: Courses, Tests & more

 



If |p| < 7 => p can be from (-7,7).
x can be -18 in case of p = -7;

x can be 38 in case of p=7

Hence the range of x = (-18,38).

IMO E
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 19:49
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If x = 4p + 10 and |p| < 7,
Find correct range of values of x ?

the value of p is -7<p<7
hence the equation value of 4p+10
will be in between -18 and 38
-18<x<38
Hence option E i.e -18 < x < 38 is correct
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  21 Dec 2022, 23:27
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Kudos
To solve this, we just need to open the modulus for P:
\(|p| < 7\), which means \(-7 < p < 7\)

Now, the limiting values of the original expression will be:
  • \(4p + 10 = 4*(-7) + 10 = \)\(-18\)
  • \(4p + 10 = 4*(7) + 10 = \)\(38\)

And as P is strictly less, not equal to |7|, then X will never actually equal to those values, it will always remain in between:
\(-18 < x < 38\)

Therefore, the answer is E.
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  22 Dec 2022, 00:24
1
Kudos
Bunuel wrote:
12 Days of Christmas GMAT Competition with Lots of Fun

If x = 4p + 10 and |p| < 7, which of the following represents the correct range of values of x ?

A. -7 < x < 7
B. x > -18
C. x < 38
D. -38 < x < 18
E. -18 < x < 38


 


This question was provided by Experts'Global
for the 12 Days of Christmas Competition

Win $25,000 in prizes: Courses, Tests & more

 





p lies from -7 to 7
therefore x is -18 to 38

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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  22 Dec 2022, 01:15
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If x = 4p + 10 and |p| < 7, which of the following represents the correct range of values of x ?

\(|p| < 7 ⟹ -7 < p < 7\)

substituting the minimum and maximum values of p in x = 4p + 10

\(x > 4(-7) + 10 ⟹ x > -18\\
x < 4(7) + 10 ⟹ x < 38\)

A. -7 < x < 7
B. x > -18
C. x < 38
D. -38 < x < 18
E. -18 < x < 38- Correct
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  22 Dec 2022, 02:44
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If x = 4p + 10 and |p| < 7, which of the following represents the correct range of values of x?

To find the domain of x, first, it is essential to find the range of values of |p|<7. Finally, to substitute p in the equation with the beginning and the end values of the range of p.
-7<p<7

Min:x=4*(-7)+10 => x=-18
Max: x=4*7+10 => x=38
-18<x<38
Answer E
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  22 Dec 2022, 02:57
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Kudos
Based on given details
-7<p<7
Hence x=4p+10
xmin=-18 and xmax=38
Hence answer E
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink] New post  22 Dec 2022, 03:24
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Kudos
If x = 4p + 10 and |p| < 7, which of the following represents the correct range of values of x ?

-7 <p <7
4p will be -28 <p <28
4p+10 will be -18 <p < 38
Hence IMO E.
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Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| [#permalink]
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