GMAT Club Forum :: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| : Problem Solving (PS)

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12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\| https://gmatclub.com/forum/12-days-of-christmas-gmat-competition-day-8-if-x-4p-10-and-p-404321-20.html	Page 2 of 3

Author:	Bhartii [ 21 Dec 2022, 10:02 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
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

Author:	LeopardLiu [ 21 Dec 2022, 10:07 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
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

Author:	divyadna [ 21 Dec 2022, 10:47 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
\|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 Posted from my mobile device

Author:	kavitaverma [ 21 Dec 2022, 10:48 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
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

Author:	kratos0906 [ 21 Dec 2022, 11:16 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
\|p\|<7 means -7<p<7. x=4p+10 so, -74+10<x<74+10 -18<x<38. Hence, IMO E.

Author:	GautamKhanduja [ 21 Dec 2022, 11:26 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
\|p\| < 7 -7<p<7 -28<4p<28 -18<4p+10<38 Option E

Author:	Aks111 [ 21 Dec 2022, 11:48 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
\|p\|<7 => -7 < p < 7 x = 4p + 10 If p = 7 then x = 47+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

Author:	arya251294 [ 21 Dec 2022, 11:59 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
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.

Author:	snowbee15 [ 21 Dec 2022, 12:20 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
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

Author:	mysterymanrog [ 21 Dec 2022, 12:33 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
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.

Author:	limuengaoey [ 21 Dec 2022, 14:25 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
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

Author:

rajtare [ 21 Dec 2022, 15:56 ]

Post subject:

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

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

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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

Author:

HarshaBujji [ 21 Dec 2022, 18:11 ]

Post subject:

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

Bunuel wrote:

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for the 12 Days of Christmas Competition

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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

Author:	sampathgelam [ 21 Dec 2022, 19:49 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
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

Author:

Lizaza [ 21 Dec 2022, 23:27 ]

Post subject:

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

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.

Author:

Stanindaw [ 22 Dec 2022, 00:24 ]

Post subject:

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

Bunuel wrote:

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for the 12 Days of Christmas Competition

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

Posted from my mobile device

Author:	rahulp11 [ 22 Dec 2022, 01:15 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
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

Author:	Bekobod [ 22 Dec 2022, 02:44 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
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=47+10 => x=38 -18<x<38 Answer E

Author:	szcz [ 22 Dec 2022, 02:57 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
Based on given details -7<p<7 Hence x=4p+10 xmin=-18 and xmax=38 Hence answer E

Author:	Catman [ 22 Dec 2022, 03:24 ]
Post subject:	Re: 12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and \|p\|
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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