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Sub 505 (Easy)|   Absolute Values|   Inequalities|         
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12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| 21 Dec 2022, 07:00
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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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E
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12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| 21 Dec 2022, 07:13
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given

If x = 4p + 10 and |p| < 7
p = x-10 /4

l (x-10)/4)-7<0
case 1 :
x-10-28<0
x-38<0
x<38

case 2
-x+10-28<0
-x-18<0
-x<18
x>-18


Option E is correct -18 < x < 38

Bunuel
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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12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| 21 Dec 2022, 07:13
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-7<p<7;
x=4(p)+10;
4(-7)+10=-18
4(7)+10=38

x ranges from -18 to 38
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12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| 21 Dec 2022, 07:22
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From the absolute value concept, p ranges from -7<p<7, therefore consider -7 and 7 as the boundary values. Put in the boundary values of p in x=4p+10 and the boundary values of x will come out as -18 and 38.
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12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| 21 Dec 2022, 23:27
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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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12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| 22 Dec 2022, 06:56
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Given \(|p| < 7\)
i.e \(-7<p<7\)
\(-7*4<4p<7*4\) ( Multiplying by 4 )
\(-28<4p<28\)

\(-28+10<4p+10<28+10\) (Adding 10 )

\(-18<4p+10<38\)

Given \(x = 4p + 10 \)

=>\( -18<x<38\)

Answer - E. -18 < x < 38
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12 Days of Christmas GMAT Competition - Day 8: If x = 4p + 10 and |p| 24 Jan 2026, 00:13
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