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01 Jun 2020, 03:25
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A
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Difficulty:
25%
(medium)
Question Stats:
77% (01:25) correct
23%
(01:37)
wrong
based on 850
sessions
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What is the sum of all possible integer values of p at which |6p + 33| has the least value?
(A) -11
(B) -6
(C) -5
(D) -1
(E) 1
(A) -11
(B) -6
(C) -5
(D) -1
(E) 1
01 Jun 2020, 03:26
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OFFICIAL EXPLANATION:
To find:
The sum of integer values of p at which |6p + 33| has the least value.
Approach:
We know that
Absolute value of any number ≥ 0
|6p + 33| ≥ 0
The least possible value is
|6p + 33| = 0
Solving this we get
6p = -33
p = -5.5
But we know that p is an integer.
So,
The lease possible value of |6p + 33| occurs at the integer value of p closest to -5.5
Integer values that are equally close to -5.5 is -5 and -6
So the possible integer values of p at which |6p + 33| has the least value is -5 and -6.
Therefore
Sum of all possible integer values integer values of p = -5 + -6 = -11
Alternate solution
|6p + 33| will have least value when 6p is closest to -33
As 6p is a multiple of 6,
The multiples of 6 that are closest to -33 is -30 and -36
This happens when p = -5 and -6
Sum of possible values of p is therefore,
-5 + -6 = -11
To find:
The sum of integer values of p at which |6p + 33| has the least value.
Approach:
We know that
Absolute value of any number ≥ 0
|6p + 33| ≥ 0
The least possible value is
|6p + 33| = 0
Solving this we get
6p = -33
p = -5.5
But we know that p is an integer.
So,
The lease possible value of |6p + 33| occurs at the integer value of p closest to -5.5
Integer values that are equally close to -5.5 is -5 and -6
So the possible integer values of p at which |6p + 33| has the least value is -5 and -6.
Therefore
Sum of all possible integer values integer values of p = -5 + -6 = -11
Alternate solution
|6p + 33| will have least value when 6p is closest to -33
As 6p is a multiple of 6,
The multiples of 6 that are closest to -33 is -30 and -36
This happens when p = -5 and -6
Sum of possible values of p is therefore,
-5 + -6 = -11
Correct Answer: Option A
General Discussion
shameekv1989
GMAT 3: 720 Q50 V38
Posts: 816
01 Jun 2020, 03:29
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coreyander
if p is integer so would be the value of |6p+33|
Least value would be 3 since multiple of 6 closest to 33 is 30 and 36 at which the values of p would be -5 and -6 and the value of modulus would be 3.
Thus p = -6, -5 => Sum = -11
Answer - A
