kassim wrote:thank you for the explanation below is the exact question and in the question answers in the book they started with , a=5 when -2<= b<=3 before evaluate the statements, i want to know how they came up with these 2 numbers.
If a and b are integers and a= |b+2| + |3-b| , does a= 5 ?
1) b<3
2) b>-2
Is |b+2| + |3-b| = 5?
|x-y| = the DISTANCE between x and y.
Thus:
|b+2| = |b-(-2)| = the distance between b and -2.
|3-b| = the distance between 3 and b.
Question rephrased:
Is the sum of the distance between b and -2 and the distance between b and 3 equal to 5?
Draw a number line:
...........-2.....................................3................
The distance between -2 and 3 is 5.
If b>3, then the distance between b and -2 will be greater than 5.
If b<-2, then the distance between b and 3 will be greater than 5.
Thus, if b>3 or b<-2, then the answer to the question stem is NO: the sum of the two distances will NOT be equal to 5.
For the sum of the two distances to be equal to 5, b must be BETWEEN -2 and 3, inclusive:
............-2
<---|b+2|--->b
<---|3-b|--->3................
As the number line shows, when b is between -2 and 3, inclusive, the sum of the two distances is equal to 5.
Question rephrased: Is b between -2 and 3, inclusive?
Statement 1: b<3
Statement 2: b>-2
When the two statements are combined, we know that b is between -2 and 3.
SUFFICIENT.
The correct answer is
C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
