eiv ch. 6 #14 p. 101

[dhlee922]

if x and y are integers such that (x+1)^2 < 36 and (y-1)^2 < 64, what is the largest possible value of xy?

answer possibilities:

x = -7 y = -6, xy = 42
x = -7 y = 8, xy = -56
x = 5 y = -6, xy = -30
x = 5 y = 8, xy = 40

my question is that the question stem above asks for largest possible value, but the answer choice then mentions maximum value. does largest always mean maximum rather than minimum? or will gmat questions be more clear about max or min. because i feel that the largest value is actually -56


also, for optimization problems, when maximum or minimum is clearly stated in the question stem, does maximum always refer to positive value and minimum always refers to negative values?

thanks

[RonPurewal]

if x and y are integers such that (x+1)^2 < 36 and (y-1)^2 < 64, what is the largest possible value of xy?

answer possibilities:

x = -7 y = -6, xy = 42
x = -7 y = 8, xy = -56
x = 5 y = -6, xy = -30
x = 5 y = 8, xy = 40

my question is that the question stem above asks for largest possible value, but the answer choice then mentions maximum value. does largest always mean maximum rather than minimum? or will gmat questions be more clear about max or min. because i feel that the largest value is actually -56

"Largest"
"maximum"
"farthest to the right on the number line"
All the same.

also, for optimization problems, when maximum or minimum is clearly stated in the question stem, does maximum always refer to positive value and minimum always refers to negative values?

Not necessarily.
For instance, if a variable could be 3, 5, or 7, then the minimum value of that variable is 3, and the maximum value is 7.
If a variable could be -6, -4, or -1, then the minimum value of that variable is -6, and the maximum value is -1.

[dhlee922]

then i guess my follow up question is, would "smallest" number mean to the left of the number line, therefore negative? or is that a not necessarily case as well?

or is it if they want a negative value, they will clearly state "negative" value or "maximum/minimum value less than zero"

[RonPurewal]

"Smallest"
"minimum"
"least"
"farthest to the left on the number line"
All the same.


If you had the numbers -2, 1, and 3, then -2 is the smallest value.
1 has the smallest absolute value -- i.e., it's the "smallest" number if you ignore signs -- which seems to be the concept you have in mind. But that's not what smallest/least/minimum means.