anksm22 wrote:if 0<r<1<s<2 which of the following must be less than 1?
a. r/s
b. rs
c. s-r
A a only
B b only
C c only
D a and b only
E a and c only
0 < r < 1.
1 < s < 2.
An alternate approach is to perform the 3 operations -- r/s, rs, and s-r -- using EVERY COMBINATION OF ENDPOINTS.
Here, there are four endpoints to consider:
lower limit for r = 0.
upper limit for r = 1.
lower limit for s = 1.
upper limit for s = 2.
a: r/s
(lower limit for r)/(lower limit for s) = 0/1 = 0.
(lower limit for r)/(upper limit for s) = 0/2 = 0.
(upper limit for r)/(lower limit for s) = 1/1 = 1
(upper limit for r)/(upper limit for s) = 1/2 = 1/2.
The smallest result -- 0 -- is the lower limit for r/s.
The greatest result -- 1 -- is the upper limit for r/s.
Thus:
0 < r/s < 1.
Since r/s must be less than 1, the correct answer choice must include a.
Eliminate B and C.
b: rs
(lower limit for r)/(lower limit for s) = 0*1 = 0.
(lower limit for r)/(upper limit for s) = 0*2 = 0.
(upper limit for r)/(lower limit for s) = 1*1 = 1
(upper limit for r)/(upper limit for s) = 1*2 = 2.
The smallest result -- 0 -- is the lower limit for rs.
The greatest result -- 2 -- is the upper limit for rs.
Thus:
0 < rs < 2.
Since rs does NOT have to be less than 1, the correct answer choice cannot include b.
Eliminate D.
c: s-r
(lower limit for s)/(lower limit for r) = 1-0 = 1.
(lower limit for s)/(upper limit for r) = 1-1 = 0.
(upper limit for s)/(lower limit for r) = 2-0 = 2.
(upper limit for s)/(upper limit for r) = 2-1 = 1.
The smallest result -- 0 -- is the lower limit for s-r.
The greatest result -- 2 -- is the upper limit for s-r.
Thus:
0 < s-r < 2.
Since s-r does NOT have to be less than 1, the correct answer choice cannot include c.
Eliminate E.
The correct answer is
A.
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
