Consider the following equation:
5x + 7y = 70.
If x and y are nonnegative integers, the following solutions are possible:
x=0, y=10
x=7, y=5
x=14, y=0.
Notice the following:
The value of x changes in increments of 7 (the coefficient for y).
The value of y changes in increments of 5 (the coefficient for x).
This pattern will be exhibited by any fully reduced equation that has two variables constrained to nonnegative integers.
BTGmoderatorLU wrote:Source: Veritas Prep
A store sells erasers for 0.23$ per piece and pencil for 0.11$ per piece. How many eraser and pencils did Jessica buy?
1) She bought 5 erasers.
2) She spent a total of 1.70$.
Statement 1:
Since the number of pencils can be any nonnegative value, INSUFFICIENT.
Statement 2:
23E + 11P = 170.
This equation is constrained to nonnegative integers.
Test a case that also satisfies Statement 1.
If E = 5, we get:
23*5 + 11P = 170
115 + 11P = 170
11P = 55
P = 5.
Thus, one solution for 23E + 11P = 170 is E=5 and P=5.
Since the value of E may change only in increments of 11 -- the coefficient for P -- we get the following alternate options for E:
16, 27, 38...
All of these alternate options for E will yield a sum greater than 170 and thus are not viable.
Thus, the only viable solution for 23E + 11P = 170 is E=5 and P=5.
SUFFICIENT.
The correct answer is
B.
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
