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tagged by: BTGmoderatorLU

## A store sells erasers for 0.23$per piece and pencil for ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Veritas Prep A store sells erasers for 0.23$ per piece and pencil for 0.11$per piece. How many eraser and pencils did Jessica buy? 1) She bought 5 erasers. 2) She spent a total of 1.70$.

The OA is B

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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$. Statement 1: Since the number of pencils can be any nonnegative value, INSUFFICIENT. Statement 2: 23E + 11P = 170. This equation is constrained to nonnegative integers. Test a case that also satisfies Statement 1. If E = 5, we get: 23*5 + 11P = 170 115 + 11P = 170 11P = 55 P = 5. Thus, one solution for 23E + 11P = 170 is E=5 and P=5. Since the value of E may change only in increments of 11 -- the coefficient for P -- we get the following alternate options for E: 16, 27, 38... All of these alternate options for E will yield a sum greater than 170 and thus are not viable. Thus, the only viable solution for 23E + 11P = 170 is E=5 and P=5. SUFFICIENT. The correct answer is B. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1766 messages Followed by: 28 members Upvotes: 470 BTGmoderatorLU wrote: Source: Veritas Prep A store sells erasers for 0.23$ per piece and pencil for 0.11$per piece. How many eraser and pencils did Jessica buy? 1) She bought 5 erasers. 2) She spent a total of 1.70$.

The OA is B
Say Jessica bought x numbers of erasers and y x numbers of pencils.

Thus, she spent a total of 0.23x + 0.11y to buy (x + y) items.

We have to get the value of (x + y).

Let's take each statement one by one.

1) She bought 5 erasers.

No information about the numbers of pencils. Insufficient.

2) She spent a total of 1.70$. => 0.23x + 0.11y = 1.70 23x + 11y = 170 x = (170 - 11y)/23 x = (161 + 9 - 11y)/23 x = 161/23 + (9 - 11y)/23 x = 7 + (9 - 11y)/23 Since x and y are positive integers, 9 - 11y must be a multiple of 23. With some hit and trail, you'll find one eligible value for y = 5. At y = 5, we have x = 7 + (9 - 11y)/23 => x = 7 + (9 - 11*5)/23 => x = 7 + (9 - 55)/23 => x = 7 + (-46/23) => x = 7 - 2 = 5. So, one solution is x = y = 5, thus, x + y = 10. There is no need to try for higher qualified values of y since at higher values x would turn out to be negative, unqualified value. So, the unique value of x + y = 10. Sufficient. The correct answer: B Hope this helps! -Jay _________________ Manhattan Review Locations: Manhattan Review New Delhi | GMAT Prep Malleswaram | GRE Prep Vijayawada | Mumbai GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12655 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 This question illustrates a common trap on the GMAT. As Jay has shown, with statement 2, we're able to write the equation 23x + 11y = 170 , and in high school we learned that, if we're given 1 equation with 2 variables, we cannot find the value of either variable. However, if we restrict the variables to positive integers within a certain range of values, then there are times when we can, indeed, find the value of a variable if we're given 1 equation with 2 variables. Here's a very similar Official GMAT question to practice with: https://www.beatthegmat.com/why-does-the-variable-rule-not-apply-here-t111112.html Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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