Data Sufficiency

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
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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-th ... 11112.html

Cheers,
Brent