Problem Solving

AAPL wrote:Gina and Tina's average grade is 23 points higher than Tina's grade. What is the difference between their grades?

A. 46
B. 23
C. 16
D. 15
E. 11.5

The OA is A.

Experts, I think that I can solve this PS question writing an equation,

G = grade of Gina.
T = grade of Tina.
$$\frac{\left(G+T\right)}{2}=23+T$$
$$\frac{\left(G+T\right)}{2}=23+T-->G+T=46+2T-->G-T=46$$
Is there a strategic approach to solve this question? Can any experts help, please? Thanks!

Your solution is perfect, AAPL!

Cheers,
Brent

AAPL wrote:Gina and Tina's average grade is 23 points higher than Tina's grade. What is the difference between their grades?

A. 46
B. 23
C. 16
D. 15
E. 11.5

We can let Gina and Tina's average grade = (g + t)/2. Since Gina and Tina's average grade is 23 points higher than Tina's grade:

(g + t)/2 = 23 + t

g + t = 46 + 2t

g = 46 + t

g - t = 46

Answer: A

Hi AAPL,

We're told that Gina and Tina's average grade is 23 points higher than Tina's grade. We're asked for the difference between their grades. This question involves a pattern that exists in ALL average questions that involve just 2 entities.

When you calculate the average of 2 numbers, the result will be in the exact 'middle' of the two numbers. For example, the average of 2 and 4 is (2+4)/2 = 3. The difference between the smaller value and the average is the SAME as the difference between the larger value and the average. Thus, the difference between the larger number and the smaller number is EXACTLY TWICE the difference between either number and the average.

Here, we know that the difference between the average and Tina's grade is 23 points; this means that the difference between the average and Gina's score is ALSO 23 points and the difference between Gina's score and Tina's score is 2(23) = 46

Final Answer: A

GMAT assassins aren't born, they're made,
Rich