12 cashews and 13 pears cost $43.50, while 8 cashews and 17 pears cos

Question

12 cashews and 13 pears cost $43.50, while 8 cashews and 17 pears cost $41.50. How much will 6 cashews and and 9 pears cost?

A $15.5
B $25.5
C $32.5
D $45.5
E $57.5

playthegame · Answer

chetan2u  any elegant solutions for this one, I went down the linear equations way and takes me time to get to solving for cost of 1 pear and cost of 1 cashew to get to the answer 25.5

Thanks!

Bunuel · Answer

12c + 13p = $43.5
8c + 17p = $41.5

Sum these two:

20c + 30p = $85

Multiply by 3/10:

6c + 9p = $85*3/10 = $8.5*3 = $25.5

Answer: B.

playthegame · Answer

Thanks for the solution, does this approach always apply? Meaning adding or subtracting the two will lead to a faster solution. For example how about this example?

12 pencils and 8 erasers cost $28, while 4 pencils and 16 erasers cost $27. How much will 2 erasers and 3 pencils cost?

Thanks again.

chetan2u · Answer

playthegame

In most scenarios it should but the answer would depend on the equations that you can make. 
In your example, 12 pencils and 8 erasers can be easily converted to 2 erasers and 3 pencils by dividing it by 4. Thus cost 28 too gets divided by 4. Hence, answer is 28/4 or 7.

chetan2u · Answer

12 cashews and 13 pears cost $43.50, while 8 cashews and 17 pears cost $41.50. How much will 6 cashews and and 9 pears cost?

A $15.5
B $25.5
C $32.5
D $45.5
E $57.5

Although shortest and best solution is as given by  Bunuel , one could eliminate options by a bit of logic.

12 cashews and 13 pears cost $43.50, Means 12/2 or 6 cashews and 13/2 or 7.5 pears cost $43.50/2 or 21.75$. Thus, an addition of just 1.5 pears should keep the answer slightly more than 21.75$. 
Similarly the other equation will give you 4 cashews and 8.5 pears cost as nearly $21. 
Only 25.5$ fits in.

Bunuel · Answer

Understanding  when and how to add/subtract inequalities  could indeed be very helpful in many cases. However, it's not a silver bullet for all inequality questions and cannot possibly be!

luisdicampo · Answer

Deconstructing the Question

Let the cost of one cashew be   c   and the cost of one pear be   p  .

Then the given information becomes

12c + 13p = 43.5

8c + 17p = 41.5

We need to find

6c + 9p

Step-by-step

Start with

12c + 13p = 43.5

8c + 17p = 41.5

Multiply the first equation by   2  :

24c + 26p = 87

Multiply the second equation by   3  :

24c + 51p = 124.5

Subtract:

25p = 37.5

p = 1.5

Substitute into

8c + 17p = 41.5

8c + 17(1.5) = 41.5

8c + 25.5 = 41.5

8c = 16

c = 2

Now compute

6c + 9p = 6(2) + 9(1.5) = 12 + 13.5 = 25.5

Answer: B

12 cashews and 13 pears cost $43.50, while 8 cashews and 17 pears cos

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

­12 cashews and 13 pears cost $43.50, while 8 cashews and 17 pears cos

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

12 cashews and 13 pears cost $43.50, while 8 cashews and 17 pears cos