MGMAT CAT question; plead for efficient solution!

[54siwei]

At a restaurant, a group of friends ordered four main dishes and three side dishes at a total cost of $89. The prices of the seven items, in dollars, were all different integers, and every main dish cost more than every side dish. What was the price, in dollars, of the most expensive side dish?

(1) The most expensive main dish cost $16.

(2) The least expensive side dish cost $9.

OA is A.

I read the answer explanations provided; however, the same method took me 4.5 minutes to solve this question.

Anyone could suggest a good way to solve this type of problems within 2 mins?

Thanks!

[mandhana.sourabh]

let the 4 main dishes be M1,M2,M3 and M4.
And 3 side dishes be S1,S2 and S3.

Given: M1,M2,M3,M4 > {S1,S2,S3} and
M1 + M2 + M3 + M4 + S1+ S2 + S3 = 89

Let M1 > M2 > M3 > M4 and
S1 > S2 > S3
QUESTION IS M1 = ?


using statement 1 alone:
M1 = 16
This directly answers the question of the cost of the most expensive side dish.
There can be various combinations for the other dishes, but that's not our our question.
Hence Statement 1 alone is sufficient.

Statement 2 alone: S3 = 9
Possible combinations : 16 + 15 + 14 + 13 + 12 + 10 + 9 = 89
20 + 14 + 13 +12 + 11 + 10 + 9 = 89
19 + 15 + 13 +12 + 11 + 10 + 9 = 89 etc..

Hence this statement alone is not sufficient.

Hence correct answer is A

[tim]

mandhana, you are answering the wrong question. the best way to solve this problem is first to find some numbers that actually work and then try to manipulate the numbers to get something else that works as well. if this process takes 4.5 minutes, you just need to get faster at adding the numbers..

[rkafc81]

hi - i'm having trouble setting up problems like this one using the methodology outlined in the Thursday's with Ron session titled "Organisation for Word Problems".

Can someone please explain how you would go about identifying the quantities, mathematical relationships and then forming a chart for this problem?

thanks!

[jlucero]

This isn't a great problem to set up algebraically, because you aren't trying to solve all of the different variables. Instead, you are trying to establish a relationship between seven unique prices.

[RonPurewal]

hi - i'm having trouble setting up problems like this one using the methodology outlined in the Thursday's with Ron session titled "Organisation for Word Problems".

Can someone please explain how you would go about identifying the quantities, mathematical relationships and then forming a chart for this problem?

thanks!

in this case, my version of a "chart" would just be seven blanks -- the first four representing the main dishes, the last three representing the side dishes.
then, left-to-right would represent decreasing order (since all the main dishes are more expensive).

from there, you would just start throwing numbers into the blanks, but the (admittedly simple) principle of "left = bigger, right = smaller" could be a game-changer.

[rkafc81]

ah cool, didn't think to solve it like that

thanks Ron

[jlucero]

Glad it helped

[nocheivyirene]

At a restaurant, a group of friends ordered four main dishes and three side dishes at a total cost of $89. The prices of the seven items, in dollars, were all different integers, and every main dish cost more than every side dish. What was the price, in dollars, of the most expensive side dish?

(1) The most expensive main dish cost $16.
(2) The least expensive side dish cost $9.

Main Side
_ _ _ _ _ _ _ = 89 with unique integers

(1) I plugged in 16 and without thinking much tried descending numbers

16 15 14 13 , 12 11 10 = 91, I have excess of 2. I made adj.
16 15 14 13 , 12 10 9 = 89, Nice! But is it always 12. Try 11.
16 15 14 13 , [11] 10 9 = 88, Then reducing it will trip off the balance of having 89 for its sum.

SUFFICIENT!

(2) I plugged in 9 and without think much just wrote ascending number from 9.

15 14 13 12 , 11 10 9

You can use the pattern on statement (1) to quickly get the total. Compare it with 16 15 14 13, 12 11 8 = 89

-1,-1,-1,-1,-1,-1,+1 = 89 -5 = 84 WRONG! Let's adjust.

15 14 13 12 , 11 10 9 = 84, Add +5
20 14 13 12, 11 10 9 = 89, most expensive side d. is 11.

15 14 13 12 , 11 10 9 = 84, Add +5
16 15 14 13 , 12 10 9 = 89, most expensive side d. is 12

INSUFFICIENT!


Answer: A

[tim]

:)