Equation # 2

Question

I went through this question while preparing. Not sure if this is typical GMAT Question. But curious to know if someone can come up with easy solution to this question

Q.) There are seven children standing in the line, not all of whom have the same number of cakes with them. If the first child distributes his cakes to the remaining six children such that he doubles their respective number of cakes, then he will be left with four cakes. Instead, if the second child takes away two cakes from each of the remaining six children, then he will be left with three cakes less than the number of cakes that the first child initially had. What is the total number of cakes that are there with the third to the seventh child?

A) 10
B) 14
C) 12
D) 13
E) 11

jamifahad · Answer

Can this be done under two minutes? That's the question.

cleetus · Answer

Yes it seems. If u are good in calculation and if u know the short methode, this can be solved in 2 mins. If u approach in algebraic methode / step by step methode, it may consume more time. Unfortunately, am not aware of either methodes. i hav posted this here hoping to get the best way to solve this

Sudhanshuacharya · Answer

Lets see:

Let the 7 children have a,b,c,d,e,f,g cakes respectively.

First statement: The first child distributes his cake such that he is left with 4 cakes and rest have double their initial number of cakes:
hence:

a-(b+c+d+e+f+g) = 4 --- (i)

Second statement: the 2nd boy takes 2 cakes each from every one and is still 3 short of initial value of 1st.
Hence:

b+2 cakes(6 children) = a-3
or a-b = 15 --- (ii)

substituting this value in eq - 1. 
a-b -(c+d+e+f+g) = 4

We get (c+d+e+f+g) = 11.

vinayrsm · Answer

I did this is 2:36. it is indeed a bit wordy but can certainly be done in ~2min. good question.

varunmaheshwari · Answer

Nice ques.. I took 3 mins bcoz I started in the wrong way initially..

jamifahad · Answer

@Sudhanshuacharya Wow! you made it look ridiculously easy. 
+1.

Sudhanshuacharya · Answer

Thanks jamifahad. Glad you liked the solution

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Equation # 2

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