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1 + 3 + 6 + 10 + ..... + Tn = 8436abhasjha wrote:There are 8436 steel balls, each with a radius of 1 cm stacked in a pile with 1 ball on top,3 balls in the second layer,6 in the 3rd layer,10 in the fourth and so on, the number of horizontal layers in the pile is
(a) 30
(b) 42
(c) 36
(d)45
[email protected] wrote:Hi abhasjha,
I agree with Brent that is question, as designed, is outside the scope of the GMAT Quant section.
1+2+3+4+5+6+7+8+9+10 = 55
This is an LONG way to do things.
Instead, you can "bunch" the numbers and spot a pattern:
1+10 = 11
2+9 = 11
3+8 = 11
etc.
There are 5 groups of 11, so 5x11 = 55
bunch the numbers and spot the pattern -
are the numbers 1, 3,6, 10,15 not following a pattern ??
0+1 = 1 (this is the first term of the sequence)
1+2 = 3 (this is the second term of the sequence)
1+2+3=6 (this is the third term of the sequence )
so on and so forth......
The number 8436 is a large one so I can not do it manually ...
is it also not true rich that in the question of such nature you find out the nth term of the series(by following the pattern)... (as is done by ganesh r kamath and vipul goyal ) and then do summation of those n terms ..
After sum{n(n+1)}/2 = 8436... I was looking for some kind of estimation(by looking at the answer choices ) .experts often talk of doing some estimation faced with difficult choice . they have even written articles on this ..on beat the GMAT as well as other places .. but failed to apply what they preach ...
Ganesh r kamath had already given a way to estimate . Then what was so Un GMAT about this problem??By the way does GMAC ask these experts or for that matter any person before setting questions that what questions are they going to set ? IF not then how can Brent and Rich be so sure about this ? I could have understood if I asked questions on American history and then some one pointing me that this is not what GMAT asks ... not otherwise ... what ever I have asked is well within the realm of GMAT...
Firstly, this problem has only 4 options.abhasjha wrote:Ganesh r kamath had already given a way to estimate . Then what was so Un GMAT about this problem??By the way does GMAC ask these experts or for that matter any person before setting questions that what questions are they going to set ? IF not then how can Brent and Rich be so sure about this ?
Quite the contrary. I have encountered RC's with American history as the theme.abhasjha wrote: I could have understood if I asked questions on American history and then some one pointing me that this is not what GMAT asks ... not otherwise ... what ever I have asked is well within the realm of GMAT...
Concepts of American history are not tested independently. It is within the context of the RC in question. If GMAC were to give the formulas for the summations mentioned above, I would agree that this problem is definitely in scope. Unfortunately, GMAC does no such thing.abhasjha wrote:well in that case I will say if concepts of American history are tested when it is known to GMAC that Asians , African and people from other countries write the exam .. (even then American history not considered outside the scope of test .. then how summation of n natural numbers or summation of squares of n natural number or sum of cube of n natural number can fall outside the scope of this test??
Could you please post the problem here? If this is true, I will take back my words.abhasjha wrote:1. The problem involves a huge calculation (8436*6)
if 84368*6 is a huge calculation then from the gprep it self I will show you questions which asks you to calculate cube of 26...
This is precisely why I said that such a question is highly unlikely.abhasjha wrote:2. It will definitely take more than 2 minutes for an average GMAT test taker to solve this problem
well no where GMAC writes that all question can be answered in two minutes . The average for those 37 questions is 2 minute per question. some questions will take less than two minutes and some can take more than 2 minutes .... Avg should be closer to 2 minutes ....
By numerous, I didn't mean 4 concepts that include 3 formulas! Do go through the OG to get a hang of the questions that will appear on the GMAT. I agree that the actual GMAT questions will be tad bit tougher than those in OG, but this is a whole different level. I, for one, haven't encountered such a question in any of my mocks or the official test.abhasjha wrote:3. It uses multiple concepts: finding the nth term, sum to n, sum to n^2, and finding n from the options.
This I need not answer ganeshrkamath because you have answered it for me in your post when you wrote
"GMAT is more focused on your ability to stitch numerous concepts to solve a problem. "
GMAT doesn't expect you to calculate 26^3. That's just ridiculous! It wants you to find the units digit. But then again, the problem at hand also doesn't require 8346*6. It just requires the units digit. So calculating 8346*6 was wrong on my part. Thanks for the correction.abhasjha wrote:Dear Ganesh ,
Here I am posting the question . the question is taken out of grpep and is discussed on manhattan forum under G Prep question .... (the experienced instructors of manhattan would not allow you to post questions which are not from gprep in that section...) you can even google out the question...here it goes ..
A certain stock exchange designates each stock with a one, two or three letter code , where each letter is selected from the 26 letters of the alphabet. if the letters may be repeated and if the same letters used in a different order constitute a different code , how many different stocks is it possible to uniquely designate with these codes?
a) 2,951
b)8,125
c)15,600
d) 16,302
e) 18,278
OA is E.....18,278
what would you now say to this ... is it a miniscule calculation compared to 8346x6????
I'd like to jump in and say that this question does not require major calculations (see https://www.beatthegmat.com/permutations ... 93716.html for full solution).abhasjha wrote:Dear Ganesh ,
Here I am posting the question . the question is taken out of grpep and is discussed on manhattan forum under G Prep question .... (the experienced instructors of manhattan would not allow you to post questions which are not from gprep in that section...) you can even google out the question...here it goes ..
A certain stock exchange designates each stock with a one, two or three letter code , where each letter is selected from the 26 letters of the alphabet. if the letters may be repeated and if the same letters used in a different order constitute a different code , how many different stocks is it possible to uniquely designate with these codes?
a) 2,951
b)8,125
c)15,600
d) 16,302
e) 18,278
OA is E.....18,278
what would you now say to this ... is it a miniscule calculation compared to 8346x6????
ganeshrkamath's solution above is awesome, and it uses some great number sense to arrive at the correct answer without tedious calculations. So, all of this seems to make it GMAT-worthy, but in my opinion, the question is not GMAT-worthy.ganeshrkamath wrote:1 + 3 + 6 + 10 + ..... + Tn = 8436abhasjha wrote:There are 8436 steel balls, each with a radius of 1 cm stacked in a pile with 1 ball on top,3 balls in the second layer,6 in the 3rd layer,10 in the fourth and so on, the number of horizontal layers in the pile is
(a) 30
(b) 42
(c) 36
(d)45
Tn = n(n+1)/2
sum(Tn) = sum(n^2 + n)/2
8436 = (n(n+1)(2n+1)/6 + n(n+1)/2)/2
16872 = n(n+1)(2n+1)/6 + n(n+1)/2
33744 = n(n+1)(2n+1)/3 + n(n+1)
33744 = n(n+1)*((2n+1)/3 + 1)
33744 = n(n+1)*(2n+4)/3
33744 = n(n+1)(n+2)*2/3
50616 = n(n+1)(n+2)
So the units digit is 6.
Only option that satisfies this is [spoiler](C)[/spoiler]
Cheers
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