Problem Solving

scoobydooby wrote:would go for C

1) w13 = w1+12d
w5 = w1+4d

(w13+w5)*(w13-w5) = (2w1+16d)(8d) = 16d(w1+8d)=244
=>4d(w1+8d) = 61
we do not know w1 or d. not sufficient

2) w9=61
=>w1+8d=61
we do not know w1 or d. not sufficient

together, putting value of w9=w1+8d=61 in statement 1 we get
4d*61=61
=>d=1/4 or 0.25

w1+d=61, d=0.25 we can work out w1 and, w17 and hence the sum

maihuna wrote:A:

It is an AP with assumed first player wt a and diff d

w13 = a+12d
w5 = a+4d

(w13+w5)*(w13-w5) = (2a+16d)(8d) = 16d(a+8d)=244
=>4d(a+8d) = 61

61 is a prime no, since wt are natural no, a ad d all will be prime so multiplication of two natural no cant be prime

check if 244 is correct? It should be some different no? Otherwise the question stem will be correct. Assuming it to be 240
d(a+8d) = 15 it will have d as 1, a as 7, there is no other possibility as 15 has two factors and 5 so the pairs will be(1, 15), (3,5) ,(5,3), (15,1)

3 and 5 cant be there as weight cant be negative and 8 is bigger than 5 so the only factors will be 1, 15

so the sequence will be: 7, 8 , 9 , 10, ..., 23

total et= 17/2(7+23) = 15*17

B: Doesnt tell anything


C: assuming the data is something other than 240 in case it has two possible factors satisying a/d and above eqn C can be an ane...

maihuna wrote:
SchoolBoy the issue is no more solving the eqn here: Issue is that the weights are integer so a as well as d both need be integer and that way their product cant be prime, see my post above,

dtweah wrote:

maihuna wrote:A:


No clue what you have done above. Why are you going into a discussion of primes? The answer will be C as solved by Scooby. Why do you have to check if 244 is correct? It is part of the problem. As long as (1) bears no relationship to the sum of the 17 terms, such as by equating the two we could derive some value of w1 or d, 1 is insufficient, since we can't get d and w1 from it. These two are given in 2) so C is the answer.

dtweah: what i mean here is the data as posted is incorrect, it can never be 244 in gmatish question, as it clearly mentions the weight are integers so (integer+integer)*(integer-integer) will be equal to product of two integers. here in terms of a and d each being integer their combination cannt be an prime as shown above, as it meant an non-integer weights which is ruled out in question...

schoolboy,
i dont understand the part of agony you went through in my last post, what actually has turned u raising attitude and show it elsewhere words...i m clueless,,,

dumb.doofus wrote:I think the answer should be D.. Here is my solution.. but before that I want to say that -

The question is worded wrongly!!! Mention of Natural numbers should be omitted from the question.. This series cannot have natural numbers at all.. Scoobydooby already found out d as 0.25 in his post.. although as you'll see ahead that its not necessary to find d.


Alrighty.. we need to find the sum of weight here of an AP

AP formula for sum = n(2a + (n-1)d)/2
putting n = 17 we get,

sum = 17(a+8d)... so this is what we want..

1. (w13)^2 - (w5)^2 = 244
or as you guys have already solved..
16d(a+8d) = 244 = 4*61

61 is a prime number.. so it can't be a product of two numbers.. unless the other number is 1..

d cannot be 61.. why? well basic common sense here.. its too big a number for the above equation to give a result as low as 244 if d were to be 61.. and 16d can never give an odd number i.e. 61.. so essentially it means that 61 is actually equal to a + 8d.. yipeee!!! and so equation is sufficient..


2. w9 = 61

this means a + 8d = 61..... Voila!!! that's what we want .. isnt it? the value of a + 8d.. so this equation is sufficient

Of course if you change any wording of the question, you are probably answering a different question than the one posed. Under the given question D and C are both correct depending on whether integer or natural number is used. Both yield two different series that sum to 244 hence the logical inconsistency of the question. If the question had only said integers, then Scooby might have known d can't be 1/4 and would probably have analyzed differently. So since question is logically inconsistent it will be thrown out by GMAT and not affect any score. (Laugh)