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gre_nidhi
10-21-2004, 05:40 PM
IF n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is :

A. 6
B. 12
C. 24
D. 36.
E. 48.

jing
10-21-2004, 06:24 PM
is it a.?

Dingus
10-21-2004, 09:14 PM
N^2 /72 = x
N^2 = 9 * 4 * 2 * x
N= 3*2* 2^1/2 * x
Hence N definitely divisible by 6.
Is that the way to do this?

Econ
10-21-2004, 09:16 PM
(E)

(1) The largest positive integer that divides n is n.
(2) n^2= 48*48 is divisible by 72 ----------------> n=48
(3) Upon combining (1) and (2) we take E (?)

Dingus
10-21-2004, 09:37 PM
This is definitely more plausible!

gre_nidhi
10-21-2004, 09:58 PM

Econ i like ur explanation and i think it shud be E, but in ETS official guide of gmat it's B. If anybody wants to check it's q.no. 412(problem solving).

awhig
10-23-2004, 12:57 PM

Econ i like ur explanation and i think it shud be E, but in ETS official guide of gmat it's B. If anybody wants to check it's q.no. 412(problem solving).
'B' is justified to be the correct answer.

Consider n^2 = 72 * K , where K is any constant integer.

Now n^2 is perfect square, so K should be such that right hand side is perfect square.

Now if K = 2 then 72*2 = 144 exactly fits in the condition.

thus , n^ 2 = 144 => n = 12.

Now as Econ says, n is divisble by n so 12 is divisble by 12
such that it the largest number that divides 12.

Thus ETS people are right here!!!!!!:)

Econ
10-23-2004, 03:47 PM
Awhig:
Because (B) is justified to be the correct answer this does not implies that necessarily (B) is the correct answer. For this, notice that applying your method:
n^2 = 72*k
For n=24 and k=8 still the relationship holds perfectly (and 24>12)
Thus, (C) is justified to be the correct answer (and (D) and (E))

I think that (i) either there is a typo on the answer sheet and the answer must be (E) (ii) or (probably) there is a typo on the question. Instead the question should have been ''what is the minimum number..'' since for (A) 6 the relationship does not hold and the answer is indeed (B).

awhig
10-23-2004, 03:59 PM
Awhig:
Because (B) is justified to be the correct answer this does not implies that necessarily (B) is the correct answer. For this, notice that applying your method:
n^2 = 72*k
For n=24 and k=8 still the relationship holds perfectly (and 24>12)
Thus, (C) is justified to be the correct answer (and (D) and (E))

I think that (i) either there is a typo on the answer sheet and the answer must be (E) (ii) or (probably) there is a typo on the question. Instead the question should have been ''what is the minimum number..'' since for (A) 6 the relationship does not hold and the answer is indeed (B).
I think you are correct on this. 48 should be the answer here.

lmtuan
10-24-2004, 07:04 AM

nutan606
10-25-2004, 02:33 AM
hi,
i think that b is the only correct answer for the word "MUST" in the question stem.

dustino
10-25-2004, 06:23 AM
Few interesting things to note...

I can't agree that the answer would ever be (B) given that anything divisible by 72 will ALWAYS be divisible by 6, 12, 24, and 36. This leads us to ask the question, will 48, which obviously does not divide evenly by just 72, always be included in these squared numbers? Our first number comes at n = 12, where the answer is yes, they all divide. Will anywhere down the line break this trend?

I'm at a bit rusty on the insight / mathematical proof that would break this question, so I coded up a little program to run through those integers and see if any of the numbers fail to divide correctly. I ran the program up to n=10,000, and the results?

It always worked. The last number that works before 10,000 is 9996^2 = 99920016, which sure enough ends up ok, so unless there is some very large number (which I highly doubt), it looks like the answer is (E).

Econ
10-25-2004, 07:04 AM
Yes dustino, I agree. I also had observed that for nearly any number you plague in the result was fiting. Thus, it must be a typo on the question. Maybe the question intended to be ''was it the smallest number that....'' and thus (B) would be justified.

amishera2007
10-08-2007, 05:10 PM
Why this unnecessary fuss?

The question ask for the largest integer that MUST divide n.

If we take n=12 then we get 144 which is divided by 72.

But according to your claim does 48 MUST divide n=12?

12 is divided by 1, 3, 4, 6 and 12 and the largest of which that divide n = 12 is 12

if n = 24 then you get 24 as the largest number

if n = 48 then u get 48 largest number.

But which number MUST divide in every case? its 12.

Does 24, 48 MUST divide every n? In order for MUST condition to be satisfied 48 should always divide every n including n=12.

Then how is 48 is the largest integer that MUST divide n?