Integers

Expert replies

moneyman: Master | Next Rank: 500 Posts; Posts: 468; Joined: Sat Mar 03, 2007 10:17 pm; Thanked: 5 times

by moneyman » Tue May 06, 2008 5:03 am

if the integers a and n are greater than iand the product of the first 8 positive integers is a multiple of a^n , what is the value of a?

(1)a^n=64

(2)n=6

Ans B

Maxx

Like this post

Source: Beat The GMAT — Data Sufficiency | Tue May 06, 2008 5:03 am

dk_gmat: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Thu Jan 10, 2008 11:28 am

by dk_gmat » Tue May 06, 2008 12:55 pm

Hey Money !!!!

What is the first statement in the post .

Greater than iand !!!

Looks like a typo

DK...

Like this post

GMAT/MBA Expert

lunarpower: GMAT Instructor; Posts: 3380; Joined: Mon Mar 03, 2008 1:20 amFollowed by: 1535 members; Thanked: 2256 times; GMAT Score:800

Re: Integers

by lunarpower » Thu May 08, 2008 1:09 am

moneyman wrote:if the integers a and n are greater than iand the product of the first 8 positive integers is a multiple of a^n , what is the value of a?

(1)a^n=64

(2)n=6

Ans B

i shall assume that the text is supposed to read as follows:
if the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n , what is the value of a?

--

as with just about all other divisibility problems, you need to break down the number in question - in this case the product of the first eight positive integers - into primes.
this is 2 x 3 x 4 x 5 x 6 x 7 x 8
= 2 x 3 x 2 x 2 x 5 x 2 x 3 x 7 x 2 x 2 x 2
= 2^7 x 3^2 x 5 x 7

--

statement (1)
this statement establishes a^n = 64, but the problem is that there are multiple pairs (a, n) that satisfy this criterion: 2^6, 4^3, 8^2. this statement is therefore insufficient.

interestingly enough, this statement renders the whole bit about 8! completely irrelevant, because it just hands you the value of a^n. (that statement is only useful if it helps you figure out what a^n is, as in the next part)

--

statement (2)
this statement says that some number to the sixth power is a factor of 8!. this means that some number must appear at least six times in the prime factorization above. the only number 'a' that comes anywhere close to satisfying this condition is a = 2.
sufficient.

--

answer = b

--

also, note the following general piece of wisdom:
on a problem such as this one, on which the two statements together are OBVIOUSLY sufficient, you should be extremely suspicious of choice c.

remember, these guys are tricky. in this problem, it is crystal clear that the two statements together are good enough (they give a^6 = 64, so a is definitely 2);
they would very rarely write a problem with an answer that obvious, so, if you have to guess on a problem like this, DON'T guess c (or e, which is impossible). instead, bank on at least one of the 2 statements being sufficient, and so guess a, b, or d.

Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions Ã Ron en franÃ§ais
Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi

--

Quand on se sent bien dans un vÃªtement, tout peut arriver. Un bon vÃªtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

Like this post

deepakdewani: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Nov 29, 2009 3:00 am; GMAT Score:770

by deepakdewani » Sun Jun 20, 2010 10:14 am

also, note the following general piece of wisdom:
on a problem such as this one, on which the two statements together are OBVIOUSLY sufficient, you should be extremely suspicious of choice c.

remember, these guys are tricky. in this problem, it is crystal clear that the two statements together are good enough (they give a^6 = 64, so a is definitely 2);
they would very rarely write a problem with an answer that obvious, so, if you have to guess on a problem like this, DON'T guess c (or e, which is impossible). instead, bank on at least one of the 2 statements being sufficient, and so guess a, b, or d.

This is super advice!!

Thanks Ron.

Greed is good!

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review