Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

K^4 is divisible by 32. What is the remainder when K is [#permalink]

Show Tags

12 May 2005, 08:48

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct
0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

K^4 is divisible by 32. What is the remainder when K is divided by 32?
1) The remainder is 3 when K is divided by 4
2) The remainder is 2 when K is divided by 3

is this really going to appear in the test? my friend wrote a very complicated solution which for sure cannot take 2-3 minutes. his answer was also E. if you are interested i can post it.

1st statement indicates that K is odd but our problem states that
((k/2)^4)*(1/2). That is, K must be even to have this statement. So, statement contradicts with the problem. I guess it can't be sufficient. It's something different

2nd statement is insufficient. When k=8 (it also satisfies original statement) the remainder is 1. When k=20, the remainder is 5.

Combining statements won't suffice either. 1st one is weird

Answer is E. july05, please post the explanation of your friend. Thanks.

answer is B :D <-- this is smilly not d :d [#permalink]

Show Tags

18 May 2005, 00:35

this question is bit diffy not one of the most diffy questions those who r targetting 700+ can xpect even harder questions in last five Qs
anyways coming back to the solution from statment B K can b 5,8 and so on as 5 do not fit in orginal statment so it is 8 then 8*8*8*8 leaves remainder as 0, then it cant b 11, 14.... (x*3+2 where x can b from 1...32)
32 may work but i havent checked till tht value.
_________________

i believe that all the problem solving calculations in Quantitative section have simple calculations. No Long Mahcine requiring calculations r required :D

here it is. i pasted this from an email, so the power sign "^" was gone. i tried to fix it, but if you find any more inconsistences like that, please let me know.

---------------

If you are still interested, you can refer to K. Rosen's "Discrete Mathematics," the part dealing with modular arithmetic.

The original statement
K^4 = 0 mod 32 (K^4 is divisible by 32)
can be reduced to
K = 0 mod 4 (K is divisible by 4)

Let's look at this closely.
K^4 = n * 32
K^4 = n * 2^5
K^4 = 2n * 2^4
K = rt4(2n) * 2

Since K is an integer, rt4(2n) must also be an integer. This is the case
only when n is divisible by 8, let n = 8m.
K = rt4(2*8m) * 2 = rt4(16m) * 2 = 2 * rt4(m) * 2 = 4 * rt4(m)

In this expression rt4(m) may be any integer. In other words, K = 4x. This is sufficient and necessary condition on K. The statements K=4x and K^4 is divisible by 32 are equivalent.

Let us proceed. Original statement in its new form K=4x contradicts (1).
Therefore we should not consider (1). Let us look into (2). Taken alone, (2) suggests the number set K = 2+3y: 2, 5, 8, 11, 14, etc.

Let us combine (2) with our original condition of K=4x:
K = 4x
K = 2+3y

Since 3 and 4 are mutually prime, by some theorem (maybe it's Chinese
Remainder Theorem, i'm not sure), the solution to this equation set is a
number range with a period of 3*4 = 12. The first number satisfying both
conditions is 8. All the numbers can be represented as K = 8 + 12z, where z
is some integer.

They are 8, 20, 32, 44, etc.

These numbers have different remainders by 32, for example 8 has 8, 20 has
20, and 32 has 0. It means that (2) is insufficient.

(1) and (2) taken together contradict the (0) condition because (1)
contradicts (0).

The answer is (E). Neither (1), nor (2) is sufficient.