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.

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 and L are each four-digit positive integers with thousands [#permalink]
27 Jan 2012, 23:32

2

This post received KUDOS

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

69% (02:50) correct
31% (02:49) wrong based on 205 sessions

K and L are each four-digit positive integers with thousands, hundreds, tens, and units digits defined as a, b, c, and d, respectively, for the number K, and p, q, r, and s, respectively, for the number L. For numbers K and L, the function W is defined as 5^a 2^b 7^c 3^d ÷ 5^p 2^q 7^r 3^s. The function Z is defined as (K – L) ÷ 10. If W = 16, what is the value of Z?

(A) 16 (B) 20 (C) 25 (D) 40 (E) It cannot be determined from the information given.

Re: K&L four digit positive integers [#permalink]
28 Jan 2012, 01:53

11

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

enigma123 wrote:

K and L are each four-digit positive integers with thousands, hundreds, tens, and units digits defined as a, b, c, and d, respectively, for the number K, and p, q, r, and s, respectively, for the number L. For numbers K and L, the function W is defined as 5^a 2^b 7^c 3^d ÷ 5^p 2^q 7^r 3^s. The function Z is defined as (K – L) ÷ 10. If W = 16, what is the value of Z?

(A) 16 (B) 20 (C) 25 (D) 40 (E) It cannot be determined from the information given.

Given: w=\frac{5^a*2^b*7^c*3^d}{5^p*2^q*7^r*3^s}=16 --> w=5^{a-p}*2^{b-q}*7^{c-r}*3^{d-s}=2^4 --> the powers of 3, 5, and 7 must be zero and the power of 2 must be 4: a=p, b-q=4, c=r and d=s

Now, as thousands, tens, and units digits in K and L are equal and the difference between hundreds' digits is 4, then K-L=400 (for example K=1923 and L=1523 --> K-L=1923-1523=400).

K and L are each four-digit positive integers with thousands, hundreds, tens, and units digits defined as a, b, c, and d, respectively, for the number K, and p, q, r, and s, respectively, for the number L. For numbers K and L, the function W is defined as 5^a 2^b 7^c 3^d ÷ 5^p 2^q 7^r 3^s. The function Z is defined as (K – L) ÷ 10. If W = 16, what is the value of Z?

(A) 16 (B) 20 (C) 25 (D) 40 (E) It cannot be determined from the information given.

Given: w=\frac{5^a*2^b*7^c*3^d}{5^p*2^q*7^r*3^s}=16 --> w=5^{a-p}*2^{b-q}*7^{c-r}*3^{d-s}=2^4 --> the powers of 3, 5, and 7 must be zero and the power of 2 must be 4: a=p, b-q=4, c=r and d=s

Now, as thousands, tens, and units digits in K and L are equal and the difference between hundreds' digits is 4, then K-L=400 (for example K=1923 and L=1523 --> K-L=1923-1523=400).

I couldn’t help myself but stay impressed. young leader who can now basically speak Chinese and handle things alone (I’m Korean Canadian by the way, so...