GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Nov 2019, 10:03

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

K and L are each four-digit positive integers with thousands

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
K and L are each four-digit positive integers with thousands  [#permalink]

Show Tags

New post Updated on: 07 Sep 2012, 10:58
7
46
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

69% (02:36) correct 31% (02:47) wrong based on 590 sessions

HideShow timer Statistics

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.

As the OA is not given this is how I am trying to solve this question, but I am stuck now. Can someone help please?

Digits of K are a,b,c and d i.e. K is 1000 a + 100 b + 10 c + d ----------------------------------------(1)

Digits of L are p, q, r and s i.e. L is 1000 p + 100 q + 10 r + s ----------------------------------------(2)

f(w) = \(5^a 2^b 7^c 3^d\) / \(5^p 2^q 7^r 3^s\)-----------------------------------------(3)

Also, f(16) = \(5^a 2^b 7^c 3^d\) / \(5^p 2^q 7^r 3^s\)-----------------------------------(4)

Therefore, \(5^a 2^b 7^c 3^d\) / \(5^p 2^q 7^r 3^s\) = 16 i.e. \(2^4\)----------------(5)

f(z) = (1000 a + 100 b + 10 c + d) - 1000 p + 100 q + 10 r + s / 10 ----------------------------------(6)

Now, I am stuck and no OA doesn't help either. Therefore, your help will be much appreciated guys.

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Originally posted by enigma123 on 28 Jan 2012, 00:32.
Last edited by Bunuel on 07 Sep 2012, 10:58, edited 2 times in total.
Added the OA
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59089
Re: K&L four digit positive integers  [#permalink]

Show Tags

New post 28 Jan 2012, 02:53
19
19
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).

Z=(K-L)/10=400/10=40.

Answer: D.

Also discussed here: functions-concepts-testing-91004.html
Similar questions:
the-function-f-is-defined-for-each-positive-three-digit-100847.html
for-any-four-digit-number-abcd-abcd-3-a-5-b-7-c-11-d-126522.html

Hope it helps.
_________________
General Discussion
Senior Manager
Senior Manager
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: K and L are each four-digit positive integers with thousands  [#permalink]

Show Tags

New post 28 Jan 2012, 16:14
2
Bunuel thanks - you super star.
_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Senior Manager
Senior Manager
avatar
B
Joined: 24 Aug 2009
Posts: 442
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: K&L four digit positive integers  [#permalink]

Show Tags

New post 14 Sep 2012, 04:27
Bunuel wrote:
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).

Z=(K-L)/10=400/10=40.

Answer: D.

Also discussed here: functions-concepts-testing-91004.html
Similar question: the-function-f-is-defined-for-each-positive-three-digit-100847.html

Hope it helps.



Hi Bunuel ,

Can you move this question to the quant section
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59089
Re: K&L four digit positive integers  [#permalink]

Show Tags

New post 14 Sep 2012, 04:32
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59089
Re: K and L are each four-digit positive integers with thousands  [#permalink]

Show Tags

New post 21 Jun 2013, 03:47
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 384
Location: India
GMAT 1: 760 Q50 V44
K and L are each four-digit positive integers with thousands  [#permalink]

Show Tags

New post 01 Dec 2015, 01:03
2
2
[quote="enigma123"]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:
K = abcd = 1000a + 100b + 10c + d
L = pqrs = 1000p + 100q + 10r + s
W = \(5^a 2^b 7^c 3^d\) ÷ \(5^p 2^q 7^r 3^s\) = \(5^{a-p} 2^{b-q} 3^{c-r} 5^{d-s}\) = 16 = \(2^4\)

W can 16 only when W carries the powers of 2 only.
Hence b - q = 4 (i)
And the rest of the powers will be 0.
a= p, c = r, d = s (ii)

Required: Z = (K – L) ÷ 10 =?
Z = (abcd - pqrs)÷10 = (1000a + 100b + 10c + d) - (1000p + 100q + 10r + s) ÷ 10
Z = 1000 (a - p) + 100(b - q) + 10 (c - r) + 10 (d - s) ÷ 10
From equations (i) and (ii)
Z = 100(b-q) ÷ 10 = 100*4 ÷ 10= 40
Option D
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 355
Re: K and L are each four-digit positive integers with thousands  [#permalink]

Show Tags

New post 28 Oct 2016, 17:18
This question is tricky in the sense that it is a simple recognition of 2^4=16 that is buried under quite a bit of language.

W can be rewritten to the following: 16=5^(a-p) x 2^(b-q) x 7^(c-r) x 3^(d-s)

K and L are four digit numbers, so we need to have at least 1 in a and p's position. Thus, we will let a=1, p=1

b-q needs to equal 4, so we can assign any single digits that would give us that result. b=9, q=5

The rest of the numbers can be either 0's or 1's. Doesn't matter as we will be subtracting them off when we plug values into the Z equation.

K = 1911
L = 1511

Z = (K-L)/40 = 400/10 = 40
Senior Manager
Senior Manager
User avatar
P
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 440
Premium Member
Re: K and L are each four-digit positive integers with thousands  [#permalink]

Show Tags

New post 18 Mar 2019, 14:17
Agreed that this question's biggest challenge is the wordiness...

The way I approached it:

1) f(W) shows us the division of the prime factorization of the 2 numbers, K and L. That f(W) = 16 means there's 2^4 more in the numerator K, i.e. that b-4 = q. This also means that all the other variables are equal.

2) f(Z) = (F - L)/10 ... since all the variables are equal except b and q (the hundreds place), it will be some number where the difference between them is 400 (since b is greater than q by 4). 400/10 = 40, D.
GMAT Club Bot
Re: K and L are each four-digit positive integers with thousands   [#permalink] 18 Mar 2019, 14:17
Display posts from previous: Sort by

K and L are each four-digit positive integers with thousands

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne