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

It is currently 23 May 2019, 00:09

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

If v^2 – t^2 = 24, then w^2 – u^2 =

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55236
If v^2 – t^2 = 24, then w^2 – u^2 =  [#permalink]

Show Tags

New post 12 Jul 2017, 23:38
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

84% (02:03) correct 16% (01:22) wrong based on 70 sessions

HideShow timer Statistics

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
If v^2 – t^2 = 24, then w^2 – u^2 =  [#permalink]

Show Tags

New post 13 Jul 2017, 00:35
\(v^2 – t^2 = 24\)
So, (v+t)(v-t) = 24

One way to get the product of 24 is 2*12
We can use the equations
v+t = 12
v-t = 2
Solving these two equations, we get v=7 and t=5
Since the letters represent consecutive integers, we can say that w = 8 and u = 6

Hence, the value of the expression becomes \(w^2 – u^2 = 8^2 - 6^2 = 64-36 = 28\)(Option B)
_________________
You've got what it takes, but it will take everything you've got
Director
Director
User avatar
D
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 724
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
If v^2 – t^2 = 24, then w^2 – u^2 =  [#permalink]

Show Tags

New post Updated on: 13 Jul 2017, 04:15
Bunuel wrote:
Image
The letters represent consecutive integers

If \(v^2 – t^2 = 24\), then \(w^2 – u^2 =\)

(A) 28
(B) 24
(C) 20
(D) 18
(E) 16


\(v^2 – t^2 = 24\)
(v-t)(v+t) = 24
2(v+t) = 24
(v+t) = 12
t+t+2 = 12
t = 5

so, t = 5 , u = 6, v = 7 , w = 8
\(w^2 - u^2 = (w-u)(w+u ) = 2 (6+8) = 28\)

Answer A
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Originally posted by shashankism on 13 Jul 2017, 00:53.
Last edited by shashankism on 13 Jul 2017, 04:15, edited 1 time in total.
Intern
Intern
avatar
B
Joined: 18 May 2017
Posts: 48
If v^2 – t^2 = 24, then w^2 – u^2 =  [#permalink]

Show Tags

New post 13 Jul 2017, 01:45
shashankism - can you please elaborate your calculations?

Anyway this is my approach: v^2-t^2=24 ----> (v-t)(v+t)=24. As there is one number between v and t (u) the difference between v and t is necessarily even, whether v and t are odd or even numbers (odd-odd=even, even-even=even). So 24 is build from a multiplication of two even numbers. The options for the multiplications are 2 and 12 as well as 4 and 6. As we checking the options we revealed that 4 and 6 is impossible because if (v-t)=4 and (v+t)=6 ----> v=5. It means that t=3 and it doesn't satisfy the equation (5^2-3^2 equal 16 not 24). So the only option is 2 and 12. When we add the equations (v-t=2 and v+2=12) we get that v=7 and t=5. It satisfies the equation in the question (7^2-5^2=24). Now, as we deal with consecutive numbers, we can also calculate to value of u and w (6 and 8) and solve the question: 8^2-6^2 ----> 64-36 ----> 28.

Answer: A
Director
Director
User avatar
D
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 724
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If v^2 – t^2 = 24, then w^2 – u^2 =  [#permalink]

Show Tags

New post 13 Jul 2017, 02:20
oryahalom wrote:
shashankism - can you please elaborate your calculations?

Anyway this is my approach: v^2-t^2=24 ----> (v-t)(v+t)=24. As there is one number between v and t (u) the difference between v and t is necessarily even, whether v and t are odd or even numbers (odd-odd=even, even-even=even). So 24 is build from a multiplication of two even numbers. The options for the multiplications are 2 and 12 as well as 4 and 6. As we checking the options we revealed that 4 and 6 is impossible because if (v-t)=4 and (v+t)=6 ----> v=5. It means that t=3 and it doesn't satisfy the equation (5^2-3^2 equal 16 not 24). So the only option is 2 and 12. When we add the equations (v-t=2 and v+2=12) we get that v=7 and t=5. It satisfies the equation in the question (7^2-5^2=24). Now, as we deal with consecutive numbers, we can also calculate to value of u and w (6 and 8) and solve the question: 8^2-6^2 ----> 64-36 ----> 28.

Answer: A


Since t, u, v .... represent consecutive integers... the difference between them is 1 and hence difference between v and t is 2.
Simply v-t = 2
u = t+1
v = t+2
w = t+3
x = t+4
y = t+5
z = t+6

I donno why are u even trying to decode from the factors of 24,... This step is not at all required...
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Intern
Intern
avatar
B
Joined: 18 May 2017
Posts: 48
Re: If v^2 – t^2 = 24, then w^2 – u^2 =  [#permalink]

Show Tags

New post 13 Jul 2017, 03:38
Thanks! Your approach is much easier. You mentioned mistakenly that t+t+2=24 instead of t+t+2=12


Sent from my iPhone using GMAT Club Forum
Director
Director
User avatar
D
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 724
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If v^2 – t^2 = 24, then w^2 – u^2 =  [#permalink]

Show Tags

New post 13 Jul 2017, 04:17
oryahalom wrote:
Thanks! Your approach is much easier. You mentioned mistakenly that t+t+2=24 instead of t+t+2=12


Sent from my iPhone using GMAT Club Forum



Yes t+t+2 = 12... I have done a mistake there.. Edited in the original solution.. :)
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Director
Director
avatar
P
Joined: 14 Nov 2014
Posts: 622
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: If v^2 – t^2 = 24, then w^2 – u^2 =  [#permalink]

Show Tags

New post 13 Jul 2017, 04:48
Bunuel wrote:
Image
The letters represent consecutive integers

If \(v^2 – t^2 = 24\), then \(w^2 – u^2 =\)

(A) 28
(B) 24
(C) 20
(D) 18
(E) 16


assume t = x -----1
as these are consecutive integer ..
v = x + 2
t = x

v^2 - t ^2 = 24-------2
replacing the values in equation 2
(x+2-x)(x+2+x) = 24
x+1 = 6
x = 5
t= 5-----------------------3

using 3 we will get

w = 8
u=6

8^2 - 6^2 = 28 ...
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2755
If v^2 – t^2 = 24, then w^2 – u^2 =  [#permalink]

Show Tags

New post 13 Jul 2017, 11:40
shashankism wrote:
Bunuel wrote:
Image
The letters represent consecutive integers

If \(v^2 – t^2 = 24\), then \(w^2 – u^2 =\)

(A) 28
(B) 24
(C) 20
(D) 18
(E) 16


\(v^2 – t^2 = 24\)
(v-t)(v+t) = 24
2(v+t) = 24

(v+t) = 12
t+t+2 = 12
t = 5

so, t = 5 , u = 6, v = 7 , w = 8
\(w^2 - u^2 = (w-u)(w+u ) = 2 (6+8) = 28\)

Answer A

shashankism, maybe I need more coffee, but I don't follow how you got from:

(v-t)(v+t) = 24, to

2(v+t) = 24

Please explain?
_________________
Listen, are you breathing just a little, and calling it a life?
-- Mary Oliver

For practice SC questions go to SC Butler, here.


Please DO NOT write short answers in your verbal posts! Such answers will be deleted.
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Re: If v^2 – t^2 = 24, then w^2 – u^2 =  [#permalink]

Show Tags

New post 13 Jul 2017, 11:48
1
genxer123

v = t+2(since v and t are consecutive numbers)
So, in essence, v-t =(t+2)-t = 2

Hence, (v-t)(v+t) becomes 2(v+t)

Hope that helps!
_________________
You've got what it takes, but it will take everything you've got
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2755
If v^2 – t^2 = 24, then w^2 – u^2 =  [#permalink]

Show Tags

New post 13 Jul 2017, 11:51
pushpitkc wrote:
genxer123

v = t+2(since v and t are consecutive numbers)
So, in essence, v-t =(t+2)-t = 2

Hence, (v-t)(v+t) becomes 2(v+t)

Hope that helps!

It does. Beautifully explained. Thanks!
_________________
Listen, are you breathing just a little, and calling it a life?
-- Mary Oliver

For practice SC questions go to SC Butler, here.


Please DO NOT write short answers in your verbal posts! Such answers will be deleted.
GMAT Club Bot
If v^2 – t^2 = 24, then w^2 – u^2 =   [#permalink] 13 Jul 2017, 11:51
Display posts from previous: Sort by

If v^2 – t^2 = 24, then w^2 – u^2 =

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.