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

It is currently 22 Oct 2019, 23:20

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 the difference between the squares of the first and last terms of a

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

Hide Tags

Find Similar Topics 
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1224
If the difference between the squares of the first and last terms of a  [#permalink]

Show Tags

New post 01 Jun 2017, 20:54
1
22
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

71% (02:53) correct 29% (02:35) wrong based on 132 sessions

HideShow timer Statistics

If the difference between the squares of the first and last terms of a sequence of consecutive odd positive integers is 720,
and the first and last terms share the same ones unit, what is the sum of the first and last terms?

A. 64
B. 68
C. 72
D. 76
E. 80
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58435
Re: If the difference between the squares of the first and last terms of a  [#permalink]

Show Tags

New post 01 Jun 2017, 21:20
2
3
gracie wrote:
If the difference between the squares of the first and last terms of a sequence of consecutive odd positive integers is 720,
and the first and last terms share the the same ones unit, what is the sum of the first and last terms?

A. 64
B. 68
C. 72
D. 76
E. 80


Say the first term is y and the last term is y (notice y > x).

\(y^2 - x^2 = 720\);

\((y - x)(y + x) = 2^4*3^2*5\).

Since both x and y are odd then both y - x and y + x are even.
Since the units digits of x and y are the same then the units digit of y - x is 0.

So, y - x is at least 5*2 = 10 and y + x is at most 3^2*2^3 = 72. In this case y = 41 and x = 31. These two numbers satisfy all the conditions and since a PS question cannot have two correct answer then y + x = 72.

Answer: C.

Alternatively for the last step: y - x is at least 5*2 and y + x is at most 3^2*2^3 = 72. From this:
y - x cannot be 5*2*3 = 30 and x = 3*2^3 = 24 because in this case y - x < y + x, which cannot happen.
y - x cannot be 5*2^2 = 20 and x = 3^2*2^2 = 36 because in this case in this case both x and y turn to be even, not odd.

Those were only two other cases, so y - x = 5*2 = 10 and y + x = 3^2*2^3 = 72

Hope it's clear.
_________________
Most Helpful Community Reply
Manager
Manager
avatar
B
Joined: 27 Mar 2016
Posts: 110
GMAT ToolKit User CAT Tests
Re: If the difference between the squares of the first and last terms of a  [#permalink]

Show Tags

New post 01 Jun 2017, 21:31
4
1
Answer should be C.
Since the number share the same unit digit, difference between the terms would be in multiple of 10.
Let no be x & y => x^2-y^2=720
(x+y)(x-y)=720
(X+y )*10n = 720
X+y=72/n
Since n is an integer and there is no factor of 72 present in the list, answer should be 72.

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
General Discussion
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1224
If the difference between the squares of the first and last terms of a  [#permalink]

Show Tags

New post Updated on: 12 Nov 2018, 12:50
gracie wrote:
If the difference between the squares of the first and last terms of a sequence of consecutive odd positive integers is 720,
and the first and last terms share the same ones unit, what is the sum of the first and last terms?

A. 64
B. 68
C. 72
D. 76
E. 80


if the first and last terms share the same units digit,
then the range of the sequence will be a multiple of 10
because all the answer choices have only two digits, assume the range is 10
let x=the first term; y=the last term
(y+x)(y-x)=720
y-x=range=10
y+x=720/10=72
C

Originally posted by gracie on 01 Jun 2017, 22:10.
Last edited by gracie on 12 Nov 2018, 12:50, edited 1 time in total.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13410
Re: If the difference between the squares of the first and last terms of a  [#permalink]

Show Tags

New post 20 Oct 2018, 09:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: If the difference between the squares of the first and last terms of a   [#permalink] 20 Oct 2018, 09:29
Display posts from previous: Sort by

If the difference between the squares of the first and last terms of a

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





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