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

It is currently 21 Oct 2019, 04:40

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

W, X, Y and Z are four different positive integers. When X

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

Hide Tags

Find Similar Topics 
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4015
Location: Canada
W, X, Y and Z are four different positive integers. When X  [#permalink]

Show Tags

New post 08 Mar 2019, 12:27
1
Top Contributor
11
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

15% (02:36) correct 85% (02:34) wrong based on 52 sessions

HideShow timer Statistics

W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. If W = X – 7, what is the sum of all possible values of W?
A) 19
B) 20
C) 21
D) 22
E) 23

_________________
Test confidently with gmatprepnow.com
Image
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8003
Re: W, X, Y and Z are four different positive integers. When X  [#permalink]

Show Tags

New post 08 Mar 2019, 18:36
3
1
GMATPrepNow wrote:
W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. If W = X – 7, what is the sum of all possible values of W?
A) 19
B) 20
C) 21
D) 22
E) 23



Let us convert the information into an equation..
X=YZ+W..
Substitute W=X-7, so X=YZ+X-7, or YZ=7=1*7..
Since 7 is prime only product of YZ will be 1*7, and Y cannot be 1, as X and Z will be same then 7=1*7+0
So Y=7, now the remainder W has to be less than Y, so less than 7, but it cannot be 1 as Z is 1 and all numbers are different.
Thus, the possible values of W are 2, 3, 4, 5 and 6 and sum of these values is 2+3+4+5+6=20

B
_________________
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4015
Location: Canada
Re: W, X, Y and Z are four different positive integers. When X  [#permalink]

Show Tags

New post 09 Mar 2019, 10:30
1
Top Contributor
GMATPrepNow wrote:
W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. If W = X – 7, what is the sum of all possible values of W?
A) 19
B) 20
C) 21
D) 22
E) 23


Given: When X is divided by Y, the quotient is Z and the remainder is W.
------ASIDE-------
There's a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
---------------------------------------
So, from the given information, we can write: X = YZ + W

Also given: W = X – 7
Take X = YZ + W and replace X with X - 7 to get: X = YZ + X - 7
Subtract X from both sides: 0 = YZ - 7
Rewrite as: 7 = YZ

We're told that Y and Z are positive INTEGERS. So, there are only 2 possible cases:
case i: Y = 1 and Z = 7
case ii: Y = 7 and Z = 1

case i yields a CONTRADICTION.
If Y = 1, then we are dividing X by 1, and if we divide by 1, the remainder will always be ZERO.
In other words, if Y = 1, then W = 0
However, we are told that W is a POSITIVE integer.
So, we can definitely rule out case i, which means it MUST be the case that Y = 7 and Z = 1 (case ii)

So, we have: When X is divided by 7, the quotient is 1 and the remainder is W
This tells us that 7 divides into X 1 time
So, the possible values of X are: 7, 8, 9, 10, 11, 12 and 13 (since 7 divides into each value 1 time.
Let's check each case.

If X = 7, then the remainder (W) is 0. Since we're told W is POSITIVE, we can ELIMINATE this case.
If X = 8, then the remainder (W) is 1. Since Y already equals 1, and since we're told the numbers are DIFFERENT, we can ELIMINATE this case.
If X = 9, then the remainder (W) is 2. So, when X (9) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 2. PERFECT!
If X = 10, then the remainder (W) is 3. So, when X (10) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 3. PERFECT!
If X = 11, then the remainder (W) is 4. So, when X (11) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 4. PERFECT!
If X = 12, then the remainder (W) is 5. So, when X (12) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 5. PERFECT!
If X = 13, then the remainder (W) is 6. So, when X (13) is divided by 7 (Y), the quotient (Z) is 1, and the remainder (W) is 6. PERFECT!

What is the sum of all possible values of W?
Sum = 2 + 3 + 4 + 5 + 6
= 20

Answer: B

Cheers,
Brent

RELATED VIDEO FROM MY COURSE

_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Bot
Re: W, X, Y and Z are four different positive integers. When X   [#permalink] 09 Mar 2019, 10:30
Display posts from previous: Sort by

W, X, Y and Z are four different positive integers. When X

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





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