 It is currently 14 Jul 2020, 11:20 ### 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

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. # W, X, Y and Z are four different positive integers.  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: GRE Instructor Joined: 10 Apr 2015
Posts: 3535
Followers: 133

Kudos [?]: 4016  , given: 65

W, X, Y and Z are four different positive integers. [#permalink]
2
KUDOS
Expert's post 00:00

Question Stats: 29% (02:26) correct 70% (02:42) wrong based on 17 sessions
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 – 4, which of the following is a possible value of X?

Indicate ALL possible values of X.

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
(F) 9
(G) 10
(H) 11
[Reveal] Spoiler: OA

_________________

Brent Hanneson – Creator of greenlighttestprep.com Last edited by GreenlightTestPrep on 12 Mar 2019, 07:54, edited 3 times in total.
Edit the timer GRE Instructor Joined: 10 Apr 2015
Posts: 3535
Followers: 133

Kudos [?]: 4016  , given: 65

Re: W, X, Y and Z are four different positive integers. [#permalink]
1
KUDOS
Expert's post
GreenlightTestPrep 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 – 4, which of the following is a possible value of X?

Indicate ALL possible values of X.

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
(F) 9
(G) 10
(H) 11

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 – 4
Take X = YZ + W and replace X with X - 4 to get: X = YZ + X - 4
Subtract X from both sides: 0 = YZ - 4
Rewrite as: 4 = YZ

We're told that Y and Z are DIFFERENT positive INTEGERS. So, there are only 2 possible cases:
case i: Y = 1 and Z = 4
case ii: Y = 4 and Z = 1

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 = 4 and Z = 1 (case ii)

So, we have: When X is divided by 4, the quotient is 1 and the remainder is W
This tells us that 4 divides into X 1 time
So, the possible values of X are: 4, 5, 6, and 7 (since 4 divides into each value 1 time).
Let's check each case.

If X = 4, then the remainder (W) is 0. Since we're told W is POSITIVE, we can ELIMINATE this case.
If X = 5, 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 = 6, then the remainder (W) is 2. So, when X (6) is divided by 4 (Y), the quotient (Z) is 1, and the remainder (W) is 2. PERFECT!
If X = 7, then the remainder (W) is 3. So, when X (7) is divided by 4 (Y), the quotient (Z) is 1, and the remainder (W) is 3. PERFECT!

Cheers,
Brent

RELATED VIDEO FROM MY COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com Manager Joined: 17 Feb 2020
Posts: 63
Followers: 1

Kudos [?]: 37 , given: 17

Re: W, X, Y and Z are four different positive integers. [#permalink]
Why in the second case answer can't be 5? Because previously you outlined that the case Y=1 and X=4 is incorrect since when Y is divided by 1 remainder always 0, and now you say that 5 is inviavle, cause Y is already 1? However we should only consider the second case where Y is predetermined as 4? Could you please explain? Re: W, X, Y and Z are four different positive integers.   [#permalink] 29 Jun 2020, 19:16
Display posts from previous: Sort by

# W, X, Y and Z are four different positive integers.  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.