It is currently 21 Nov 2017, 11:02

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha

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

Hide Tags

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42283

Kudos [?]: 132935 [2], given: 12391

W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha [#permalink]

Show Tags

New post 21 Jul 2016, 05:09
2
This post received
KUDOS
Expert's post
13
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

24% (02:21) correct 76% (02:14) wrong based on 232 sessions

HideShow timer Statistics

Kudos [?]: 132935 [2], given: 12391

1 KUDOS received
Manager
Manager
avatar
B
Joined: 16 Apr 2016
Posts: 66

Kudos [?]: 34 [1], given: 49

Location: United States (TX)
Concentration: Technology, Marketing
GMAT 1: 730 Q48 V42
GPA: 3.3
WE: Engineering (Energy and Utilities)
GMAT ToolKit User Reviews Badge
W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha [#permalink]

Show Tags

New post 21 Jul 2016, 06:31
1
This post received
KUDOS
Given WX * YZ = 1995

With Statement (1), knowing X is prime does not help us determine W. We know that either X or Z has to be 5, but we dont know which one.

With Statement (2), we are told Z is not prime. This means X has to be 5, which is prime (Note that we don't need to know statement 1 here).

Prime factors of 1995 are 3, 5, 7 and 19.

In order for our product to have a 5 in the units digit, we need an odd number to multiply by 5.

If Z is not prime, then it can be either 1 or 9 (rest of the odd integers are prime)

We know so far: W5 * Y(1 or 9) = 1995

Two possibilities: If X is 9, then YZ = 19 (one of the prime factors). But we would need WX to be 105 (3*5*7), which does not make sense.

The other option is that X is 1, which gives us YZ = 21 (3 * 7). Now WX is 95 (5*19) and this satisfies our two digit constraint. Thus W is 9.

Answer is B (Statement 2 alone)

Please let me know if I committed an error in my thinking.

Kudos [?]: 34 [1], given: 49

Director
Director
avatar
G
Joined: 26 Nov 2012
Posts: 592

Kudos [?]: 175 [0], given: 45

Premium Member CAT Tests
W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha [#permalink]

Show Tags

New post 21 Jul 2016, 07:08
Bunuel wrote:
W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. What is the value of W?

(1) X is a prime number
(2) Z is not a prime number



Factors of 1995 are 5 * 3 * 7 * 19 and also given that WX * YZ = 1995.. we are not sure which all factors take the values of w,x,y and z respectively.

Stat 1: X is a prime number , we have four different prime numbers... Insufficient.

Stat 2: Z is not a prime number..there is no such number...Insufficient...

IMO E is correct answer.

OA please...will correct if I missed anything.

Kudos [?]: 175 [0], given: 45

Expert Post
Top Contributor
4 KUDOS received
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1850

Kudos [?]: 2614 [4], given: 362

Location: Canada
W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha [#permalink]

Show Tags

New post 21 Jul 2016, 07:42
4
This post received
KUDOS
Expert's post
Top Contributor
3
This post was
BOOKMARKED
Bunuel wrote:
W, X, Y, and Z represent distinct digits such that (WX)(YZ) = 1995. What is the value of W?

(1) X is a prime number
(2) Z is not a prime number


Target question: What is the value of W?

Given: W, X, Y, and Z represent distinct digits such that (WX)(YZ) = 1995
Let's take a close look at what we can conclude from this info.
Whenever I see a big number like 1995, I consider finding its PRIME FACTORIZATION
1995 = (3)(5)(7)(19)
In what ways can we take this and rewrite 1995 as the product of two 2-digit integers?
We get 4 possible cases;
(WX)(YZ) = 1995
a) (21)(95) = 1995
b) (95)(21) = 1995
c) (35)(57) = 1995
d) (57)(35) = 1995

HOWEVER, since all 4 digits must be DISTINCT, we must eliminate cases c and c, which leaves us with only 2 possible cases.
(WX)(YZ) = 1995
a) (21)(95) = 1995
b) (95)(21) = 1995

Statement 1: X is a prime number
Since 1 is not prime, we can rule out case a.
This leaves only case b, which means W must equal 9
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Z is not a prime number
1 is the only NON-PRIME number, so this rules out case a.
This leaves only case b, which means W must equal 9
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer =
[Reveal] Spoiler:
D


RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image


Last edited by GMATPrepNow on 22 Jul 2016, 06:50, edited 1 time in total.

Kudos [?]: 2614 [4], given: 362

1 KUDOS received
Intern
Intern
avatar
Joined: 28 Mar 2014
Posts: 9

Kudos [?]: 2 [1], given: 32

Re: W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha [#permalink]

Show Tags

New post 22 Jul 2016, 04:17
1
This post received
KUDOS
GMATPrepNow wrote:
Bunuel wrote:
W, X, Y, and Z represent distinct digits such that (WX)(YZ) = 1995. What is the value of W?

(1) X is a prime number
(2) Z is not a prime number


Target question: What is the value of W?

Given: W, X, Y, and Z represent distinct digits such that (WX)(YZ) = 1995
Let's take a close look at what we can conclude from this info.
Whenever I see a big number like 1995, I consider finding its PRIME FACTORIZATION
1995 = (3)(5)(7)(19)
In what ways can we take this and rewrite 1995 as the product of two 2-digit integers?
We get 4 possible cases;
(WX)(YZ) = 1995
a) (21)(95) = 1995
b) (95)(21) = 1995
c) (35)(57) = 1995
d) (57)(35) = 1995

Statement 1: X is a prime number
This means that cases b, c and d are possible.
In cases b, c and d, W can equal 9, 3 or 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Z is not a prime number
The possible values of Z are 5, 1 and 7
1 is the only NON-PRIME number, so this rules out cases a, c and d.
This leaves only case b, which means W must equal 9
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer =
[Reveal] Spoiler:
B


RELATED VIDEO



The Option is D .Because W,X,Y,Z are distinct numbers so in the above scenario case C & D will not exist. 1 is not prime so only option is 95*21.

Kudos [?]: 2 [1], given: 32

Expert Post
Top Contributor
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1850

Kudos [?]: 2614 [0], given: 362

Location: Canada
Re: W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha [#permalink]

Show Tags

New post 22 Jul 2016, 06:51
Expert's post
Top Contributor
inshor wrote:
The Option is D .Because W,X,Y,Z are distinct numbers so in the above scenario case C & D will not exist. 1 is not prime so only option is 95*21.

Good catch. I carelessly missed the word "distinct"
I've edited my response.

Cheers and thanks,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2614 [0], given: 362

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15576

Kudos [?]: 283 [0], given: 0

Premium Member
Re: W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha [#permalink]

Show Tags

New post 30 Jul 2017, 05:19
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Intern
Intern
avatar
B
Joined: 21 Mar 2012
Posts: 17

Kudos [?]: 10 [0], given: 45

Location: India
GMAT 1: 710 Q49 V38
GMAT ToolKit User
Re: W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha [#permalink]

Show Tags

New post 30 Jul 2017, 06:05
What is the best way to solve this under two minutes? How are we to recognize such questions - any leads to similar questions?
VeritasPrepKarishma Bunuel

bumpbot wrote:
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.

Kudos [?]: 10 [0], given: 45

Expert Post
Math Expert
User avatar
P
Joined: 02 Aug 2009
Posts: 5222

Kudos [?]: 5867 [0], given: 118

Re: W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha [#permalink]

Show Tags

New post 30 Jul 2017, 06:40
Bunuel wrote:
W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. What is the value of W?

(1) X is a prime number
(2) Z is not a prime number


Hi..

factorize 1995..
\(1995=3*5*7*19\)
now 19 has to be multiplied with another prime factor otherwise the other integer becomes 3 digit integer 105.. 19*105
so possiblities--
1)19*3 and 5*7 that is 57 and 35... NOT possible as 5 is repeated
2) 19*5 and 3*7 that is 95 and 21.. possible
3) 19*7 and 3*5... NOT possible as 19*7 becomes 3-digit integer

WX can be 95 or 21..
so W can be 9 or 2


lets see the statements..
(1) X is a prime number
If X is prime WX has to be 95... so W is 9
suff

(2) Z is not a prime number
If Z is not prime, YZ must be 21.
so WZ is 95 and W is 9
suff

D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5867 [0], given: 118

1 KUDOS received
Senior Manager
Senior Manager
User avatar
G
Joined: 29 Jun 2017
Posts: 374

Kudos [?]: 70 [1], given: 66

GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha [#permalink]

Show Tags

New post 30 Jul 2017, 08:55
1
This post received
KUDOS
D is the Answer

factorization of 1995 yields 5x3x7x19 of which 95x21 is the combination we are interested in.

95x21=1995
the distinct digits are 1,2,9,5
w9 x5 y2 z1

1) X is prime = 95x21=1995 , w=9 , hence A or D. ( where X=5)
2) Z is not prime= 95x21=1995, w=9 hence Only D (where Z = 1) ( Therefore A is rejected)
_________________

Give Kudos for correct answer and/or if you like the solution.

Kudos [?]: 70 [1], given: 66

Manager
Manager
avatar
B
Joined: 22 Sep 2016
Posts: 215

Kudos [?]: 24 [0], given: 42

Location: India
GMAT 1: 710 Q50 V35
GPA: 4
Re: W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha [#permalink]

Show Tags

New post 01 Aug 2017, 19:56
Purvil311 wrote:
Given WX * YZ = 1995

With Statement (1), knowing X is prime does not help us determine W. We know that either X or Z has to be 5, but we dont know which one.

With Statement (2), we are told Z is not prime. This means X has to be 5, which is prime (Note that we don't need to know statement 1 here).

Prime factors of 1995 are 3, 5, 7 and 19.

In order for our product to have a 5 in the units digit, we need an odd number to multiply by 5.

If Z is not prime, then it can be either 1 or 9 (rest of the odd integers are prime)

We know so far: W5 * Y(1 or 9) = 1995

Two possibilities: If X is 9, then YZ = 19 (one of the prime factors). But we would need WX to be 105 (3*5*7), which does not make sense.

The other option is that X is 1, which gives us YZ = 21 (3 * 7). Now WX is 95 (5*19) and this satisfies our two digit constraint. Thus W is 9.

Answer is B (Statement 2 alone)

Please let me know if I committed an error in my thinking.


chetan2u please correct the OA. The answer should be B, as explained above.

1995 = 3*5*7*19
The only two digit couples that can be formed are
35*57
21*95
from statement 1, x is prime
it could be either of the two pairs as both have atleast one number with 5 as unit's digit.

statement 2, z isn't prime.
Only 21*95 will qualify. 1 is neither prime nor composite.
_________________

Desperately need 'KUDOS' !!

Kudos [?]: 24 [0], given: 42

Manager
Manager
avatar
B
Joined: 22 Sep 2016
Posts: 215

Kudos [?]: 24 [0], given: 42

Location: India
GMAT 1: 710 Q50 V35
GPA: 4
W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha [#permalink]

Show Tags

New post 01 Aug 2017, 19:58
chetan2u wrote:
Bunuel wrote:
W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. What is the value of W?

(1) X is a prime number
(2) Z is not a prime number


Hi..

factorize 1995..
\(1995=3*5*7*19\)
now 19 has to be multiplied with another prime factor otherwise the other integer becomes 3 digit integer 105.. 19*105
so possiblities--
1)19*3 and 5*7 that is 57 and 35... NOT possible as 5 is repeated
2) 19*5 and 3*7 that is 95 and 21.. possible
3) 19*7 and 3*5... NOT possible as 19*7 becomes 3-digit integer

WX can be 95 or 21..
so W can be 9 or 2


lets see the statements..
(1) X is a prime number
If X is prime WX has to be 95... so W is 9
suff

(2) Z is not a prime number
If Z is not prime, YZ must be 21.
so WZ is 95 and W is 9
suff

D


Statement 1 can easily qualify for both of the two.
Isn't 7 prime? Isn't 5 prime? Then, what's wrong with 35*57?
Why only 95?
The statement isn't saying that "ONLY" x is prime, right? :)
_________________

Desperately need 'KUDOS' !!

Kudos [?]: 24 [0], given: 42

W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha   [#permalink] 01 Aug 2017, 19:58
Display posts from previous: Sort by

W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. Wha

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.