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

It is currently 18 Nov 2018, 10:42

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 in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th

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

Hide Tags

Board of Directors
User avatar
P
Joined: 01 Sep 2010
Posts: 3306
The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

Show Tags

New post 23 Jul 2017, 11:30
5
Top Contributor
14
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

71% (02:07) correct 29% (02:03) wrong based on 576 sessions

HideShow timer Statistics

The product of 3,305 and the 1-digit integer x is a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of all possible values of y, then which of the following gives the members of A and B?

A AND B


A. {1,3,5,7,9} (0,1,2,3,4,5,6,7,8,9}

B. {1,3,5,7,9} {1,3,5,7,9}

C. {3,5,7,9} {1,5,7,9}

D. {5,7,9} {1,5,7}

E. {5,7,9} {1,5,9}

_________________

COLLECTION OF QUESTIONS AND RESOURCES
Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection - The Next Generation 3. Bunuel Signature Collection ALL-IN-ONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos
Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Reading-comprehension_Oldy but goldy question banks

Most Helpful Expert Reply
Manhattan Prep Instructor
User avatar
G
Joined: 04 Dec 2015
Posts: 635
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

Show Tags

New post 23 Jul 2017, 14:11
11
1
3
carcass wrote:
The product of 3,305 and the 1-digit integer x is a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of all possible values of y, then which of the following gives the members of A and B?

A AND B


A. {1,3,5,7,9} (0,1,2,3,4,5,6,7,8,9}

B. {1,3,5,7,9} {1,3,5,7,9}

C. {3,5,7,9} {1,5,7,9}

D. {5,7,9} {1,5,7}

E. {5,7,9} {1,5,9}


Wow. There are a lot of steps to this one. The key is going to be extremely careful organization (you should pick up on that when you see how many numbers there are in the answer choices, and the complexity of the question they're asking you.)

First, I read the whole thing. Then I approached the first sentence:

3305x is a 5-digit integer.

That probably limits the possible values for x. For instance, x can't be 1, 2, or 3, because the product would be too small. Is there an upper limit to the values of x? For instance, could x be 9? To check, I multiplied 3305*9 on my paper and found that the result had 5 digits. So, the acceptable values for x will be 4, 5, 6, 7, 8, and 9 (so far). I jotted those down on my scratch paper (large & clear).

4 5 6 7 8 9

The problem also says that the units digit of 3305x is 5. That means x must be odd. If x was even, the units digit would come out to 0. So, I crossed off all of the even numbers:

4 5 6 7 8 9

Now there are only three possible values for x. I don't see anything that limits it further than that, so I write down on my paper:

A = {5, 7, 9}

At this point, I also jot down the answer choices, A B C D E, and cross off everything except for D and E.

To figure out the values of y, we need to find the hundreds digit of 3305x. There's a rule that says that if you only want a particular digit, you can ignore everything past that digit. We can ignore the first 3 in 3305 and just treat it like 305, since it won't affect the hundreds digit of the result. That'll speed up the multiplication.

305 * 5 = 1525, hundreds digit = 5
305 * 7 = 2135, hundreds digit = 1
305 * 9 = 2745, hundreds digit = 7

So now I know B = {1, 5, 7}.

Finally, check this against the two remaining answer choices. D is correct.
_________________

Image

Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

My upcoming GMAT trial classes | GMAT blog archive

General Discussion
Manager
Manager
avatar
S
Joined: 13 Mar 2013
Posts: 165
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)
Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

Show Tags

New post 30 Jul 2017, 06:31
looks difficult .. but easy equation to solve .
So challenge if any will be the language of the question .
_________________

Regards ,

Manager
Manager
avatar
B
Joined: 11 Feb 2017
Posts: 190
The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

Show Tags

New post 03 Aug 2017, 07:55
ccooley wrote:
carcass wrote:
The product of 3,305 and the 1-digit integer x is a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of all possible values of y, then which of the following gives the members of A and B?

A AND B


A. {1,3,5,7,9} (0,1,2,3,4,5,6,7,8,9}

B. {1,3,5,7,9} {1,3,5,7,9}

C. {3,5,7,9} {1,5,7,9}

D. {5,7,9} {1,5,7}

E. {5,7,9} {1,5,9}


Wow. There are a lot of steps to this one. The key is going to be extremely careful organization (you should pick up on that when you see how many numbers there are in the answer choices, and the complexity of the question they're asking you.)

First, I read the whole thing. Then I approached the first sentence:

3305x is a 5-digit integer.

That probably limits the possible values for x. For instance, x can't be 1, 2, or 3, because the product would be too small. Is there an upper limit to the values of x? For instance, could x be 9? To check, I multiplied 3305*9 on my paper and found that the result had 5 digits. So, the acceptable values for x will be 4, 5, 6, 7, 8, and 9 (so far). I jotted those down on my scratch paper (large & clear).

4 5 6 7 8 9

The problem also says that the units digit of 3305x is 5. That means x must be odd. If x was even, the units digit would come out to 0. So, I crossed off all of the even numbers:

4 5 6 7 8 9

Now there are only three possible values for x. I don't see anything that limits it further than that, so I write down on my paper:

A = {5, 7, 9}

At this point, I also jot down the answer choices, A B C D E, and cross off everything except for D and E.

To figure out the values of y, we need to find the hundreds digit of 3305x. There's a rule that says that if you only want a particular digit, you can ignore everything past that digit. We can ignore the first 3 in 3305 and just treat it like 305, since it won't affect the hundreds digit of the result. That'll speed up the multiplication.

305 * 5 = 1525, hundreds digit = 5
305 * 7 = 2135, hundreds digit = 1
305 * 9 = 2745, hundreds digit = 7

So now I know B = {1, 5, 7}.

Finally, check this against the two remaining answer choices. D is correct.



If I am a 600-650 scorer , then is it possible to solve this question in just 2 minutes?
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

Show Tags

New post 09 Aug 2017, 11:43
2
1
carcass wrote:
The product of 3,305 and the 1-digit integer x is a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of all possible values of y, then which of the following gives the members of A and B?

A AND B


A. {1,3,5,7,9} (0,1,2,3,4,5,6,7,8,9}

B. {1,3,5,7,9} {1,3,5,7,9}

C. {3,5,7,9} {1,5,7,9}

D. {5,7,9} {1,5,7}

E. {5,7,9} {1,5,9}


We are given that the product of 3,305 and the 1-digit integer x is a 5-digit integer, the units (ones) digit of the product is 5, and the hundreds digit is y. In order for the product to be a 5-digit integer, we see that x cannot be 1, 2, or 3. In order for the product to have 5 as its ones digit, we can also eliminate 4, 6, and 8 from consideration.

Thus, x can only be 5, 7, or 9.

Let’s now solve for y:

When x is 5, since 5 x 3,305 = 16,525, y is 5.

When x is 7, since 7 x 3,305 = 23,135, y is 1.

When x is 9, since 9 x 3,305 = 29,745, y is 7.

Thus, A = 5, 7, and 9 and B = 1, 5, and 7.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Intern
avatar
B
Joined: 06 Jul 2017
Posts: 1
GMAT ToolKit User
Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

Show Tags

New post 01 Sep 2017, 03:16
"The product of 3,305 and the 1-digit integer x is a 5-digit integer"

It is slightly confusing. I thought, above statement meant, product of three integers i.e. 3, 305 and another integer x.
Manager
Manager
User avatar
B
Joined: 21 Jun 2017
Posts: 84
Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

Show Tags

New post 10 Sep 2017, 03:03
2
carcass wrote:
The product of 3,305 and the 1-digit integer x is a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of all possible values of y, then which of the following gives the members of A and B?

A AND B


A. {1,3,5,7,9} (0,1,2,3,4,5,6,7,8,9}

B. {1,3,5,7,9} {1,3,5,7,9}

C. {3,5,7,9} {1,5,7,9}

D. {5,7,9} {1,5,7}

E. {5,7,9} {1,5,9}



_ _ Y _ 5 = 3305 x X
we know x cannot equal 1 or 3 because the product of that does not equal 5 digits, but only 4
therefore eliminate answers a,b,c

for x, we are left with 5,7,9 -- just plug these in for x

3305 x 5 = 16,525 wherein y = 5
3305 x 7 = 23,135 wherein y = 1
3305 x 9 = 29,745 wherein y = 7

therefore the answer is D

hope that helps
Manager
Manager
User avatar
B
Joined: 21 Jun 2017
Posts: 84
Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

Show Tags

New post 10 Sep 2017, 03:04
nareshlawadia wrote:
"The product of 3,305 and the 1-digit integer x is a 5-digit integer"

It is slightly confusing. I thought, above statement meant, product of three integers i.e. 3, 305 and another integer x.



When you are translating english to math, "product" means multiplication, and "is" translates to equals sign

so 3,305 x X = a five digit integer

hope that helps
Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1253
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

Show Tags

New post 24 Jun 2018, 04:33
niks18 chetan2u VeritasPrepKarishma

Can I skip calculation part as shown by JeffTargetTestPrep
knowing that 9*9 = 81 ?
All individual set elements must result in product as 5 in unit digit.
_________________

It's the journey that brings us happiness not the destination.

PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

Show Tags

New post 24 Jun 2018, 05:40
1
adkikani wrote:
niks18 chetan2u VeritasPrepKarishma

Can I skip calculation part as shown by JeffTargetTestPrep
knowing that 9*9 = 81 ?
All individual set elements must result in product as 5 in unit digit.


Hi adkikani

Once you have identified the elements of set x, then only two options remain D & E.

concentrate on the last three digits of the number 3305 when you multiply 05 by x, then the product will not have any carry over for the hundred's digit. for e.g 05*9=45 and there is no carry forward.

Hence the hundreds digit of the resulting product will be simply unit's digit of 3*x

so y = 3*5=15

y=3*7=21 & y=3*9=27

so you can save yourself from calculation if you have visualized this step
Director
Director
avatar
G
Joined: 19 Oct 2013
Posts: 502
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
GMAT ToolKit User CAT Tests
Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th  [#permalink]

Show Tags

New post 25 Oct 2018, 07:05
carcass wrote:
The product of 3,305 and the 1-digit integer x is a 5-digit integer. The units (ones) digit of the product is 5 and the hundreds digit is y. If A is the set of all possible values of x and B is the set of all possible values of y, then which of the following gives the members of A and B?

A AND B


A. {1,3,5,7,9} (0,1,2,3,4,5,6,7,8,9}

B. {1,3,5,7,9} {1,3,5,7,9}

C. {3,5,7,9} {1,5,7,9}

D. {5,7,9} {1,5,7}

E. {5,7,9} {1,5,9}


To understand this we need to keep this thought in mind that x > 4 because 3,305 * 3 is less than 5 digits.

Since the ones digit is 5 that means x has to be an odd integer greater than 4. These are 5,7, and 9.

Now we are concerned with hundreds digit.

We can take 300 * 5 = 1,500

300 * 7 = 2,100

and 300 * 9 = 2,700

So we get 1,5, and 7

Answer choice D
GMAT Club Bot
Re: The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th &nbs [#permalink] 25 Oct 2018, 07:05
Display posts from previous: Sort by

The product of 3,305 and the 1-digit integer xis a 5-digit integer. Th

  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®.