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

It is currently 21 Oct 2019, 20:45

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

For the positive integers q, r, s, and t, the remainder when

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
Status: Still Struggling
Joined: 03 Nov 2010
Posts: 111
Location: India
GMAT Date: 10-15-2011
GPA: 3.71
WE: Information Technology (Computer Software)
For the positive integers q, r, s, and t, the remainder when  [#permalink]

Show Tags

New post Updated on: 23 Sep 2019, 05:45
2
14
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

56% (02:19) correct 44% (02:29) wrong based on 280 sessions

HideShow timer Statistics

For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT

A. 32
B. 38
C. 44
D. 52
E. 63

_________________
Appreciation in KUDOS please!
Knewton Free Test 10/03 - 710 (49/37)
Princeton Free Test 10/08 - 610 (44/31)
Kaplan Test 1- 10/10 - 630
Veritas Prep- 10/11 - 630 (42/37)
MGMAT 1 - 10/12 - 680 (45/34)

Originally posted by krishnasty on 09 Oct 2011, 07:27.
Last edited by Bunuel on 23 Sep 2019, 05:45, edited 2 times in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Current Student
User avatar
V
Joined: 19 Mar 2012
Posts: 4263
Location: India
GMAT 1: 760 Q50 V42
GPA: 3.8
WE: Marketing (Non-Profit and Government)
Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

Show Tags

New post 21 Jul 2012, 14:09
3
9
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:

1)32
2)38
3)44
4)52
5)63

Its obvious from the prompt that r is greater than 7 and t is greater than 3
so the product of rt must have at least 2 factors, one which is greater than 7 and other greater than 3
Now lets break down the possible factors so that this condition is validated
The (r,t) pairs for the options can be:
for 32, (8,4)
for 44, (11,4)
for 52 (13,4)
for 63 (9,7)
however 32 can only be written as 38*1 or 19*2 none of which can validate the prompt.
Hence answer is B
Hope this helps
Cheers
_________________
Most Helpful Community Reply
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1571
Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

Show Tags

New post 09 Oct 2011, 08:28
4
1
krishnasty wrote:
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT

32
38
44
52
63


r>=8 And t>=4

32=8*4(Possible)
38=19*2 OR 38*1, none of which is possible because 2 AND 1 are both less than 4 OR 8.
44=11*4
52=13*4
63=9*7

Ans: "B"
_________________
General Discussion
VP
VP
User avatar
Joined: 02 Jul 2012
Posts: 1103
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

Show Tags

New post 24 Oct 2012, 23:24
1
Jp27 wrote:
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT

32
38
44
52
63

OA

From the question we know that r >= 8 and s >=4

So A is possible, from there how to proceed?

Cheers


\(32 = 2^5\)
\(38 = 2^1 * 19^1\)
\(44 = 2^2 * 11^1\)
\(52 = 2^2 * 13^1\)
\(63 = 3^2 * 7^1\)
All options other than B can be represented as a product of two numbers one being greater than or equal to 4 and the other being greater than or equal to 8.

So, answer should be B

Kudos Please... If my post helped.
_________________
Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58398
For the positive integers q, r, s, and t, the remainder when  [#permalink]

Show Tags

New post 23 Nov 2013, 06:03
4
7
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT
A. 32
B. 38
C. 44
D. 52
E. 63

Important property: remainder cannot be greater than the divisor.

Therefore, since the remainder when q is divided by r is 7, then r>7;
Similarly, since the remainder when s is divided by t is 3, then t>3.

Now, all answers, except 38 can be represented as the product of two multiples one of which is greater than 7 and another is greater than 3:

32=8*4
44=11*4
52=13*4
63=9*7

However, 38=1*38 or 19*2, thus rt cannot equal to 38.

Answer: B.
_________________
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1224
Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

Show Tags

New post 29 Aug 2017, 19:06
TechWithNoExp wrote:
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:

A. 32
B. 38
C. 44
D. 52
E. 63


r>7
t>3
rt factor can't be<4
38 has two sets of factors: 1*38*and 2*19
1 and 2 are both<4
B
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4016
Location: Canada
Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

Show Tags

New post 28 Aug 2018, 13:55
Top Contributor
TechWithNoExp wrote:
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:

A. 32
B. 38
C. 44
D. 52
E. 63


Great question!!

USEFUL PROPERTY:
When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
Conversely, if I know that, when k is divided by w, the remainder is 5, then I know that w must be greater than 5

The remainder when q is divided by r is 7
This tells us that r is greater than 7

s is divided by t is 3
This tells us that t is greater than 3

Now check the answer choices...

A) 32
Is it POSSIBLE for rt to equal 32?
Yes, if r = 8 and t = 4, then rt = 32
ELIMINATE A

B) 38
Is it POSSIBLE for rt to equal 38?
NO.
There are only two ways to write 38 as the product of POSITIVE INTEGERS:
i) (2)(19) = 38
ii) (1)(38) = 38
If r is greater than 7 and t is greater than 3, there's no way that one of the values (r or t) can equal 1 or 2.

Answer: B

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Image
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13385
Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

Show Tags

New post 23 Sep 2019, 05:44
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: For the positive integers q, r, s, and t, the remainder when   [#permalink] 23 Sep 2019, 05:44
Display posts from previous: Sort by

For the positive integers q, r, s, and t, the remainder when

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





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