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

 It is currently 22 Oct 2018, 11:42

### 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

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

Author Message
Manager
Status: Still Struggling
Joined: 03 Nov 2010
Posts: 121
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

Updated on: 23 Nov 2013, 06:02
1
10
00:00

Difficulty:

65% (hard)

Question Stats:

58% (01:07) correct 42% (00:43) wrong based on 127 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-the-positive-integers-q-r-s-and-t-the-remainder-when-141251.html

_________________

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 Nov 2013, 06:02, edited 1 time in total.
Renamed the topic and edited the question.
Retired Moderator
Joined: 20 Dec 2010
Posts: 1835
Re: positive integers q, r, s, and t  [#permalink]

### Show Tags

09 Oct 2011, 08:28
4
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"
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 50042
Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

### Show Tags

23 Nov 2013, 06:03
4
5
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-the-positive-integers-q-r-s-and-t-the-remainder-when-141251.html
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 8536
Re: For the positive integers q, r, s, and t, the remainder when  [#permalink]

### Show Tags

21 Sep 2018, 04:28
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.
_________________
Re: For the positive integers q, r, s, and t, the remainder when &nbs [#permalink] 21 Sep 2018, 04:28
Display posts from previous: Sort by