Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 26 Sep 2016, 09:03

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# a, b, c, and d are positive integers. If the remainder is 9

Author Message
TAGS:

### Hide Tags

Current Student
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 152
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
Followers: 10

Kudos [?]: 271 [1] , given: 35

a, b, c, and d are positive integers. If the remainder is 9 [#permalink]

### Show Tags

07 Jan 2013, 06:59
1
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:23) correct 29% (02:04) wrong based on 178 sessions

### HideShow timer Statistics

a, b, c, and d are positive integers. If the remainder is 9 when a is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d?

(A) 20
(B) 19
(C) 18
(D) 16
(E) 15
[Reveal] Spoiler: OA

_________________

Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Manager
Joined: 12 Mar 2012
Posts: 94
Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q49 V36
GPA: 3.2
WE: Information Technology (Computer Software)
Followers: 9

Kudos [?]: 313 [3] , given: 22

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]

### Show Tags

07 Jan 2013, 07:21
3
KUDOS
When a is divided by b remainder is 9 that means b is greater than or equals to 10, similarly d is greater than or equals to 6.
b + d cannot be 15, hence E is the answer.
Current Student
Joined: 27 Jun 2012
Posts: 418
Concentration: Strategy, Finance
Followers: 72

Kudos [?]: 715 [0], given: 183

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]

### Show Tags

09 Jan 2013, 16:12
1
This post was
BOOKMARKED
a/b gives reminder 9, hence $$b\geq{10}$$
c/d gives reminder 5, hence $$d\geq{6}$$

$$(b+d)\geq{16}$$

Among the answer choices, the only value that does NOT satisfy above constraint is 15.

_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Manager
Joined: 25 Jun 2012
Posts: 71
Location: India
WE: General Management (Energy and Utilities)
Followers: 4

Kudos [?]: 95 [0], given: 15

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]

### Show Tags

10 Jan 2013, 04:15
PraPon wrote:
a/b gives reminder 9, hence $$b\geq{10}$$
c/d gives reminder 5, hence $$d\geq{6}[/ m] Add above inequalities: [m](b+d)\geq{16}$$

Among the answer choices, the only value that does NOT satisfy above constraint is 15.

Hi can u please explain highlighted part? I missing sumthing here..
Math Expert
Joined: 02 Sep 2009
Posts: 34862
Followers: 6484

Kudos [?]: 82677 [0], given: 10116

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]

### Show Tags

10 Jan 2013, 04:31
Expert's post
1
This post was
BOOKMARKED
bhavinshah5685 wrote:
PraPon wrote:
a/b gives reminder 9, hence $$b\geq{10}$$
c/d gives reminder 5, hence $$d\geq{6}[/ m] Add above inequalities: [m](b+d)\geq{16}$$

Among the answer choices, the only value that does NOT satisfy above constraint is 15.

Hi can u please explain highlighted part? I missing sumthing here..

If $$x$$ and $$y$$ are positive integers, there exist unique integers $$q$$ and $$r$$, called the quotient and remainder, respectively, such that $$y =divisor*quotient+remainder= xq + r$$ and $$0\leq{r}<x$$.

For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since $$15 = 6*2 + 3$$.

Notice that $$0\leq{r}<x$$ means that remainder is a non-negative integer and always less than divisor.

For more check Remainders chapter of Math Book: remainders-144665.html

a, b, c, and d are positive integers. If the remainder is 9 when a is divided by b, and the remainder is 5 when c is divided by d, which of the following is NOT a possible value for b + d?

(A) 20
(B) 19
(C) 18
(D) 16
(E) 15

According to the above, since the remainder is 9 when a is divided by b, then b (divisor) must be greater than 9 (remainder). So, the least value of b is 10.

Similarly, since he remainder is 5 when c is divided by d, then d must be greater than 5. So, the least value of d is 6.

Hence, the least value of b + d is 10 + 6 = 16. Therefore 15 (option E) is NOT a possible value for b + d.

Hope it's clear.
_________________
Intern
Joined: 04 Aug 2013
Posts: 30
Concentration: Finance, Real Estate
GMAT 1: 740 Q47 V46
GPA: 3.23
WE: Consulting (Real Estate)
Followers: 1

Kudos [?]: 14 [0], given: 12

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]

### Show Tags

06 Apr 2014, 10:27
what if a = 1 and b= 9...then wouldn't 1/9 still have a remainder of 9? doesn't the rule that b must be greater than or equal to 10 not hold in this case?

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 34862
Followers: 6484

Kudos [?]: 82677 [1] , given: 10116

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]

### Show Tags

06 Apr 2014, 10:39
1
KUDOS
Expert's post
HCalum11 wrote:
what if a = 1 and b= 9...then wouldn't 1/9 still have a remainder of 9? doesn't the rule that b must be greater than or equal to 10 not hold in this case?

Posted from my mobile device

No.

Let me ask you a question: how many leftover apples would you have if you had 1 apple and wanted to distribute in 9 baskets evenly? Each basket would get 0 apples and 1 apple would be leftover (remainder).

When a divisor is more than dividend, then the remainder equals to the dividend, for example:
3 divided by 4 yields the reminder of 3: $$3=4*0+3$$;
9 divided by 14 yields the reminder of 9: $$9=14*0+9$$;
1 divided by 9 yields the reminder of 1: $$1=9*0+1$$.

Theory on remainders problems: remainders-144665.html

All DS remainders problems to practice: search.php?search_id=tag&tag_id=198
All PS remainders problems to practice: search.php?search_id=tag&tag_id=199

_________________
Manager
Joined: 28 Jul 2011
Posts: 239
Followers: 3

Kudos [?]: 103 [0], given: 16

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]

### Show Tags

02 Feb 2015, 10:13
Given
a,b,c,d > 0 Int

b+d != ? (! = not)

a=bq+9 (q=1,2,3.....)
c=dr+5 (r=1,2,3.....)

when q=r=1

a=b+9 amd c=d+5
b=a-9 and d=c-5

=b+d
=a-9+c-5
=a+c-14

as a,b,c,d > 0 Int
therefore a+b-14 > 1
hence 15 is the only exception.

But Bunuel's explanation is more logical
Re: a, b, c, and d are positive integers. If the remainder is 9   [#permalink] 02 Feb 2015, 10:13
Similar topics Replies Last post
Similar
Topics:
4 C/D = 9.75 When dividing positive integer C by positive 5 05 Aug 2014, 11:31
If a·b·c·d=390, where a, b, c and d are positive integers 2 24 Mar 2014, 05:13
3 a, b, c, and d are positive consecutive integers and a < b < 3 17 Aug 2013, 10:34
16 If a, b, c and d are positive integers and a/b < c/d, which 9 27 May 2013, 14:36
30 Positive integers a, b, c, d and e are such that a<b<c<d<e 13 18 Oct 2010, 10:57
Display posts from previous: Sort by