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

 It is currently 16 Oct 2019, 08:04 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  a, b, c, and d are positive integers. If the remainder is 9

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

Hide Tags

Manager  Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 132
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33 GPA: 3.5
WE: Information Technology (Investment Banking)
a, b, c, and d are positive integers. If the remainder is 9  [#permalink]

Show Tags

4
16 00:00

Difficulty:   35% (medium)

Question Stats: 70% (01:55) correct 30% (02:12) wrong based on 247 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

_________________
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: 79
Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q49 V36 GPA: 3.2
WE: Information Technology (Computer Software)
Re: a, b, c, and d are positive integers. If the remainder is 9  [#permalink]

Show Tags

4
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.
Senior Manager  Joined: 27 Jun 2012
Posts: 350
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
Re: a, b, c, and d are positive integers. If the remainder is 9  [#permalink]

Show Tags

2
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.

Hence choice(E) is the answer.
_________________
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
Finance your Student loan through SoFi and get \$100 referral bonus : Click here
Manager  Joined: 25 Jun 2012
Posts: 61
Location: India
WE: General Management (Energy and Utilities)
Re: a, b, c, and d are positive integers. If the remainder is 9  [#permalink]

Show Tags

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.

Hence choice(E) is the answer.

Hi can u please explain highlighted part? I missing sumthing here..
Math Expert V
Joined: 02 Sep 2009
Posts: 58378
Re: a, b, c, and d are positive integers. If the remainder is 9  [#permalink]

Show Tags

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.

Hence choice(E) is the answer.

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: 28
Concentration: Finance, Real Estate
GMAT 1: 740 Q47 V46 GPA: 3.23
WE: Consulting (Real Estate)
Re: a, b, c, and d are positive integers. If the remainder is 9  [#permalink]

Show Tags

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 V
Joined: 02 Sep 2009
Posts: 58378
Re: a, b, c, and d are positive integers. If the remainder is 9  [#permalink]

Show Tags

1
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: http://gmatclub.com/forum/remainders-144665.html

All DS remainders problems to practice: http://gmatclub.com/forum/search.php?se ... tag_id=198
All PS remainders problems to practice: http://gmatclub.com/forum/search.php?se ... tag_id=199

_________________
Manager  Joined: 28 Jul 2011
Posts: 159
Re: a, b, c, and d are positive integers. If the remainder is 9  [#permalink]

Show Tags

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
Director  G
Joined: 26 Oct 2016
Posts: 613
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44 GPA: 4
WE: Education (Education)
Re: a, b, c, and d are positive integers. If the remainder is 9  [#permalink]

Show Tags

To answer, we must recognize an important rule: the divisor must be greater than the remainder. Let's look at a few examples:
10 ÷ 4 = 2 remainder 2 (divisor 4 is greater than remainder 2)
23 ÷ 6 = 3 remainder 5 (divisor 6 is greater than remainder 5)

If the divisor weren't greater than the remainder, the divisor would be able to divide into the dividend at least one more time. Let's take an incorrect example to illustrate:
23 ÷ 6 = 2 remainder 11.

In this case, we've framed the operation such that the divisor is LESS than the remainder (6 is less than 11). The error is that 6 actually goes into 23 three times. The remainder is what is left over when the divisor has been divided into the dividend as many times as possible. Therefore, if a divided by b gives a remainder of 9, we can conclude that b is greater than 9: b ≥ 10.

Likewise, if c divided by d gives a remainder of 5, we can conclude that d is greater than 5: d ≥ 6. Therefore, we can determine a minimum for the sum: b + d ≥ 16.
Only 15 is too small.

The correct answer is E.
_________________
Thanks & Regards,
Anaira Mitch
Intern  B
Joined: 23 Sep 2016
Posts: 10
Location: India
Concentration: Operations, Strategy
GMAT 1: 750 Q50 V41 GPA: 3
WE: Operations (Energy and Utilities)
Re: a, b, c, and d are positive integers. If the remainder is 9  [#permalink]

Show Tags

a/b = Q (9), so 'b' cant be 9 or less than 9. It has to be greater than 9.
c/d = Q (5), so 'd' cant be d or less than 5. It has to be greater than 5.

Now by adding the least values of b & c,
b+c = 10+6 = 16. (Considering only the least values.)

Among the answer choices, the only value that does NOT satisfy above constraint is option E i.e. 15.
Non-Human User Joined: 09 Sep 2013
Posts: 13199
Re: a, b, c, and d are positive integers. If the remainder is 9  [#permalink]

Show Tags

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: a, b, c, and d are positive integers. If the remainder is 9   [#permalink] 06 Feb 2019, 19:54
Display posts from previous: Sort by

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

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

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