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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
07 Jan 2013, 05:59

1

This post received KUDOS

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

76% (02:24) correct
24% (01:54) wrong based on 113 sessions

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?

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
06 Apr 2014, 09:39

1

This post received 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.

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
07 Jan 2013, 06:21

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.

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.

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.

Re: a, b, c, and d are positive integers. If the remainder is 9 [#permalink]
06 Apr 2014, 09:27

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

gmatclubot

Re: a, b, c, and d are positive integers. If the remainder is 9
[#permalink]
06 Apr 2014, 09:27

1. My favorite football team to infinity and beyond, the Dallas Cowboys, currently have the best record in the NFL and I’m literally riding on cloud 9 because...

I couldn’t help myself but stay impressed. young leader who can now basically speak Chinese and handle things alone (I’m Korean Canadian by the way, so...