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

 It is currently 15 Nov 2019, 13:54 ### 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.  # If x and y are positive integers such that x/y=33.375,

Author Message
TAGS:

### Hide Tags

Intern  Joined: 18 Mar 2012
Posts: 45
GPA: 3.7
If x and y are positive integers such that x/y=33.375,  [#permalink]

### Show Tags

3
5 00:00

Difficulty:   35% (medium)

Question Stats: 68% (01:35) correct 32% (01:47) wrong based on 296 sessions

### HideShow timer Statistics

If x and y are positive integers such that x/y=33.375, which of the following could be the remainder when x is divided by y?

A. 8
B. 21
C. 25
D. 44
E. 47

I assumed that the remainder would be a number "b" where b / y = 0.375. But didn't know how to proceed.
Thanks!
Math Expert V
Joined: 02 Sep 2009
Posts: 59075
Re: If x and y are positive integers such that x/y=33.375,  [#permalink]

### Show Tags

3
4
alexpavlos wrote:
If x and y are positive integers such that x/y=33.375, which of the following could be the remainder when x is divided by y?

A. 8
B. 21
C. 25
D. 44
E. 47

I assumed that the remainder would be a number "b" where b / y = 0.375. But didn't know how to proceed.
Thanks!

$$x$$ divided by $$y$$ yields the remainder of $$r$$ can always be expressed as: $$\frac{x}{y}=q+\frac{r}{y}$$ (which is the same as $$x=qy+r$$), where $$q$$ is the quotient and $$r$$ is the remainder.

$$\frac{x}{y}=33.375=33\frac{375}{1,000}=33\frac{3}{8}=33+\frac{3}{8}$$, so according to the above $$\frac{r}{y}=\frac{3}{8}$$, which means that $$r$$ must be a multiple of 3. Only option B offers answer which is a multiple of 3.

Hope it's clear.
_________________
##### General Discussion
Intern  Joined: 04 Mar 2012
Posts: 36
Re: f x and y are positive integers such that x / y = 33.375, wh  [#permalink]

### Show Tags

1
IMO B

You are correct upto b/y, where b is the remainder..

0.375 can be represented as 3/8, so in our case, b must be the multiple of 3.. from the options given, only B(21) matches this criteria, hence B is the answer
SVP  P
Joined: 24 Jul 2011
Posts: 1897
GMAT 1: 780 Q51 V48 GRE 1: Q800 V740 Re: f x and y are positive integers such that x / y = 33.375, wh  [#permalink]

### Show Tags

The answer is B - 21 because 21/0.375 yields an integer (= 56) and none of the other options does

x/y = Integer + Remainder
=> x/y = 33 + 0.375

Multiplying both sides by 56,
56(x/y) = 56*33 + 21

ALTERNATIVELY,you may calculate as follows:
x/y = 33.375
=> x/y = 33375/1000 = 267/8 = (33*8 + 3)/8

Multiply both sides by 7 to get
x/y = (33*56 + 21)/8 which can be written as 33*56/8 + 21/8

Once we know that we can get 3 as a remainder, we can select the answer choice that is a multiple of 3 (21 in this case)

The answer is therefore choice (B)
_________________

Awesome Work | Honest Advise | Outstanding Results

Reach Out, Lets chat!
Email: info at gyanone dot com | +91 98998 31738 | Skype: gyanone.services
Senior Manager  Joined: 23 Oct 2010
Posts: 319
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38 Re: If x and y are positive integers such that x/y=33.375,  [#permalink]

### Show Tags

x/y=33.375 or x/y=33 + 375/1000

remainder/y=375/1000=5*5*5*3/5*5*5*2*2*2=3/8
R/y=3/8
8R=3y

so, ur remainder must be divisible by 3. only answer choice B is divisible by 3.
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth
Director  Joined: 03 May 2007
Posts: 622
Schools: University of Chicago, Wharton School
Re: If x and y are positive integers such that x/y=33.375,  [#permalink]

### Show Tags

alexpavlos wrote:
If x and y are positive integers such that x/y=33.375, which of the following could be the remainder when x is divided by y?

A. 8
B. 21
C. 25
D. 44
E. 47

I assumed that the remainder would be a number "b" where b / y = 0.375. But didn't know how to proceed.
Thanks!

x/y=33.375
x = 33y + 0.375y

quotient (q) = 33
reminder (r) = 0.375y

Since x and y are positive integers, quotient and reminder are always integers or whole numbers. Then, r must be one of these whole numbers from the answer choices. We need to find which one of these answer choices is divisible by 0.375.
r = 0.375y
r = 3y/8

A. If r = 8, 3y/8 = 8, y = 64/3
B. If r = 21, 3y/8 = 21, y = 56
C. If r = 25, 3y/8 = 25, y = 200/3
D. If r = 44, 3y/8 = 44, y = 353/3
E. If r = 47, 3y/8 = 47, y = 376/3

So only, B has integer value/whole number. So its B.
Manager  B
Joined: 12 Oct 2012
Posts: 106
WE: General Management (Other)
Re: If x and y are positive integers such that x/y=33.375,  [#permalink]

### Show Tags

[Decimal of the Quotient] = $$\frac{Remainder}{Divisor}$$

Now, x/y = 33.375

$$\frac{R}{Y}$$ = $$\frac{375}{1000}$$=$$\frac{3}{8}$$

Hence, R (remainder) will always be a multiple of 3. Ans is B => 21
Manager  Joined: 18 Jan 2010
Posts: 238
Re: If x and y are positive integers such that x/y=33.375,  [#permalink]

### Show Tags

alex1233 wrote:
If x and y are positive integers such that x/y=33.375, which of the following could be the remainder when x is divided by y?

A. 8
B. 21
C. 25
D. 44
E. 47

I assumed that the remainder would be a number "b" where b / y = 0.375. But didn't know how to proceed.
Thanks!

$$\frac{x}{y} = \frac{33.375}{1} =\frac{33.375 *2}{2} =\frac{66.75}{2} = \frac{66.75 * 2}{4} = \frac{133.5}{4}= \frac{133.5 * 2}{8} =\frac{267}{8}$$

One of the numbers given in the options is left as a remainder when x is divided by y. So if these numbers are added to x, then they should be divisible by y.

267+8 = 275 --> Not divisible by 8.
267+21 = 288 --> divisible by 8. --> Required answer. (we are lucky that in the 2nd option itself we got such a number. Otherwise we might have to test all given options)

Another way

(267/8) --> remainder is 3. IF I add 5 to it then it will be divisible by 8

Select such a number which when divided by 8, leaves a remainder 5. B is again the option.
Senior Manager  S
Joined: 12 Sep 2017
Posts: 306
If x and y are positive integers such that x/y=33.375,  [#permalink]

### Show Tags

Hello everyone!

Just to clarify concepts,

$$\frac{x}{y}=q+\frac{r}{y}$$

$$\frac{x}{y}=33.375=33\frac{375}{1,000}=33\frac{3}{8}=33+\frac{3}{8}$$

Does the above means that y is a multiple of 8 and the remainder must be a multiple of 3?

Kind regards! If x and y are positive integers such that x/y=33.375,   [#permalink] 22 Jan 2019, 15:04
Display posts from previous: Sort by

# If x and y are positive integers such that x/y=33.375,  