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

 It is currently 22 Feb 2019, 04:52

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# How many integers from 0 to 1000 inclusive, have a remainder of 3 when

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

### Hide Tags

Senior Manager
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 289
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22
GPA: 3.7
WE: Information Technology (Consulting)
How many integers from 0 to 1000 inclusive, have a remainder of 3 when  [#permalink]

### Show Tags

Updated on: 01 Oct 2017, 03:12
2
3
00:00

Difficulty:

55% (hard)

Question Stats:

66% (01:40) correct 34% (01:31) wrong based on 80 sessions

### HideShow timer Statistics

How many integers from 0 to 1000 inclusive, have a remainder of 3 when divided by 16?

A. 61

B. 62

C. 63

D. 64

E. 65

Originally posted by RMD007 on 30 Sep 2017, 04:20.
Last edited by Bunuel on 01 Oct 2017, 03:12, edited 1 time in total.
Renamed the topic.
Retired Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
Re: How many integers from 0 to 1000 inclusive, have a remainder of 3 when  [#permalink]

### Show Tags

30 Sep 2017, 04:39
1
1
RMD007 wrote:
How many integers from 0 to 1000 inclusive, have a remainder of 3 when divided by 16?

A. 61

B. 62

C. 63

D. 64

E. 65

First no that will leave a remainder of 3 when divide by 16, $$a=3$$

Last no that will leave the remainder 3 when divide by 16 $$T_n= 995$$

every no from 3 to 995 will have a difference between them $$d=16$$. Hence using AP formula

$$T_n=a+(n-1)d$$ or $$995=3+(n-1)*16$$

Thus $$n=63$$

Option C
Senior SC Moderator
Joined: 22 May 2016
Posts: 2491
Re: How many integers from 0 to 1000 inclusive, have a remainder of 3 when  [#permalink]

### Show Tags

30 Sep 2017, 05:25
1
RMD007 wrote:
How many integers from 0 to 1000 inclusive, have a remainder of 3 when divided by 16?

A. 61

B. 62

C. 63

D. 64

E. 65

Combined approach: using arithmetic, find first and last term with remainder 3. Then calculate the number of multiples of 16 in an evenly spaced sequence.

First term: $$\frac{0}{16}$$ = 0 + R3, first term is 3

Last term: is 16(n) + 3 $$\leq{1,000}$$. Ignore the 3 for a bit.

$$\frac{1,000}{16} = 62.x$$

$$(16)(62) = 992$$. Now add 3.
$$(992+3) = 995$$ = Last Term

Number of terms: $$\frac{Last-First}{Increment}+ 1$$ =

$$\frac{995-3}{16} + 1$$ =
$$62 + 1 = 63$$

Shortcut: Above calculation shows 62 multiples of 16 in 1,000. Highest multiple + 3 is not > 1,000. Add one more multiple (because for $$\frac{1,000}{16}$$, first multiple of 16 is 16): 0 is a multiple of every integer. 62 + 1 = 63 terms
_________________

To live is the rarest thing in the world.
Most people just exist.

Oscar Wilde

Intern
Joined: 03 Sep 2017
Posts: 18
Location: Brazil
GMAT 1: 730 Q49 V41
Re: How many integers from 0 to 1000 inclusive, have a remainder of 3 when  [#permalink]

### Show Tags

30 Sep 2017, 15:58
1
I did it in a more ''muscle'' way:

For the remainder to be 3 when divided by 16, must follow the equation:
3+16*n (n is integer)
n=0 -> 3
n=1 -> 19

Whats in biggest n, that the result of the equation is smaller than 1.000 (inclusive)?
Let the +3 aside for a bit..

16*10 = 160
16*20 = 320
16*40 = 640
16*60 = 640+320 = 960
16*61 = 976
16*62 = 992 (enough) + 3 = 995 (last number that follows the equation)

Answer: 62 + (n = 0) option = 63 possibilities

What you guys think?
Intern
Joined: 15 Mar 2017
Posts: 38
Location: India
Concentration: International Business, Strategy
GMAT 1: 720 Q50 V37
GPA: 4
Re: How many integers from 0 to 1000 inclusive, have a remainder of 3 when  [#permalink]

### Show Tags

30 Sep 2017, 19:18
1
RMD007 wrote:
How many integers from 0 to 1000 inclusive, have a remainder of 3 when divided by 16?

A. 61

B. 62

C. 63

D. 64

E. 65

a = 3
an = 995

a + (n-1)d = an

3 + (n-1)x16 = 995

n = 63
_________________

You give kudos, you get kudos. :D

Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: How many integers from 0 to 1000 inclusive, have a remainder of 3 when  [#permalink]

### Show Tags

01 Oct 2017, 03:16
1
RMD007 wrote:
How many integers from 0 to 1000 inclusive, have a remainder of 3 when divided by 16?

A. 61

B. 62

C. 63

D. 64

E. 65

$$x = 16q + 3$$

$$0 \leq 16q + 3 \leq 1000$$

$$-3 \leq 16q \leq 997$$

$$-0.something \leq q \leq 62.something$$

q can take 63 integer values from 0 to 62 inclusive, thus x can also take 63 values.

_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 2491
How many integers from 0 to 1000 inclusive, have a remainder of 3 when  [#permalink]

### Show Tags

01 Oct 2017, 04:04
vitorcbarbieri wrote:
I did it in a more ''muscle'' way:

For the remainder to be 3 when divided by 16, must follow the equation:
3+16*n (n is integer)
n=0 -> 3
n=1 -> 19

Whats in biggest n, that the result of the equation is smaller than 1.000 (inclusive)?
Let the +3 aside for a bit..

16*10 = 160
16*20 = 320
16*40 = 640
16*60 = 640+320 = 960
16*61 = 976
16*62 = 992 (enough) + 3 = 995 (last number that follows the equation)

Answer: 62 + (n = 0) option = 63 possibilities

What you guys think?

vitorcbarbieri

I think you found an approach with a smart pattern that works! It is a bit similar to mine, above.

I do not think your approach is "brute force" except maybe in one place where, had the upper limit of the range been an ugly number, you might have been calculating for awhile.

I didn't use round multiples of 10, times 16, to "multiply up" to the highest term. Maybe that is faster. It is certainly smart. Next time, if numbers aren't bad, I'll try your way. Just one tiny cautionary thought . . .

If you were to get some heinous number, say 173,619, as the last of the range, you might be multiplying for awhile, even if you used thousands, hundreds, and then tens. In a case such as that, to find multiples, you may want to try the reverse: divide the heinous number by the multiple to get the greatest number that "n" in 16n can be.

In other words: to find the highest multiple of 16 close to but less than 1,000: divide 1000 by 16 to get 62.xx.

It's 62.5, but I didn't calculate that. The second I saw I had a decimal coming, I just noted the .xx. Then I took the integer, 62, and multiplied by 16 to give me that highest value, 992. Added 3. Done on that front (very similar to your conclusion). If this cautionary thought seems dumb, of course, ignore it.

In any event, nice work! Glad you posted. Kudos.
_________________

To live is the rarest thing in the world.
Most people just exist.

Oscar Wilde

Director
Joined: 21 Mar 2016
Posts: 521
Re: How many integers from 0 to 1000 inclusive, have a remainder of 3 when  [#permalink]

### Show Tags

01 Oct 2017, 08:30
SaGa wrote:
RMD007 wrote:
How many integers from 0 to 1000 inclusive, have a remainder of 3 when divided by 16?

A. 61

B. 62

C. 63

D. 64

E. 65

a = 3
an = 995

a + (n-1)d = an

3 + (n-1)x16 = 995

n = 63

This approach is understandable,,,, thanks,,,
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4955
Location: United States (CA)
Re: How many integers from 0 to 1000 inclusive, have a remainder of 3 when  [#permalink]

### Show Tags

04 Oct 2017, 15:49
RMD007 wrote:
How many integers from 0 to 1000 inclusive, have a remainder of 3 when divided by 16?

A. 61

B. 62

C. 63

D. 64

E. 65

The first number from 0 to 1000 inclusive that has a remainder of 3 when divided by 16 is 3, and the last number is 995.

Thus, there are (995 - 3)/16 + 1 = 63 integers from 0 to 1000 inclusive that have a remainder of 3 when divided by 16.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Non-Human User
Joined: 09 Sep 2013
Posts: 9888
Re: How many integers from 0 to 1000 inclusive, have a remainder of 3 when  [#permalink]

### Show Tags

06 Feb 2019, 21:10
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: How many integers from 0 to 1000 inclusive, have a remainder of 3 when   [#permalink] 06 Feb 2019, 21:10
Display posts from previous: Sort by

# How many integers from 0 to 1000 inclusive, have a remainder of 3 when

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.